text:
GENDER AND INCOME INEQUALITY IN
UNITED STATES TARIFF BURDEN
Arthur Gailes
Tamara Gurevich
Serge Shikher
Marinos Tsigas

ECONOMICS WORKING PAPER SERIES
Working Paper 2018–08–B
500 E Street SW
Washington, DC 20436
August 2018

Office of Economics working papers are the result of ongoing professional research of USITC Staff and are solely meant to represent the opinions and professional research of individual authors. These papers are not meant to represent in any way the views of the U.S. International Trade Commission or any of its individual Commissioners. Working papers are circulated to promote the active exchange of ideas between USITC Staff and recognized experts outside the USITC and to promote professional development of Office Staff by encouraging outside professional critique of staff research. Please address all correspondence to Tamara.Gurevich@usitc.gov or Serge.Shikher@usitc.gov.

Gender and Income Inequality in United States Tariff Burden
Arthur Gailes, Tamara Gurevich, Serge Shikher, Marinos Tsigas
Office of Economics Working Paper 2018–08–B
August 2018

Abstract

The combination of different tariff rates across products and different consumption patterns across households results in different tariff burdens across consumer groups. We investigate the distribution of tariff burden among U.S. households of different incomes and consumers of different genders. As a share of total household consumption expenditure in 2015, the tariff burden was a nearly constant 0.25 percent across all income deciles, meaning that tariffs act as a flat consumption tax. Since a flat consumption tax is a regressive tax on income, tariffs fall disproportionately on the poor. Across genders, we find large differences in tariff burden. Focusing on apparel products, which were responsible for about 75% of the total tariff burden on U.S. households, we find that the majority, 66%, of the tariff burden was from women’s apparel products. In 2015, the tariff burden for U.S. households on women’s apparel was $2.77 billion more than on men’s clothing. This gender gap grew about 11% in real terms between 2006 and 2016. Arthur Gailes, Haas Institute, UC Berkeley arthurgailes@berkeley.edu Tamara Gurevich, Research Division, Office of Economics, USITC tamara.gurevich@usitc.gov Serge Shikher, Research Division, Office of Economics, USITC serge.shikher@usitc.gov Marinos Tsigas, Research Division, Office of Economics, USITC marinos.tsigas@usitc.gov ## Gender and Income Inequality in United States Tariff Burden August 15, 2018 Abstract The combination of different tariff rates across products and different consumption patterns across households results in different tariff burdens across consumer groups. We investigate the distribution of tariff burden among U.S. households of different incomes and consumers of different genders. As a share of total household consumption expenditure in 2015, the tariff burden was a nearly constant 0.25 percent across all income deciles, meaning that tariffs act as a flat consumption tax. Since a flat consumption tax is a regressive tax on income, tariffs fall disproportionately on the poor. Across genders, we find large differences in tariff burden. Focusing on apparel products, which were responsible for about 75% of the total tariff burden on U.S. households, we find that the majority, 66%, of the tariff burden was from women’s apparel products. In 2015, the tariff burden for U.S. households on women’s apparel was$2.77 billion more than on men’s clothing. This gender gap grew about 11% in real terms between 2006 and 2016.

JEL codes: F10, F14, D12, D63

Keywords: non-homotheticity, gender bias

### 1 Introduction

Tariffs have generally been decreasing around the world in the last several decades, but still remain a sizable cost of international trade. Even in the United States, generally a low-tariff country, tariffs continue to be imposed on the majority of goods coming from most countries. In 2015, the average applied U.S. tariff was around 1.5%.1

Behind a relatively low average U.S. tariff, there is a great variation of tariffs across goods. For example, some apparel imported to the U.S. has applied tariffs as high as 31% while other apparel items have low or zero tariffs.2 At the same time, consumption patterns vary across different groups of consumers. For example, men and women tend to consume different sets of products. People with different incomes also tend to consume different baskets of goods: poorer households spend a larger share of their total expenditures on necessities while wealthier households tend to purchase more luxury goods (Henry2014). Therefore, different groups of consumers carry different shares of the tariff burden.3 Equivalently, different groups of consumers would get different benefits from the removal of tariffs. Across some groups, these differences are small. Across other groups, these differences are significant. In this paper, we report large differences in tariff burden across genders in the United States.

In order to calculate tariff burdens we combine data on tariffs with information on consumption patterns of different consumer groups, for example consumers of different incomes or genders. We then calculate the reduction in the cost of the consumption basket for each consumer group that can be attributed to the removal of tariffs. The reduction in the cost of the consumption basket is the tariff burden. Our focus is on the consumer side, so we do not study the effects of tariff on wages.

The fact that U.S. tariffs rates are different for different groups of consumers has been previously documented. Gresser (2002) and Moran (2014) document that average tariffs rates are different for rich and poor U.S. consumers. Barbaro (2007) and Taylor and Dar (2015) provide an overview of the unequal U.S. tariff rates for men’s and women’s apparel. Fajgelbaum and Khandelwal (2016) use a structural gravity model with nonhomothetic preferences to estimate gains from trade for consumers with different incomes. They find that gains from trade are higher for poorer consumers because they spend a higher share of their income on traded goods. Furman, Russ and Shambaugh (2017) calculate tariff burden on U.S. consumers in different income groups and find that U.S. tariffs act as a regressive income tax.4

In this paper, we also examine the tariff burden on U.S. consumers with different levels of income. Similar to the previous literature, we find that poor consumers pay a greater share of their income as tariffs. However, unlike the previous literature we also look at tariff burden as a share of consumption spending. We find that the tariff burden is about the same as a share of consumption spending for consumers in different income deciles. Therefore, U.S. tariffs act as a flat consumption tax. Since poor consumers spend a much greater share of income than rich ones, the tariffs act as a regressive income tax, just like a sales tax.5 Thus, we extend the existing literature by providing this additional prospective on the tariff burden.

Our main contribution, however, is the analysis of tariff burden on men and women. We find significant gender differences in tariff burden, which come from several sources. First, the average tariff rates on the women-specific products are higher than the average tariff rates on men’s merchandise imports. Most of the tariff burden in the U.S. comes from apparel products, and while the average applied U.S. tariff on men’s apparel is about 12%, the average applied U.S. tariff on women’s apparel is about 15%. Second, U.S. consumers spend twice as much money women’s clothing than on men’s clothing and the vast majority of this clothing is imported. The combination of higher tariff rates and and greater spending on imported goods means that women carry a significantly higher share of total tariff burden compared to men.

### 4 Results

In this section, we present the results of our analysis of the tariff burden across households with different income levels. We also present the results of our analysis of the tariff burden across genders.

#### 4.1 Tariff burden across income deciles

We begin by replicating the results of Furman et al. (2017) using our data. We analyze the effects of tariff reduction on 20 final consumer goods that are subject to significant U.S. tariffs. We calculate the burden of tariffs on households in ten income deciles using the methodology described in Section 2.3 and assumptions about price responses described in Section 2.4.1. Our results are similar to Furman et al. (2017), but about 20% smaller since we focus only on products with significant tariffs.17 Our tariff burden estimates are shown on Figure 2 as blue bars. The bars show the tariff burden for each of the ten household deciles under the two alternative assumptions about price changes for domestic goods, with the top end representing a 50% response of domestic prices to tariffs and the bottom end representing a no response.

In addition to assuming exogenous price changes, we also solve for price changes using a CGE model, as explained in Section 2.4.2. The counterfactual experiment simulated by the CGE model involves eliminating tariffs on 23 goods (20 consumption goods and 3 intermediate goods). The experiment is a comparative static one. The resulting estimated tariff burdens are shown as orange dots on Figure 2. As evident from this figure, tariff burden estimates from the CGE model are lower than the estimates from our two assumptions about exogenous price changes because the tariff pass-through to prices of imported goods in the USAGE model is below 100%, which is consistent with the literature.

The annual tariff burden, calculated using the price changes estimated by the CGE model, varies from $41 for the poorest households to$233 for the richest households. Therefore, the tariff burden, in dollars, is increasing in income: wealthier households pay more due to tariffs because they spend more than poorer households. On average, each U.S. household pays $96 in tariffs per year. For the U.S. population, the poorest 10% of the U.S. households face a$525 million tariff burden. The burden of the richest 10% is nearly $3 billion. Total tariff burden for all U.S. households is$12.3 billion.18 Table C1 shows the distribution of tariff burden across all income deciles.

We also calculate the effects of tariffs on the consumer price index faced by households in different income deciles. We use the methodology described in Section 2.2 and price changes estimated by the comparative static analysis from the USAGE model. The change in the price index represents the change in the purchasing power of the households. It also represents the share of tariff in household expenditure. The results are shown as the blue bars on Figure 3. They show that as a share of total household consumption expenditure, the tariff burden is flat at about 0.25 percent across all income deciles.19

This information provides a new view of tariff burden across income deciles. Previous literature found that tariffs act as a regressive (income) tax. Our results show that U.S. tariffs act as a flat consumption tax. Since a flat consumption tax is a regressive tax on income, our results do not contradict existing literature, but provide additional information for the analysis.

#### 4.2 Tariff burden across genders

In this analysis we focus on the apparel sector since we observe significant differences in tariff rates on gender-specific products in that sector and because about 95% of all tariff burden on apparel products comes from gender-specific products. In 2015 the average tariff rate for women’s apparel was 14.9%, but it was only 12.0% on men’s apparel.20 At the same time, households spend about 0.7% of their total annual expenditure on men’s apparel, while spending over 1.2% on women’s apparel (U.S. Bureau of Labor Statistics (BLS)2016).

As in the previous section, we estimate tariff burdens using the methodology described in Section 2.3 and either exogenous price changes, calculated under two alternative assumptions about the effects of tariffs on domestic goods prices, described in Section 2.4.1, or endogenous price changes, estimated by the CGE model in a comparative static simulation.

Total tariff burden on apparel products (using CGE model results) is $8.9 billion, nearly 75% of the total tariff burden of the U.S. households. However, this burden is not equally distributed between men and women. Tariff burden on women’s apparel is$5.8 billion (66% of total apparel burden), compared to men’s apparel burden of $3.1 billion. In other words, the burden of women-specific apparel tariff is nearly twice the amount of the burden of mens-specific apparel tariff. The orange points on the right panel of Figure 4 shows that in 2015 alone, U.S. consumers paid nearly$2.77 billion more due to tariffs when purchasing women’s clothing than men’s.

The tariff burdens estimated using exogenous price changes are shown on Figure 4 as blue bars, with the top end representing a 50% response of domestic goods’ prices to tariffs and the bottom end representing a no response. The tariff burden on women’s apparel ranges between $69 and$86 per household, while the tariff burden on men’s apparel ranges between $33 and$42 per household in 2015. For U.S. population, the tariff burden on women’s apparel ranges between $8.8 billion and$11.0 billion, while the tariff burden on men’s apparel ranges between $4.3 billion and$5.3 billion dollars. As in the CGE simulation results, the tariff burden from women’s apparel is about twice the tariff burden from men’s.

We combine 2006-2016 data on tariff rates, shown in Figure 1, with the 2006-2016 CE survey data to calculate historical trends in men’s and women’s tariff burden from apparel. We calculate the tariff burdens over the years using the set of assumptions about price changes described in Section 2.4.1 (CGE results for these years are not available). We use the midpoint between the two alternative assumptions about the response of domestic goods’ prices to tariffs described in that section.

Figure 5 shows that the tariff burden from apparel has been increasing during these 11 years for both men and women, in real terms. This is due to average apparel tariff increase and spending increase.21

Even though the tariff burden has been growing for both genders, it has been growing faster for women. The difference between women’s and men’s tariff burden has grown from 4.1 billion in 2006 to 4.6 billion in 2016, a change of 11 percent. This growth can be seen in Figure 6.

As we mentioned before, there are two reasons for the difference in tariff burden on women’s and men’s apparel: the average applied tariff rate on women’s apparel is higher than on men’s and women spend more than men on apparel. In Figure 6 we decompose the women-men tariff burden difference into a part that is due to tariff rate differences and a part that is due to spending differences. As evident from the figure, the growth of the gender gap in tariff burden is mainly due to the faster growth of the average applied tariff rate on women’s apparel.

### 5 Conclusion

We investigate the distribution of tariff burden among U.S. households of different incomes and consumers of different genders. To calculate the tariff burden we combine data on tariffs with with information obtained from consumption surveys. Price changes due to tariffs are estimated using either a simple set of assumptions about pass-through rates of tariffs to prices or a computable general equilibrium model, which produces our preferred set of estimates.

We begin by calculating the tariff burden on households in ten income deciles. Since richer households spend more, they also pay more in tariffs. For the U.S. population the poorest 10% of U.S. households pay $535 million in tariff per year while the richest 10% pay$3 billion. As a share of total household consumption expenditure, the tariff burden is a nearly constant 0.25 percent across all income deciles. Therefore, tariffs act as a flat consumption tax. Since a flat consumption tax is a regressive tax on income, tariffs fall disproportionately on the poor.

We then analyze the tariff burden on men’s and women’s products. Since a great portion of gender-specific products are apparel products and apparel products face some of the highest tariffs among U.S. imports, we focus on apparel in our analysis. We find that the total tariff burden from apparel products is about 75% of the total tariff burden on U.S. households. The majority, 66%, of the tariff burden from apparel is from women’s apparel products.

In 2015, the tariff burden for U.S. households on women’s clothing was $2.77 billion more than on men’s clothing. This gender gap has grown about 11% in real terms between 2006 and 2016. We find that two facts are responsible for this gender gap: women spend more on apparel than men and women’s apparel faces higher tariffs than men’s. While the difference in spending contributes more to the overall gender gap in tariff burden, it is the difference in the average applied tariff rate that caused the gap to grow during the recent years. ### Appendix A Additional data information  Table A1: Personal consumption expenditure categories Accessories and parts Alcohol in purchased meals All non-health insurance All other professional medical services Amusement parks, campgrounds, and related recreational services Audio equipment Auto leasing Bakery products Beef and veal Beer Bicycles and accessories Butter Cable and satellite television and radio services Canned tuna Carpets and other floor coverings Cellular telephone services Cereals Cheese Child care Cigarettes Clocks, lamps, lighting fixtures, and other household decorative items Clothing materials Coffee, tea, and other beverage materials Commercial and vocational schools Community food and housing/emergency/other relief services Computer software and accessories Corrective eyeglasses and contact lenses Cosmetic/perfumes/bath/nail preparations and implements Day care and nursery schools Dental services Dishes and flatware Domestic services Educational books Eggs Electric appliances for personal care Electricity Elementary and secondary schools Fats and oils Film and photographic supplies Financial services First-class postal service (by U.S. Postal Service) Fish and seafood Flowers, seeds, and potted plants Foundations and grantmaking and giving services to households Fresh milk Fruit (fresh) Fuel oil Funeral and burial services Furniture Gambling Games, toys, and hobbies Garbage and trash collection Gasoline and other motor fuel Hairdressing salons and personal grooming establishments Higher education Home health care Hospitals Household cleaning products Household linens Household paper products Intercity buses Internet access Intracity mass transit Jewelry Laundry and drycleaning services Legal services Lubricants and fluids Luggage and similar personal items Maintenance and repair of recreational vehicles and sports equipment Major household appliances Medical care and hospitalization Medical laboratories Membership clubs and participant sports centers Men’s and boys’ clothing Mineral waters, soft drinks, and vegetable juices Miscellaneous household products Motor vehicle maintenance and repair Motor vehicle rental Motorcycles Moving, storage, and freight services Musical instruments Natural gas New autos New light trucks Newspapers and periodicals Non-gendered apparel Nonelectric cookware and tableware Nursing homes Other delivery services (by non-U.S. postal facilities) Other Entertainment Other fuels Other household services Other meats Other medical products Other personal business services Other personal care goods and services Other purchased meals Other recreational vehicles Other video equipment Outdoor equipment and supplies Parking fees and tolls Personal computers and peripheral equipment Pets and related products Pharmaceutical products Photo processing Photo studios Photographic equipment Physician services Pork Poultry Prerecorded and blank audio discs/tapes/digital files/downloads Processed dairy products Processed fruits and vegetables Railway transportation Recreational books Religious organizations’ services to households Repair and hire of footwear Repair of audio-visual, photographic, and information processing equipment Repair of furniture, furnishings, and floor coverings Repair of household appliances Shoes and footwear Small electric household appliances Social advocacy and civic and social organizations Social assistance Specialty outpatient care facilities and health and allied services Spectator sports Spirits Sporting equipment, supplies, guns, and ammunition Stationery and miscellaneous printed materials Sugar Sweets Tax preparation and other related services Taxicabs Telecommunication services Telephone and facsimile equipment Televisions Therapeutic medical equipment Tires Tobacco Tools, hardware, and supplies Travel and vacation services Used autos Used light trucks Vegetables (fresh) Veterinary and other services for pets Video cassettes and discs, blank and prerecorded Video media rental Watches Water supply and sewage maintenance Window coverings Wine Women’s and girls’ clothing Table A2: Sectors with significant U.S. tariffs  Sector U.S. tariff${}^{a}$ U.S. TRQ${}^{b}$ Total Food and agriculture Cheese 7.3 8 15.3 Butter 5.8 15 20.8 Raw cane sugar 1.3 28 29.3 Refined sugar 1.6 55 56.6 Beef 1.0 0 1.0 Canned tuna 12.3 0 12.3 All textiles and apparel Fiber, yarn, and threads 5.2 0 5.2 Fabrics 5.0 0 5.0 Carpets and rugs 6.3 0 6.3 Other textile products 5.5 0 5.5 Apparel 12.8 0 12.8 Other manufacturing sectors Ball and roller bearings${}^{*}$ 5.8 0 5.8 Cellulosic organic fibers 4.7 0 4.7 Ceramic wall and floor tiles 6.2 0 6.2 China, fine earthenware, other pottery products 5.3 0 5.3 Cigarettes 6.7 0 6.7 Costume jewelry and novelties 7.5 0 7.5 Leather and allied product manufacturing 10.1 0 10.1 Other pressed and blown glass and glassware 5.3 0 5.3 Pens and mechanical pencils 5.2 0 5.2 Pesticides and agricultural chemicals (excluding fertilizers)${}^{*}$ 4.6 0 4.6 Residential electric lighting fixtures 5.0 0 5.0 Synthetic organic dyes and pigments${}^{*}$ 5.1 0 5.1 Reproduced from Table 1.1 of U.S. International Trade Commission (2017). See the report for details. ${}^{a}$ Measured as an ad valorem equivalent share of the CIF value of imports. ${}^{b}$ Measured as an export tax equivalent. ${}^{*}$ Not included in this analysis. ### Appendix B Consumption patterns across income deciles To illustrate the difference in consumption patterns of households in different income deciles, we calculate a ratio of expenditure shares of the richest and poorest household group for all consumption categories in CE. In Table B1 we show top-5 and bottom-5 ratios of expenditure shares for two groups of consumers. Column 2 of Table B1 shows the ratios of expenditure shares of households in the $9{0}^{th}$ percentile of income distribution to expenditure shares of households in the $1{0}^{th}$ percentile of income distribution, sorted in a descending order. We can see that the richest decile spends an 11-times greater share of total expenditure on photo studios than the poorest decile. The richest decile also spends a much greater share of total expenditure on watches, domestic services, and footwear repair. The poorest decile spends a much greater share of total expenditure on cigarettes, social assistance, funeral services, and home health care than the richest decile. Households in the bottom decile of income distribution spend 20 times more on health care than households in the top decile, as a share of their total expenditure. Column 3 of Table B1 compares households in the bottom of the income distribution to the median household. Expenditure patterns here are similar to the previous case: median households spend a higher share of their total expenditure on luxuries, while poor households spend a higher share on necessities. Table B1: Household expenditure on certain items, by decile  Decile 90/10 Ratio 50/10 Ratio 1 Photo studios (10.77) Photo studios (6.80) 2 Watches (8.95) Footwear repair (5.68) 3 Domestic services (7.97) Jewelry (4.66) 4 Footwear repair (7.91) Therapeutic medical equipment (4.02) 5 Commercial and vocational schools (7.64) New autos (3.62) 74 Men’s apparel (1.13) 77 Women’s apparel (1.12) 104 Women’s apparel (0.79) 110 Men’s apparel (0.76) 147 Tobacco (0.23) Nursing homes (0.21) 148 Cigarettes (0.18) Funeral and burial services (0.18) 149 Social assistance (0.14) Higher education (0.15) 150 Funeral and burial services (0.12) Social assistance (0.13) 150 Home health care (0.05) Home health care (0.01) Source: The U.S. Consumer Expenditure Survey for 2015. ### Appendix C Details on the U.S. tariff burden estimates Table C1: U.S. tariff burdens, by decile  Tariff burden CPI Household Population Decile change, % endogenous exogenous, low exogenous, high in billions 1 0.23$40.52 $64.26$69.67 0.52 2 0.26 $46.61$63.70 $69.07 0.60 3 0.22$53.57 $80.56$87.36 0.69 4 0.25 $71.05$102.55 $111.20 0.91 5 0.20$60.61 $98.29$106.57 0.78 6 0.22 $79.11$126.14 $136.78 1.01 7 0.22$92.07 $132.91$144.12 1.18 8 0.25 $125.06$172.94 $187.52 1.60 9 0.25$155.37 $212.75$230.70 1.99 10 0.26 $233.06$324.87 \$352.26 2.98

Source: The U.S. Consumer Expenditure Survey for 2015. Price changes and associated CPI changes are calculated using methodology described above in Section 3.2.

### References

Barbaro, M. (2007). In apparel, all tariffs aren’t created equal, The New York Times .

Borusyak, K. and Jaravel, X. (2018). The Distributional Effects of Trade: Theory and Evidence from the United States, Working Paper .

Dixon, P. B. and Rimmer, M. T. (2002). USAGE-ITC: Theoretical Structure. Paper presented at the Global Trade Analysis Project’s Fifth Annual Conference on Global Economic Analysis, Taipei, Taiwan, June 5–7, 2002.

Dixon, P. B. and Rimmer, M. T. (2010). Validating a Detailed, Dynamic CGE Model of the USA, Economic Record 86: 22–34. Special Issue, September 2010.

Donnelly, W. A., Johnson, K., Tsigas, M. and Ingersoll, D. L. (2004). Revised Armington Elasticities of Substitution USITC Model and the Concordance for Constructing Consistent Set for the GTAP Model. United States International Trade Commission, Office of Economics, Working Papers.

Fajgelbaum, P. D. and Khandelwal, A. K. (2016). Measuring the unequal gains from trade, The Quarterly Journal of Economics pp. 1113–1180.

Furman, J., Russ, K. and Shambaugh, J. (2017). US tariffs are an arbitrary and regressive tax, VoxEU .

Gresser, E. (2002). Toughest on the poor: America’s flawed tariff system, Foreign Affairs 81(6): 9–14.

Henry, L. M. (2014). Income Inequality and Income-Class Conspumption Patterns. Economic Commentary.

Hertel, T., Hummels, D., Ivanic, M. and Keeney, R. (2007). How confident can we be of CGE-based assessments of Free Trade Agreements, Economic Modelling 24(4): 611–635.

Hottman, C. J. and Monarch, R. (2018). Estimating Unequal Gains across U.S. Consumers with Supplier Trade Data, International Finance Discussion Papers 1220, Board of Governors of the Federal Reserve System .

Moran, T. (2014). Tariffs hit poor Americans hardest, Peterson Institute for International Economics Realtime Economic Issues Watch .

Nicita, A., Olarreaga, M. and Porto, G. (2014). Pro-poor trade policy in Sub-Saharan Africa, Journal of International Economics 92: 252–265.

Taylor, L. L. and Dar, J. (2015). Fairer trade: Removing gender bias in US import taxes, The Takeaway 6(3).

U.S. Bureau of Labor Statistics (BLS) (2016). Consumer Expenditures and Income: Handbook of Methods.

U.S. International Trade Commission (2017). The Economic Effects of Significant U.S. Import Restraints. Ninth Update 2017. Investigation No. 332-325.

*Haas Institute, UC Berkeley; formerly at the U.S. International Trade Commission.

Contact emails: tamara.gurevich@usitc.gov, serge.shikher@usitc.gov. The views expressed in this paper are strictly those of the authors and do not represent the opinions of the U.S. International Trade Commission or of any of its Commissioners.

1This average was obtained using the information from the DataWeb (USITC’s Tariff Information System). The tariff was calculated as the ratio of all duties collected in a year over total charges, insurance, and freight (CIF) values of all imported products reported in that year.

2Highest-tariff HTS10 apparel items include 6104.29.10.50 (women’s blouses, shirts and tops of artificial fibers), 6104.23.00.36 (women’s blouses, shirts and tops of synthetic fibers), and 6110.30.30.25 (girls’ garments imported as parts of playsuits). Lowest-tariff HTS10 apparel items include 6103.23.00.45 (men’s or boys’ shorts of synthetic fibers) and 6103.22.00.70 (men’s or boys’ cotton sweaters).

3“Tariff burden” and, more generally, “tax burden” are common terms used in economic analysis of the effects of tariffs on various population groups and do not express judgment.

4Other papers that investigate the effects of trade policy on consumers with different income levels include Nicita, Olarreaga and Porto (2014), Hottman and Monarch (2018), and Borusyak and Jaravel (2018). Note that unlike some of the other papers in the literature, we do not report whether trade in itself is pro-rich or pro-poor. Rather, we investigate the effects of U.S. tariffs on U.S. households of different income levels.

5A tax that falls disproportionately on the poor is called “regressive” because the tax percentage is declining with income. A tax that falls disproportionately on the rich is called “progressive” or “graduated” because the tax percentage is increasing with income. A tax with a constant percentage is called proportional or flat (true flat).

6We use BLS-provided population weight of each household called F21.

7We use HTS subheadings to identify gender-specific and non-gender-specific items. For example, many accessories, such as gloves and scarves, are non-gender-specific in the HTS.

8We use the UCC to PCE concordance provided by the BLS https://www.bls.gov/cex/cecomparison.htm.

9In total, 23 sectors were identified in U.S. International Trade Commission (2017) as having significant tariffs. These sectors are reproduced in Appendix table A2. Of these 23 sectors, households do not report consumption in 3 sectors: ball and roller bearings, pesticides and agricultural chemicals, and synthetic organic dyes. These 3 sectors are included in the USAGE model simulations, but do not directly feed into household consumption.

10These sectors are responsible for about 80% of the tariff burden (compare our estimates with Furman et al. (2017)).

12Apparel items are listed in chapters 61 and 62 of the HTS.

13These rates correspond to ${\tau }_{Mgs}$, ${\tau }_{Wgs}$, and ${\tau }_{ng}$ described Section 2.1.

15Note that as a result of this level of granularity in data collection, expenditure shares ${s}_{Djt}$ exhibit year-to-year fluctuations due to sampling and measurement error. Therefore, we use the average expenditure shares over 2013–2015.


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Encyclopedia > Lawson criterion

In nuclear fusion research, the Lawson criterion, first derived[1] by John D. Lawson in 1955 and published[2] in 1957, is an important general measure of a system that defines the conditions needed for a fusion reactor to reach ignition, that is, that the heating of the plasma by the products of the fusion reactions is sufficient to maintain the temperature of the plasma against all losses without external power input. As originally formulated the Lawson criterion gives a minimum required value for the product of the plasma (electron) density ne and the "energy confinement time" τE. Later analyses suggested that a more useful figure of merit is the "triple product" of density, confinement time, and plasma temperature T. The triple product also has a minimum required value, and the name "Lawson criterion" often refers to this inequality. The deuterium-tritium (D-T) fusion reaction is considered the most promising for producing fusion power. ... 1955 (MCMLV) was a common year starting on Saturday of the Gregorian calendar. ...

## Contents

The confinement time τE measures the rate at which a system loses energy to its environment. It is the energy content W divided by the power loss Ploss (rate of energy loss):

$tau_E = frac{W}{P_{rm loss}}$

For a fusion reactor to operate in steady state, as magnetic fusion energy schemes usually entail, the fusion plasma must be maintained at a constant temperature. Thermal energy must therefore be added to it (either directly by the fusion products or by recirculating some of the electricity generated by the reactor) at the same rate the plasma loses energy (for instance by heat conduction to the device walls or radiation losses like bremsstrahlung). (helpÂ· info), (from the German bremsen, to brake and Strahlung, radiation, thus, braking radiation), is electromagnetic radiation produced by the acceleration of a charged particle, such as an electron, when deflected by another charged particle, such as an atomic nucleus. ...

For illustration, the Lawson criterion for the D-T reaction will be derived here, but the same principle can be applied to other fusion fuels. It will also be assumed that all species have the same temperature, that there are no ions present other than fuel ions (no impurities and no helium ash), and that D and T are present in the optimal 50-50 mixture.[3] In that case, the ion density is equal to the electron density and the energy density of both together is given by

W = 3nekBT

where kB is the Boltzmann constant. Ludwig Boltzmann The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ...

The volume rate f (reactions per volume per time) of fusion reactions is

$f = n_D n_T langlesigma vrangle = frac{1}{4}n_e^2 langlesigma vrangle$

where σ is the fusion cross section, v is the relative velocity, and < > denotes an average over the Maxwellian velocity distribution at the temperature T. To meet Wikipedias quality standards, this article or section may require cleanup. ... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ...

The volume rate of heating by fusion is f times Ech, the energy of the charged fusion products (the neutrons cannot help to keep the plasma hot). In the case of the D-T reaction, Ech = 3.5 MeV.

The deuterium-tritium L function (minimum neτE needed to satisfy the Lawson criterion) minimizes near the temperature 25 keV (300 million kelvins).

The Lawson criterion is the requirement that the fusion heating exceed the losses: Image File history File links DT_ntauE.svg Summary Logarithmic plot of the Lawson criterion for deuterium-tritium fusion, or the minimum product of electron number density times energy confinement time needed to maintain the fusion plasma at a constant temperature. ... Image File history File links DT_ntauE.svg Summary Logarithmic plot of the Lawson criterion for deuterium-tritium fusion, or the minimum product of electron number density times energy confinement time needed to maintain the fusion plasma at a constant temperature. ... Deuterium, also called heavy hydrogen, is a stable isotope of hydrogen with a natural abundance in the oceans of one atom in 6400 of hydrogen (see VSMOW; the abundance changes slightly from one kind of natural water to another). ... Tritium (symbol T or 3H) is a radioactive isotope of hydrogen. ... The electronvolt (symbol eV, or, rarely and incorrectly, ev) is a unit of energy. ...

$f E_{ch} ge P_{loss}$

$leftrightarrow$

$frac{1}{4}n_e^2 langlesigma vrangle E_{ch} ge frac{3n_ek_BT}{tau_E}$

$leftrightarrow$

$n_{rm e} tau_{rm E} ge L equiv frac{12}{E_{rm ch}},frac{k_{rm B}T}{langlesigma vrangle}$

The quantity $frac{T}{langlesigma vrangle}$ is a function of temperature with an absolute minimum. Replacing the function with its minimum value provides an absolute lower limit for the product neτe. This is the Lawson criterion.

For the D-T reaction, the physical value is at least

$n_{rm e} tau_{rm E} ge 1.5times10^{20} {rm s}/mbox{m}^3$

The minimum of the product occurs near T = 25 keV. The electronvolt (symbol eV, or, rarely and incorrectly, ev) is a unit of energy. ...

## The "triple product" neTτE

A still more useful figure of merit is the "triple product" of density, temperature, and confinement time, neTτE. For most confinement concepts, whether inertial, mirror, or toroidal confinement, the density and temperature can be varied over a fairly wide range, but the maximum pressure attainable is a constant. When that is the case, the fusion power density is proportional to $p^2langlesigma vrangle/T^2$. Therefore the maximum fusion power available from a given machine is obtained at the temperature where $langlesigma vrangle/T^2$ is a maximum. Following the derivation above, it is easy to show the inequality Inertial confinement fusion using lasers rapidly progressed in the late 1970s and early 1980s from being able to deliver only a few joules of laser energy (per pulse) to a fusion target to being able to deliver tens of kilojoules to a target. ... A magnetic mirror is a magnetic field configuration where the field strength changes when moving along a field line. ...

$n_{rm e} T tau_{rm E} ge frac{12k_{rm B}}{E_{rm ch}},frac{T^2}{langlesigma vrangle}$

For the special case of tokamaks there is an additional motivation for using the triple product. Empirically, the energy confinement time is found to be nearly proportional to n1/3/P2/3. In an ignited plasma near the optimum temperature, the heating power P is equal to the fusion power and therefore proportional to n2/T2. The triple product scales as A split image of the largest tokamak in the world, the JET, showing hot plasma in the right image during a shot. ...

nTτ $propto$ nT (n1/3/P2/3) $propto$ nT (n1/3/(n2/T2)2/3) $propto$ T -1/3

Thus the triple product is only a weak function of density and temperature and therefore a good measure of the efficiency of the confinement scheme.

The quantity $frac{T^2}{langlesigma vrangle}$ is also a function of temperature with an absolute minimum at a slightly higher temperature than $frac{T}{langlesigma vrangle}$.

For the D-T reaction, the physical value is about

$n_{rm e} T tau_E ge 10^{21} mbox{keV s}/mbox{m}^3$

This number has not yet been achieved in any reactor, although the latest generations of machines have come close. For instance, the TFTR has achieved the densities and energy lifetimes needed to achieve Lawson at the temperatures it can create, but it cannot create those temperatures at the same time. ITER aims to do both. The Tokamak Fusion Test Reactor (TFTR) was an experimental fusion test reactor built at Princeton Plasma Physics Laboratory (in Princeton, New Jersey) circa 1980. ... Cutaway of the ITER Tokamak Torus in casing. ...

## Inertial confinement

The Lawson criterion applies to inertial confinement fusion as well as to magnetic confinement fusion but is more usefully expressed in a different form. Whereas the energy confinement time in a magnetic system is very difficult to predict or even to establish empirically, in an inertial system it must be on the order of the time it takes sound waves to travel across the plasma: Inertial confinement fusion using lasers rapidly progressed in the late 1970s and early 1980s from being able to deliver only a few joules of laser energy (per pulse) to a fusion target to being able to deliver tens of kilojoules to a target. ... Magnetic confinement fusion is an approach to fusion energy that uses magnetic fields to confine the fusion fuel in the form of a plasma. ...

$tau_E approx R/sqrt{k_BT/m_i}$

Following the above derivation of the limit on neτE, we see that the product of the density and the radius must be greater than a value related to the minimum of T3/2/<σv>. This condition is traditionally expressed in terms of the mass density ρ:

ρR > 1 g/cm²

To satisfy this criterion at the density of solid D-T (0.2 g/cm³) would require an implausibly large laser pulse energy. Assuming the energy required scales with the mass of the fusion plasma (Elaser ~ ρR3 ~ ρ-2), compressing the fuel to 103 or 104 times solid density would reduce the energy required by a factor of 106 or 108, bringing it into a realistic range. With a compression by 103, the compressed density will be 200 g/cm³, and the compressed radius can be as small as 0.05 mm. The radius of the fuel before compression would be 0.5 mm. The initial pellet will be perhaps twice as large since most of the mass will be ablated during the compression. Ablation is defined as the removal of material from the surface of an object by vaporization, chipping, or other erosive processes. ...

The fusion power density is a good figure of merit to determine the optimum temperature for magnetic confinement, but for inertial confinement the fractional burn-up of the fuel is probably more useful. The burn-up should be proportional to the specific reaction rate (n²<σv>) times the confinement time (which scales as T-1/2) divided by the particle density n:

burn-up fraction ~ n²<σv> T-1/2 / n ~ (nT) (<σv>/T3/2)

Thus the optimum temperature for inertial confinement fusion is that which maximizes <σv>/T3/2, which is slightly higher than the optimum temperature for magnetic confinement.

Results from FactBites:

 Fusion: Introduction and Beyond (771 words) lso known as the Lawson number or condition, this slightly more advanced concept is a quantitative measure that fusion scientists use to measure their progress towards achieving fusion at a practical level. When this number is large enough, the fusion reactions release the same amount of energy that was used to start the reactions, also known as breakeven. is the Lawson criterion for the deuterium-tritium reaction at around 100 million K. What this also tells us is that the plasma can either consist of a lot of particles for a short period of time (inertial confinement) or few particles confined for a long period of time (magnetic confinement).
More results at FactBites »

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# A note on funding and our mention in Wired

A message from Nathan Freitas, lead developer on Guardian, who has a life long bad habit of being misquoted or selectively quoted, a phenomenon he must now blame on himself, and not the reporters who interview him.

Some of you might have seen a story on Wired.com on which I am quoted, regarding the US State Department’s “Internet Freedom” agenda. In particular, I was asked to comment on the entrepreneurial angle they are taking. Overall, I think the article is good in laying out the challenges for activist technology projects to take funding from the Government. I also think the motivations of the State Department’s effort are authentic and there is great potential to benefit the overall health of the Internet.

However, I just want to clarify this portion:

Nathan Freitas of the Guardian Project, which designs Android-based tools for mobile anonymity, says he’s not going to apply for any of State’s money. “Accounting complexity of process means we’d have to spend 25 percent of it” on an accountant, he says, while praising the idea in theory

To get to the point, I just wish it had said:

While he is not going to apply direct for any of this round of State’s money, the project has received funding and support from US Gov’t funded organizations in the past.

I am not faulting the reporter on accuracy (as they will always just edit down to the most direct statement), and I hope I am not parsing words, but somewhere in my “praising the idea in theory”, I did mention that we had received small grants from US government funded organizations. The last thing I want to do is sound like a hypocrite, and so I decided to write this post to clarify the statement, while also helping shed light on how a project like ours is able to exist and grow. While the work we are doing is free as in speech, and free as in beer, paying rent and putting food on the table is definitely NOT free.

From my participation as a developer on the Tor Project (who is completely transparent with their funding sources here) and through conversations with other organizations (university research groups, Washington DC-based NGOs), I have been exposed to the significant complexity it takes to receive, process and account for this type of government funding. As mentioned in the article, it is nothing out of order for a government, which should have strong oversight on tax payer dollars, but their approach seems still pretty far from the more dynamic, flexible entrepreneurial-style we are seeing from seed and angel round venture capitalists today or efforts like YCombinator and the Knight News Challenge.

Guardian at this point is just an open-source project. We are not a non-profit or a corporation, and are not tied to a university. We exist on the coattails of a variety of other organizations, whose support we greatly benefit from. Based on this, I again just want to clarify that while this project is not applying for “any of State’s money” in this next round of $25 Million, we have received small grant funding and contract consulting work from groups funded by State department funding. The type of funding we have received historically are small grants from larger NGOs in the$10-20k range, and most of that money has gone to pay developers. The contract work we do (which is actually done as independent contractors, not through Guardian) includes training activists around the world in our how to secure their communications better, setting up specific hardware/software kits for use by NGOs in the field, and software development work for other organizations that need our expertise. At this point however, the majority of our relatively small funding comes from private donors and foundations, and not the US Government.

In the end, these are all new waters for me and the project to navigate. We believe that by keeping all of our code, designs and communications completely open to the world for scrutiny, we can help address any concerns over our motivations or the trustworthiness of our software. We hope that by taking funding from a variety of sources and being as transparent about those sources as we can, we can keep the projects vision and ideals whole.

Feel free to chime in below with your thoughts. You can also keep an eye on our partners and funding page to see who we are working with and how. Finally, if you want to work with us, we are eager to fund talented developers and designers to help us build the open-source mobile security apps the world very much needs.


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Red Blood Cell
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Red Blood Cell

Red blood cell
Scanning electron micrograph of human red blood cells (ca. 6-8 ?m in diameter)
Details
FunctionOxygen transport
Identifiers
Acronym(s)RBC
MeSHD004912
THH2.00.04.1.01001
FMA62845
Anatomical terms of microanatomy

Red blood cells (RBCs), also referred to as red cells,[1] red blood corpuscles (in humans or other animals not having nucleus in red blood cells), haematids, erythroid cells or erythrocytes (from Greek erythros for "red" and kytos for "hollow vessel", with -cyte translated as "cell" in modern usage), are the most common type of blood cell and the vertebrate's principal means of delivering oxygen (O2) to the body tissues--via blood flow through the circulatory system.[2] RBCs take up oxygen in the lungs, or in fish the gills, and release it into tissues while squeezing through the body's capillaries.

The cytoplasm of erythrocytes is rich in hemoglobin, an iron-containing biomolecule that can bind oxygen and is responsible for the red color of the cells and the blood. Each human red blood cell contains approximately 270 million[3] of these hemoglobin molecules. The cell membrane is composed of proteins and lipids, and this structure provides properties essential for physiological cell function such as deformability and stability while traversing the circulatory system and specifically the capillary network.

In humans, mature red blood cells are flexible and oval biconcave disks. They lack a cell nucleus and most organelles, to accommodate maximum space for hemoglobin; they can be viewed as sacks of hemoglobin, with a plasma membrane as the sack. Approximately 2.4 million new erythrocytes are produced per second in human adults.[4] The cells develop in the bone marrow and circulate for about 100-120 days in the body before their components are recycled by macrophages. Each circulation takes about 60 seconds (one minute).[5] Approximately 84% of the cells in the human body are 20-30 trillion red blood cells.[6][7][8] Nearly half of the blood's volume (40% to 45%) is red blood cells.

Packed red blood cells (pRBC) are red blood cells that have been donated, processed, and stored in a blood bank for blood transfusion.

## Structure

### Vertebrates

There is an immense size variation in vertebrate red blood cells, as well as a correlation between cell and nucleus size. Mammalian red blood cells, which do not contain nuclei, are considerably smaller than those of most other vertebrates.[9]
Mature red blood cells of birds have a nucleus, however in the blood of adult females of penguin Pygoscelis papua enucleated red blood cells (B) have been observed, but with very low frequency.

The vast majority of vertebrates, including mammals and humans, have red blood cells. Red blood cells are cells present in blood to transport oxygen. The only known vertebrates without red blood cells are the crocodile icefish (family Channichthyidae); they live in very oxygen-rich cold water and transport oxygen freely dissolved in their blood.[10] While they no longer use hemoglobin, remnants of hemoglobin genes can be found in their genome.[11]

Vertebrate red blood cells consist mainly of hemoglobin, a complex metalloprotein containing heme groups whose iron atoms temporarily bind to oxygen molecules (O2) in the lungs or gills and release them throughout the body. Oxygen can easily diffuse through the red blood cell's cell membrane. Hemoglobin in the red blood cells also carries some of the waste product carbon dioxide back from the tissues; most waste carbon dioxide, however, is transported back to the pulmonary capillaries of the lungs as bicarbonate (HCO3-) dissolved in the blood plasma. Myoglobin, a compound related to hemoglobin, acts to store oxygen in muscle cells.[12]

The color of red blood cells is due to the heme group of hemoglobin. The blood plasma alone is straw-colored, but the red blood cells change color depending on the state of the hemoglobin: when combined with oxygen the resulting oxyhemoglobin is scarlet, and when oxygen has been released the resulting deoxyhemoglobin is of a dark red burgundy color. However, blood can appear bluish when seen through the vessel wall and skin.[13] Pulse oximetry takes advantage of the hemoglobin color change to directly measure the arterial blood oxygen saturation using colorimetric techniques. Hemoglobin also has a very high affinity for carbon monoxide, forming carboxyhemoglobin which is a very bright red in color. Flushed, confused patients with a saturation reading of 100% on pulse oximetry are sometimes found to be suffering from carbon monoxide poisoning.

Having oxygen-carrying proteins inside specialized cells (as opposed to oxygen carriers being dissolved in body fluid) was an important step in the evolution of vertebrates as it allows for less viscous blood, higher concentrations of oxygen, and better diffusion of oxygen from the blood to the tissues. The size of red blood cells varies widely among vertebrate species; red blood cell width is on average about 25% larger than capillary diameter, and it has been hypothesized that this improves the oxygen transfer from red blood cells to tissues.[14]

### Mammals

Typical mammalian red blood cells: (a) seen from surface; (b) in profile, forming rouleaux; (c) rendered spherical by water; (d) rendered crenate (shrunken and spiky) by salt. (c) and (d) do not normally occur in the body. The last two shapes are due to water being transported into, and out of, the cells, by osmosis.

The red blood cells of mammals are typically shaped as biconcave disks: flattened and depressed in the center, with a dumbbell-shaped cross section, and a torus-shaped rim on the edge of the disk. This shape allows for a high surface-area-to-volume (SA/V) ratio to facilitate diffusion of gases.[15] However, there are some exceptions concerning shape in the artiodactyl order (even-toed ungulates including cattle, deer, and their relatives), which displays a wide variety of bizarre red blood cell morphologies: small and highly ovaloid cells in llamas and camels (family Camelidae), tiny spherical cells in mouse deer (family Tragulidae), and cells which assume fusiform, lanceolate, crescentic, and irregularly polygonal and other angular forms in red deer and wapiti (family Cervidae). Members of this order have clearly evolved a mode of red blood cell development substantially different from the mammalian norm.[9][16] Overall, mammalian red blood cells are remarkably flexible and deformable so as to squeeze through tiny capillaries, as well as to maximize their apposing surface by assuming a cigar shape, where they efficiently release their oxygen load.[17]

Red blood cells in mammals are unique amongst vertebrates as they do not have nuclei when mature. They do have nuclei during early phases of erythropoiesis, but extrude them during development as they mature; this provides more space for hemoglobin. The red blood cells without nuclei, called reticulocytes, subsequently lose all other cellular organelles such as their mitochondria, Golgi apparatus and endoplasmic reticulum.

The spleen acts as a reservoir of red blood cells, but this effect is somewhat limited in humans. In some other mammals such as dogs and horses, the spleen sequesters large numbers of red blood cells, which are dumped into the blood during times of exertion stress, yielding a higher oxygen transport capacity.

Scanning electron micrograph of blood cells. From left to right: human red blood cell, thrombocyte (platelet), leukocyte.

### Human

Two drops of blood are shown with a bright red oxygenated drop on the left and a deoxygenated drop on the right.
Animation of a typical human red blood cell cycle in the circulatory system. This animation occurs at a faster rate (~20 seconds of the average 60-second cycle) and shows the red blood cell deforming as it enters capillaries, as well as the bars changing color as the cell alternates in states of oxygenation along the circulatory system.

A typical human red blood cell has a disk diameter of approximately 6.2-8.2 µm[18] and a thickness at the thickest point of 2-2.5 µm and a minimum thickness in the centre of 0.8-1 µm, being much smaller than most other human cells. These cells have an average volume of about 90 fL[19] with a surface area of about 136 ?m2, and can swell up to a sphere shape containing 150 fL, without membrane distension.

Adult humans have roughly 20-30 trillion red blood cells at any given time, constituting approximately 70% of all cells by number.[20] Women have about 4-5 million red blood cells per microliter (cubic millimeter) of blood and men about 5-6 million; people living at high altitudes with low oxygen tension will have more. Red blood cells are thus much more common than the other blood particles: there are about 4,000-11,000 white blood cells and about 150,000-400,000 platelets per microliter.

Human red blood cells take on average 60 seconds to complete one cycle of circulation.[5][8][21]

The blood's red color is due to the spectral properties of the hemic iron ions in hemoglobin. Each hemoglobin molecule carries four heme groups; hemoglobin constitutes about a third of the total cell volume. Hemoglobin is responsible for the transport of more than 98% of the oxygen in the body (the remaining oxygen is carried dissolved in the blood plasma). The red blood cells of an average adult human male store collectively about 2.5 grams of iron, representing about 65% of the total iron contained in the body.[22][23]

## Microstructure

### Nucleus

Red blood cells in mammals anucleate when mature, meaning that they lack a cell nucleus. In comparison, the red blood cells of other vertebrates have nuclei; the only known exceptions are salamanders of the genus Batrachoseps and fish of the genus Maurolicus.[24][25]

The elimination of the nucleus in vertebrate red blood cells has been offered as an explanation for the subsequent accumulation of non-coding DNA in the genome.[26] The argument runs as follows: Efficient gas transport requires red blood cells to pass through very narrow capillaries, and this constrains their size. In the absence of nuclear elimination, the accumulation of repeat sequences is constrained by the volume occupied by the nucleus, which increases with genome size.

Nucleated red blood cells in mammals consist of two forms: normoblasts, which are normal erythropoietic precursors to mature red blood cells, and megaloblasts, which are abnormally large precursors that occur in megaloblastic anemias.

### Membrane composition

Red blood cells are deformable, flexible, are able to adhere to other cells, and are able to interface with immune cells. Their membrane plays many roles in this. These functions are highly dependent on the membrane composition. The red blood cell membrane is composed of 3 layers: the glycocalyx on the exterior, which is rich in carbohydrates; the lipid bilayer which contains many transmembrane proteins, besides its lipidic main constituents; and the membrane skeleton, a structural network of proteins located on the inner surface of the lipid bilayer. Half of the membrane mass in human and most mammalian red blood cells are proteins. The other half are lipids, namely phospholipids and cholesterol.[27]

#### Membrane lipids

The most common red blood cell membrane lipids, schematically disposed as they are distributed on the bilayer. Relative abundances are not at scale.

The red blood cell membrane comprises a typical lipid bilayer, similar to what can be found in virtually all human cells. Simply put, this lipid bilayer is composed of cholesterol and phospholipids in equal proportions by weight. The lipid composition is important as it defines many physical properties such as membrane permeability and fluidity. Additionally, the activity of many membrane proteins is regulated by interactions with lipids in the bilayer.

Unlike cholesterol, which is evenly distributed between the inner and outer leaflets, the 5 major phospholipids are asymmetrically disposed, as shown below:

Outer monolayer

Inner monolayer

This asymmetric phospholipid distribution among the bilayer is the result of the function of several energy-dependent and energy-independent phospholipid transport proteins. Proteins called "Flippases" move phospholipids from the outer to the inner monolayer, while others called "floppases" do the opposite operation, against a concentration gradient in an energy-dependent manner. Additionally, there are also "scramblase" proteins that move phospholipids in both directions at the same time, down their concentration gradients in an energy-independent manner. There is still considerable debate ongoing regarding the identity of these membrane maintenance proteins in the red cell membrane.

The maintenance of an asymmetric phospholipid distribution in the bilayer (such as an exclusive localization of PS and PIs in the inner monolayer) is critical for the cell integrity and function due to several reasons:

• Macrophages recognize and phagocytose red cells that expose PS at their outer surface. Thus the confinement of PS in the inner monolayer is essential if the cell is to survive its frequent encounters with macrophages of the reticuloendothelial system, especially in the spleen.
• Premature destruction of thallassemic and sickle red cells has been linked to disruptions of lipid asymmetry leading to exposure of PS on the outer monolayer.
• An exposure of PS can potentiate adhesion of red cells to vascular endothelial cells, effectively preventing normal transit through the microvasculature. Thus it is important that PS is maintained only in the inner leaflet of the bilayer to ensure normal blood flow in microcirculation.
• Both PS and phosphatidylinositol 4,5-bisphosphate (PIP2) can regulate membrane mechanical function, due to their interactions with skeletal proteins such as spectrin and protein 4.1R. Recent studies have shown that binding of spectrin to PS promotes membrane mechanical stability. PIP2 enhances the binding of protein band 4.1R to glycophorin C but decreases its interaction with protein band 3, and thereby may modulate the linkage of the bilayer to the membrane skeleton.

The presence of specialized structures named "lipid rafts" in the red blood cell membrane have been described by recent studies. These are structures enriched in cholesterol and sphingolipids associated with specific membrane proteins, namely flotillins, STOMatins (band 7), G-proteins, and ?-adrenergic receptors. Lipid rafts that have been implicated in cell signaling events in nonerythroid cells have been shown in erythroid cells to mediate ?2-adregenic receptor signaling and increase cAMP levels, and thus regulating entry of malarial parasites into normal red cells.[28][29]

#### Membrane proteins

Red blood cell membrane proteins separated by SDS-PAGE and silverstained[30]

The proteins of the membrane skeleton are responsible for the deformability, flexibility and durability of the red blood cell, enabling it to squeeze through capillaries less than half the diameter of the red blood cell (7-8 ?m) and recovering the discoid shape as soon as these cells stop receiving compressive forces, in a similar fashion to an object made of rubber.

There are currently more than 50 known membrane proteins, which can exist in a few hundred up to a million copies per red blood cell. Approximately 25 of these membrane proteins carry the various blood group antigens, such as the A, B and Rh antigens, among many others. These membrane proteins can perform a wide diversity of functions, such as transporting ions and molecules across the red cell membrane, adhesion and interaction with other cells such as endothelial cells, as signaling receptors, as well as other currently unknown functions. The blood types of humans are due to variations in surface glycoproteins of red blood cells. Disorders of the proteins in these membranes are associated with many disorders, such as hereditary spherocytosis, hereditary elliptocytosis, hereditary stomatocytosis, and paroxysmal nocturnal hemoglobinuria.[27][28]

The red blood cell membrane proteins organized according to their function:

Red blood cell membrane major proteins

Transport

Structural role - The following membrane proteins establish linkages with skeletal proteins and may play an important role in regulating cohesion between the lipid bilayer and membrane skeleton, likely enabling the red cell to maintain its favorable membrane surface area by preventing the membrane from collapsing (vesiculating).

• Ankyrin-based macromolecular complex - proteins linking the bilayer to the membrane skeleton through the interaction of their cytoplasmic domains with Ankyrin.
• Band 3 - also assembles various glycolytic enzymes, the presumptive CO2 transporter, and carbonic anhydrase into a macromolecular complex termed a "metabolon," which may play a key role in regulating red cell metabolism and ion and gas transport function.
• RHAG - also involved in transport, defines associated unusual blood group phenotype Rhmod.
• Protein 4.1R-based macromolecular complex - proteins interacting with Protein 4.1R.
• Protein 4.1R - weak expression of Gerbich antigens;
• Glycophorin C and D - glycoprotein, defines Gerbich Blood Group;
• XK - defines the Kell Blood Group and the Mcleod unusual phenotype (lack of Kx antigen and greatly reduced expression of Kell antigens);
• RhD/RhCE - defines Rh Blood Group and the associated unusual blood group phenotype Rhnull;
• Duffy protein - has been proposed to be associated with chemokine clearance;[32]
• Adducin - interaction with band 3;
• Dematin- interaction with the Glut1 glucose transporter.

### Surface electrostatic potential

The zeta potential is an electrochemical property of cell surfaces that is determined by the net electrical charge of molecules exposed at the surface of cell membranes of the cell. The normal zeta potential of the red blood cell is -15.7 millivolts (mV).[33] Much of this potential appears to be contributed by the exposed sialic acid residues in the membrane: their removal results in zeta potential of -6.06 mV.

## Function

### Role in transport

Recall that respiration, as illustrated schematically here with a unit of carbohydrate, produces about as many molecules of carbon dioxide, CO2, as it consumes of oxygen, O2.[34]

${\displaystyle {\ce {HCOH + O2 -> CO2 + H2O}}}$

Thus, the function of the circulatory system is as much about the transport of carbon dioxide as about the transport of oxygen. As stated elsewhere in this article, most of the carbon dioxide in the blood is in the form of bicarbonate ion. The bicarbonate provides a critical pH buffer.[35] Thus, unlike hemoglobin for O2 transport, there is a physiological advantage to not having a specific CO2 transporter molecule.

Red blood cells, nevertheless, play a key role in the CO2 transport process, for two reasons. First, because, besides hemoglobin, they contain a large number of copies of the enzyme carbonic anhydrase on the inside of their cell membrane.[36] Carbonic anhydrase, as its name suggests, acts as a catalyst of the exchange between carbonic acid and carbon dioxide (which is the anhydride of carbonic acid). Because it is a catalyst, it can affect many CO2 molecules, so it performs its essential role without needing as many copies as are needed for O2 transport by hemoglobin. In the presence of this catalyst carbon dioxide and carbonic acid reach an equilibrium very rapidly, while the red cells are still moving through the capillary. Thus it is the RBC that ensures that most of the CO2 is transported as bicarbonate.[37][38] At physiological pH the equilibrium strongly favors carbonic acid, which is mostly dissociated into bicarbonate ion.[39]

${\displaystyle {\ce {CO2 + H2O <=>> H2CO3 <=>> HCO3- + H+}}}$

The H+ ions released by this rapid reaction within RBC, while still in the capillary, act to reduce the oxygen binding affinity of hemoglobin, the Bohr effect.

The second major contribution of RBC to carbon dioxide transport is that carbon dioxide directly reacts with globin protein components of hemoglobin to form carbaminohemoglobin compounds. As oxygen is released in the tissues, more CO2 binds to hemoglobin, and as oxygen binds in the lung, it displaces the hemoglobin bound CO2, this is called the Haldane effect. Despite the fact that only a small amount of the CO2 in blood is bound to hemoglobin in venous blood, a greater proportion of the change in CO2 content between venous and arterial blood comes from the change in this bound CO2.[40] That is, there is always an abundance of bicarbonate in blood, both venous and arterial, because of its aforementioned role as a pH buffer.

In summary, carbon dioxide produced by cellular respiration diffuses very rapidly to areas of lower concentration, specifically into nearby capillaries.[41][42] When it diffuses into a RBC, CO2 is rapidly converted by the carbonic anhydrase found on the inside of the RBC membrane into bicarbonate ion. The bicarbonate ions in turn leave the RBC in exchange for chloride ions from the plasma, facilitated by the band 3 anion transport protein colocated in the RBC membrane. The bicarbonate ion does not diffuse back out of the capillary, but is carried to the lung. In the lung the lower partial pressure of carbon dioxide in the alveoli causes carbon dioxide to diffuse rapidly from the capillary into the alveoli. The carbonic anhydrase in the red cells keeps the bicarbonate ion in equilibrium with carbon dioxide. So as carbon dioxide leaves the capillary, and CO2 is displaced by O2 on hemoglobin, sufficient bicarbonate ion converts rapidly to carbon dioxide to maintain the equilibrium.[36][43][44][45]

### Secondary functions

When red blood cells undergo shear stress in constricted vessels, they release ATP, which causes the vessel walls to relax and dilate so as to promote normal blood flow.[46]

When their hemoglobin molecules are deoxygenated, red blood cells release S-Nitrosothiols, which also act to dilate blood vessels,[47] thus directing more blood to areas of the body depleted of oxygen.

Red blood cells can also synthesize nitric oxide enzymatically, using L-arginine as substrate, as do endothelial cells.[48] Exposure of red blood cells to physiological levels of shear stress activates nitric oxide synthase and export of nitric oxide,[49] which may contribute to the regulation of vascular tonus.

Red blood cells can also produce hydrogen sulfide, a signalling gas that acts to relax vessel walls. It is believed that the cardioprotective effects of garlic are due to red blood cells converting its sulfur compounds into hydrogen sulfide.[50]

Red blood cells also play a part in the body's immune response: when lysed by pathogens such as bacteria, their hemoglobin releases free radicals, which break down the pathogen's cell wall and membrane, killing it.[51][52]

### Cellular processes

As a result of not containing mitochondria, red blood cells use none of the oxygen they transport; instead they produce the energy carrier ATP by the glycolysis of glucose and lactic acid fermentation on the resulting pyruvate.[53][54] Furthermore, the pentose phosphate pathway plays an important role in red blood cells; see glucose-6-phosphate dehydrogenase deficiency for more information.

As red blood cells contain no nucleus, protein biosynthesis is currently assumed to be absent in these cells.

Because of the lack of nuclei and organelles, mature red blood cells do not contain DNA and cannot synthesize any RNA, and consequently cannot divide and have limited repair capabilities.[55] The inability to carry out protein synthesis means that no virus can evolve to target mammalian red blood cells.[56] However, infection with parvoviruses (such as human parvovirus B19) can affect erythroid precursors while they still have DNA, as recognized by the presence of giant pronormoblasts with viral particles and inclusion bodies, thus temporarily depleting the blood of reticulocytes and causing anemia.[57]

## Life cycle

Human red blood cells are produced through a process named erythropoiesis, developing from committed stem cells to mature red blood cells in about 7 days. When matured, in a healthy individual these cells live in blood circulation for about 100 to 120 days (and 80 to 90 days in a full term infant).[58] At the end of their lifespan, they are removed from circulation. In many chronic diseases, the lifespan of the red blood cells is reduced.

### Creation

Erythropoiesis is the process by which new red blood cells are produced; it lasts about 7 days. Through this process red blood cells are continuously produced in the red bone marrow of large bones. (In the embryo, the liver is the main site of red blood cell production.) The production can be stimulated by the hormone erythropoietin (EPO), synthesised by the kidney. Just before and after leaving the bone marrow, the developing cells are known as reticulocytes; these constitute about 1% of circulating red blood cells.

The functional lifetime of a red blood cell is about 100-120 days, during which time the red blood cells are continually moved by the blood flow push (in arteries), pull (in veins) and a combination of the two as they squeeze through microvessels such as capillaries. They are also recycled in the bone marrow.[59]

### Senescence

The aging red blood cell undergoes changes in its plasma membrane, making it susceptible to selective recognition by macrophages and subsequent phagocytosis in the mononuclear phagocyte system (spleen, liver and lymph nodes), thus removing old and defective cells and continually purging the blood. This process is termed eryptosis, red blood cell programmed death.[60] This process normally occurs at the same rate of production by erythropoiesis, balancing the total circulating red blood cell count. Eryptosis is increased in a wide variety of diseases including sepsis, haemolytic uremic syndrome, malaria, sickle cell anemia, beta-thalassemia, glucose-6-phosphate dehydrogenase deficiency, phosphate depletion, iron deficiency and Wilson's disease. Eryptosis can be elicited by osmotic shock, oxidative stress, and energy depletion, as well as by a wide variety of endogenous mediators and xenobiotics. Excessive eryptosis is observed in red blood cells lacking the cGMP-dependent protein kinase type I or the AMP-activated protein kinase AMPK. Inhibitors of eryptosis include erythropoietin, nitric oxide, catecholamines and high concentrations of urea.

Much of the resulting breakdown products are recirculated in the body. The heme constituent of hemoglobin are broken down into iron (Fe3+) and biliverdin. The biliverdin is reduced to bilirubin, which is released into the plasma and recirculated to the liver bound to albumin. The iron is released into the plasma to be recirculated by a carrier protein called transferrin. Almost all red blood cells are removed in this manner from the circulation before they are old enough to hemolyze. Hemolyzed hemoglobin is bound to a protein in plasma called haptoglobin, which is not excreted by the kidney.[61]

## Clinical significance

### Disease

Affected by Sickle-cell disease, red blood cells alter shape and threaten to damage internal organs.

Blood diseases involving the red blood cells include:

• Anemias (or anaemias) are diseases characterized by low oxygen transport capacity of the blood, because of low red cell count or some abnormality of the red blood cells or the hemoglobin.
• Iron deficiency anemia is the most common anemia; it occurs when the dietary intake or absorption of iron is insufficient, and hemoglobin, which contains iron, cannot be formed
• Sickle-cell disease is a genetic disease that results in abnormal hemoglobin molecules. When these release their oxygen load in the tissues, they become insoluble, leading to mis-shaped red blood cells. These sickle shaped red cells are less deformable and viscoelastic, meaning that they have become rigid and can cause blood vessel blockage, pain, strokes, and other tissue damage.
• Thalassemia is a genetic disease that results in the production of an abnormal ratio of hemoglobin subunits.
• Hereditary spherocytosis syndromes are a group of inherited disorders characterized by defects in the red blood cell's cell membrane, causing the cells to be small, sphere-shaped, and fragile instead of donut-shaped and flexible. These abnormal red blood cells are destroyed by the spleen. Several other hereditary disorders of the red blood cell membrane are known.[62]
Effect of osmotic pressure on blood cells
Micrographs of the effects of osmotic pressure
• Hemolysis is the general term for excessive breakdown of red blood cells. It can have several causes and can result in hemolytic anemia.
• The malaria parasite spends part of its life-cycle in red blood cells, feeds on their hemoglobin and then breaks them apart, causing fever. Both sickle-cell disease and thalassemia are more common in malaria areas, because these mutations convey some protection against the parasite.
• Polycythemias (or erythrocytoses) are diseases characterized by a surplus of red blood cells. The increased viscosity of the blood can cause a number of symptoms.
• In polycythemia vera the increased number of red blood cells results from an abnormality in the bone marrow.

### Transfusion

Red blood cells may be given as part of a blood transfusion. Blood may be donated from another person, or stored by the recipient at an earlier date. Donated blood usually requires screening to ensure that donors do not contain risk factors for the presence of blood-borne diseases, or will not suffer themselves by giving blood. Blood is usually collected and tested for common or serious blood-borne diseases including Hepatitis B, Hepatitis C and HIV. The blood type (A, B, AB, or O) or the blood product is identified and matched with the recipient's blood to minimise the likelihood of acute hemolytic transfusion reaction, a type of transfusion reaction. This relates to the presence of antigens on the cell's surface. After this process, the blood is stored, and within a short duration is used. Blood can be given as a whole product or the red blood cells separated as packed red blood cells.

Blood is often transfused when there is known anaemia, active bleeding, or when there is an expectation of serious blood loss, such as prior to an operation. Before blood is given, a small sample of the recipient's blood is tested with the transfusion in a process known as cross-matching.

In 2008 it was reported that human embryonic stem cells had been successfully coaxed into becoming red blood cells in the lab. The difficult step was to induce the cells to eject their nucleus; this was achieved by growing the cells on stromal cells from the bone marrow. It is hoped that these artificial red blood cells can eventually be used for blood transfusions.[63]

### Tests

Several blood tests involve red blood cells. These include a RBC count (the number of red blood cells per volume of blood), calculation of the hematocrit (percentage of blood volume occupied by red blood cells), and the erythrocyte sedimentation rate. The blood type needs to be determined to prepare for a blood transfusion or an organ transplantation.

Many diseases involving red blood cells are diagnosed with a blood film (or peripheral blood smear), where a thin layer of blood is smeared on a microscope slide. This may reveal abnormalities of red blood cell shape and form. When red blood cells sometimes occur as a stack, flat side next to flat side. This is known as rouleaux formation, and it occurs more often if the levels of certain serum proteins are elevated, as for instance during inflammation.

### Separation and blood doping

Red blood cells can be obtained from whole blood by centrifugation, which separates the cells from the blood plasma in a process known as blood fractionation. Packed red blood cells, which are made in this way from whole blood with the plasma removed, are used in transfusion medicine.[64] During plasma donation, the red blood cells are pumped back into the body right away and only the plasma is collected.

Some athletes have tried to improve their performance by blood doping: first about 1 litre of their blood is extracted, then the red blood cells are isolated, frozen and stored, to be reinjected shortly before the competition. (Red blood cells can be conserved for 5 weeks at -79 °C or -110 °F, or over 10 years using cryoprotectants[65]) This practice is hard to detect but may endanger the human cardiovascular system which is not equipped to deal with blood of the resulting higher viscosity. Another method of blood doping involves injection with erythropoietin to stimulate production of red blood cells. Both practices are banned by the World Anti-Doping Agency.

## History

The first person to describe red blood cells was the young Dutch biologist Jan Swammerdam, who had used an early microscope in 1658 to study the blood of a frog.[66] Unaware of this work, Anton van Leeuwenhoek provided another microscopic description in 1674, this time providing a more precise description of red blood cells, even approximating their size, "25,000 times smaller than a fine grain of sand".

In the 1740s, Vincenzo Menghini in Bologna was able to demonstrate the presence of iron by passing magnets over the powder or ash remaining from heated red blood cells.

In 1901, Karl Landsteiner published his discovery of the three main blood groups--A, B, and C (which he later renamed to O). Landsteiner described the regular patterns in which reactions occurred when serum was mixed with red blood cells, thus identifying compatible and conflicting combinations between these blood groups. A year later Alfred von Decastello and Adriano Sturli, two colleagues of Landsteiner, identified a fourth blood group--AB.

In 1959, by use of X-ray crystallography, Dr. Max Perutz was able to unravel the structure of hemoglobin, the red blood cell protein that carries oxygen.[67]

The oldest intact red blood cells ever discovered were found in Ötzi the Iceman, a natural mummy of a man who died around 3255 BCE. These cells were discovered in May 2012.[68]

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