text:
# Work done by force

work done by a force

who has derived the work done as the force x distance

i can say that it is force x time also (of course the second one is given the name impulse) but i want to know the basics

Andrew Mason
Homework Helper
chandran said:
work done by a force

who has derived the work done as the force x distance

i can say that it is force x time also (of course the second one is given the name impulse) but i want to know the basics
Force x distance is a measure of another quantity. It is not immediately obvious that this quantity is useful. But it is. Can find some reasons that force x distance is a useful quantity?

AM

Hello Chandran,

This is a very good question you have asked. At first glance, many people will say to you "because it is defined as force times distance;" however, this is not the answer you are looking for. Essentially, you are asking for a history question. You are asking why this choice of definition, and I like it.

I will refer you to this: http://en.wikipedia.org/wiki/Conservation_of_energy

The answer to your question deals directly with Joules experiment, shown below:

[URL]http://en.wikipedia.org/wiki/Image:Joule_apparatus.png

Looking at this picture, we can see that a known mass (which has a known force due to gravity) is displaced a vertical distance z.

This displacement causes the paddle wheel to rotate and stir a fluid inside an insulated container (thus no heat transfer between the system [the fluid] and the surroundings [everything outside the container])

The explanation of why the paddle wheel turns is relatively trivial. The rope is tied around the shaft of the paddle, and provides a torque as the mass falls and induces rotation.

Now for the subtle and tricky part, why and how does the temperature of the fluid increase? Clearly, it is not because the surroundings is making it hotter (It’s insulated remember). Also, the container is not making it hotter, or we would see the container get hotter as well if they are in equilibrium.

This means that the falling mass is responsible for the rise in temperature. If we take careful measurements of the temperature of the mass as it falls, we would find that it remains at room temperature. So we can rule out that it is not temperature itself that is being exchanged, something else must be at play here.

One possible avenue to explore is a new concept, ‘energy.’

At first glance, we would notice that the mass falls a distance z. So we would use this as our definition of Energy.

By constructing careful experiments and looking at the data, we will find that our assumption of a force x distance is the correct definition to use for energy. (but not the only definition!)

In fact, we could now test this hypothesis by rasing the mass alone to any arbitrary height z, and then letting it drop. We would find that the energy due to the displacement from the drop height to any lower point is always and exactly equal to
1/2 *m*v^2

Last edited by a moderator:
rcgldr
Homework Helper
work is defined as force x disance or as the effort it takes to create a change in energy.

I'm not sure if there's a consensus on defining work as a change in energy and then determining that this is the equivalent of force x distance or vice versa.

force x time is lacking information, specifically the speed at the point of application. force x speed x time = work, but since speed x time is the same as distance, you end up with force x distance again.

work done by an agent

i want to derive the formula for work done by an agent

intuitively work done means the effort put by the agent.

intuitively work done should be directly proportional to the force applied by the agent responsible for applying the force

intuitively work done should also be directly proportional to the distance over which the force is applied.

So work done=forcexdistance

But distance=0.5*acceleration*t*t where t is the time over which the force is applied.

since distance is proportional to time can i say

work done=forcextime.

what is wrong in this?

Hootenanny
Staff Emeritus
Gold Member
chandran said:
So work done=forcexdistance

But distance=0.5*acceleration*t*t where t is the time over which the force is applied.

since distance is proportional to time can i say

work done=forcextime.

what is wrong in this?

You cannot say just because something is proportional to something else that it is equal to it.

You could also say that;

$$W {\color{red}\propto} F\cdot t^{2}$$

Or

$$W {\color{red}\propto} F\cdot a$$

or

$$W {\color{red}\propto} F\cdot at^{2}$$

You can say any of the above. They are all proportionalities. You can also say that;

$$\boxed{W {\color{blue}=} F\cdot \left(\frac{1}{2}at^2 \right)}$$

There is a big difference between proportional to and equal to.

Last edited:
Doc Al
Mentor
chandran said:
intuitively work done should also be directly proportional to the distance over which the force is applied.

So work done=forcexdistance
Nothing wrong with this as long as the force remains constant and there is only one force acting on the object.

But distance=0.5*acceleration*t*t where t is the time over which the force is applied.
OK, assuming the object starts from rest.

since distance is proportional to time can i say
Distance is not proportional to time; it's proportional to time squared.

work done=forcextime.
Huh? What you can say (as Hoot points out), given your assumptions is:
work = force x distance = force x (0.5*acceleration*t*t)

OK... so what?

Chandran: Work isn't defined to be force x time because you could spend all day pushing a mountain, and it doesn't move an inch. So you didn't do any "work" on it, and you spent your force on heat and sweat.

But if you pushed a car instead, it moves. Once you've got it going, you could run round the front of it, put your hands on the hood, and find it's pushing you. Basically your pushing went into moving the car. Your "work" transferred "kinetic energy" to the car.

You can get a feel for how much kinetic energy you gave to the car by measuring how far the car goes before it rolls to a stop. The forces stopping the car are friction and air resistance, and are fairly constant at low speeds. The distance the car rolls is maybe 50m. So if you pushed it for 5m getting faster all the while, you know that your pushing force was ten times the stopping force.

Note that if you'd pushed the car for twice the time, it would be travelling twice as fast, but towards the end of your push you would have been almost running, and you would have covered more than twice the distance. Then when you let go of the car and let it roll to a stop, you'd find it took more than twice the distance.

In essence, you can view "kinetic energy" as something that dictates the stopping distance of that car when subjected to a constant force. Hence kinetic energy and work are defined using force x distance.

Last edited:
russ_watters
Mentor
Doc Al said:
Distance is not proportional to time; it's proportional to time squared.
In specific cases, yes, but not in general, as Farsight pointed out with the mountain example. Or how about a book sitting on a table?

chandran, the only way you can make time a variable is if you include the whole distance equation in the formula for work - but then time just cancels out of it anyway.

Doc Al
Mentor
russ_watters said:
In specific cases, yes, but not in general, as Farsight pointed out with the mountain example. Or how about a book sitting on a table?
Sorry if I wasn't clear enough: All my comments were directed at chandran's specific example with the assumptions stated: single, constant force acting on an object that starts moving from rest. (By "single" I mean that the force in question is the only force acting on the object.)

chandran, the only way you can make time a variable is if you include the whole distance equation in the formula for work - but then time just cancels out of it anyway.
I'm unclear as to what issue is troubling chandran, but--again, given the assumptions inherent in his specific example, not in general--it's perfectly OK to write work done as a function of time. (Since, trivially, the distance is a function of time.)

Andrew Mason
Homework Helper
chandran said:
So work done=forcexdistance

But distance=0.5*acceleration*t*t where t is the time over which the force is applied.

since distance is proportional to time can i say

work done=forcextime.

what is wrong in this?
Distance is not proportional to time. For an accelerating body (ie. one to which a force is applied) distance is proportional to the square of the time during which the force acts and proportional to the acceleration. If there is no acceleration, no work is done no matter how long the force is applied (in other words, if there is no acceleration there is no net force acting so no work is done).

Doc Al said:
I'm unclear as to what issue is troubling chandran, but--again, given the assumptions inherent in his specific example, not in general--it's perfectly OK to write work done as a function of time. (Since, trivially, the distance is a function of time.)
I think the OP is troubled with the difference between momentum and energy. Simply because there is a relationship between momentum and time (for a given force) and another relationship between momentum and energy, does not mean that these quantities are proportional.

A 10 gram bullet moving at 500 m/sec has the same momentum as a 2.5 gram bullet moving at 2000 m/sec. But the 2.5 gram bullet will do much more damage because it has four times the energy of the 10 gram bullet.

AM

Last edited:
I can hazard a guess.

Chandran, if you've got a mass m travelling at velocity v, and you exert a force upon it to bring it to a halt, the stopping distance can be calculated using ½mv² and the stopping time can be calculated using mv. One equates to the force times distance, the other equates to the force times time. We call the former kinetic energy, and the latter momentum.

Note that if you were moving alongside the mass, in your view it would be stationary and would have no kinetic energy. The kinetic energy is in a way relative, and has no independent existence of its own.

To be precise, we should be speaking of displacements and not distances when speaking of work.

russ_watters
Mentor
Doc Al said:
Sorry if I wasn't clear enough...

I'm unclear as to what issue is troubling chandran, but--again, given the assumptions inherent in his specific example, not in general--it's perfectly OK to write work done as a function of time. (Since, trivially, the distance is a function of time.)
My spidey sense is tingling...

Andrew Mason
Homework Helper
JohnSimpson said:
To be precise, we should be speaking of displacements and not distances when speaking of work.
The work done is the path integral of $\vec{F} \cdot d\vec{s}$. A force that is applied to move an object over a surface in a complete circle does work even though its displacment is 0.

AM

rcgldr
Homework Helper
Andrew Mason said:
The work done is the path integral of $\vec{F} \cdot d\vec{s}$. A force that is applied to move an object over a surface in a complete circle does work even though its displacment is 0.
Only if the force has a tangental component. The objects speed will be changed, or heat will be generated due to friction. If the only force on a object moving in a circle is a perpendicular force, then no work is done (for example an orbiting satellite).

Hootenanny
Staff Emeritus
Note the vector symbols above the force and distance ($W = {\color{red}\vec{{\color{black}F}}} {\mathbf\centerdot} d{\color{red}\vec{{\color{black}s}}}$). If $\vec{F}$ and $\vec{s}$ were perpendicular then $\vec{F}{\mathbf\centerdot}\vec{s} = 0$ (scalar product). Hence, no work is done.


text:
# The Moorish Wanderer

## The Roof is On Fire, Keep Calm and Carry On

The season of Budget Bill is upon us. and from what I can surmise, the planning staff at the Finances ministry is dead set on using the 5.5% growth for 2012-2016, and the target for reducing budget deficit to 3% of GDP by 2016 is maintained nonetheless.

I posted a short blog on how unreallistic these figures are, in the face of gloomy global, conjecture (even more gloomy as the IMF cut its global growth projection last week) pressure on Morocco’s foreign exchange reserves and the urge to cut the subsidies.

year|   Deficit  | Deficit| Deficit
|(Bn dirhams)| % GDP  |Reduction
----+------------+--------+---------
2012|   -49,6    |  -6,1% |  +4.9
2013|   -45,1    |  -5,3% |  +4.7
2014|   -40,7    |  -4,5% |  +4.2
2015|   -35,8    |  -3,7% |  +5.1
2016|   -29,9    |  -2,9% |  +5.8

The short communiqué on the MINEFI website points out projected growth for 2012 is 4.5% (close to IMF’s 4.3% prediction 3 months ago) and 4.8% deficit. There is a small difference between that figure and the 5.3% budget deficit for 2013 mentioned in the IMF report – which means there is margin for the government in its intent to implement this dramatic deficit reduction plan; It is dramatic, because a deficit-cutting plan from 6.1% to 4.8% means there are 11.03Bn net cuts in the budget – which in turns means larger revenues and/or expenses adjustments.

And here is the clincher: There are going to be 24,000 new openings in public service payroll – and since most of these are going into relatively high-paying jobs – in fact, they are most likely to be centered around the median entry public service salary (about 7,000 a month) 2Bn in additional expenses.

So there it is: a tax increase is unavoidable -in fact, desirable, provided discretionary loopholes are closed, though it is not certain Mr Benkirane has the guts to take on the special interests benefitting from the status-quo, and so are the cuts to subsidies.

PS: IMF seems to have considerably upgraded Morocco’s outlook on GDP growth to… 5.5% (up from the previous 4.3%) strange.

## The Worst of Trickle-down, or Zombie Keynesianism?

Posted in Dismal Economics, Flash News, Moroccan Politics & Economics, Morocco, Read & Heard by Zouhair ABH on April 19, 2012

There is enough evidence to state that more than ever, big government is alive and kicking in Morocco, and not in a nice way; it has indeed broken with a 30-years trend in 2010; this means that some additional 5.8 Bn have been spent above the 50-years long trend, accruing to the 20Bn-worth exponential break that started 3 years ago. 5Bn might not be a lot relative to the Budget -1.67%- but it does account for 4% of government expenditure in real terms, so the matching resources accounted for in the Budget as a whole.

So here we are with a government who has not broken with the fateful decision to increase dramatically government expenditure in 2010; this is, quite simply, Zombie Keynesianism: the government puts on (some) welfare programs, increases recruitment 40%, and comes up with an effective 21Bn package expenditure no government has prepared for but yet finds itself actually spending it. Most importantly however, the Compensation Fund takes a large bite out of government expenditure – the World Bank Open-Data defines it as:

“General government final consumption expenditure (formerly general government consumption) includes all government current expenditures for purchases of goods and services (including compensation of employees). It also includes most expenditures on national defence and security, but excludes government military expenditures that are part of government capital formation. Data are in current local currency.”

HP-detrended aggregates. Government expenditure at its highest level away from 50-years trend since 1976

And considering the available data on that subject, the negative effects of the present course of action are just as equally showing on the short as well as the long run: depending on how the economy fares in 2013, the combined effects of the generous increases in public service payroll and the Compensation Fund will deteriorate an already compromised Budget Balance, and later on, the government will have to increases taxes, or cut spending, or both.

It seems this moment the government is trying for some shadow stimulus package, and it shows: the latest Treasury monthly survey points out the structure of Government Budget has been markedly altered compared to that of 2011: the Budget represents only 14.6% compared to the 23.2% in 2011 (and there goes the government’s boasting about the 188Mds committed to investment) while payroll and subsidies increased their contribution from 36.7%, 12.1% to 41.2%, 18.2%, respectively. And contrary to the government’s claim, the Compensation Fund does not benefit the middle class as much as a few wealthy households.

Les dépenses du budget général ont atteint 68,3 MMDH à fin mars 2012, en légère hausse de 0,8% par rapport à leur niveau à fin mars 2011, qui s’explique par une augmentation de 17,6% des dépenses de fonctionnement conjuguée à une baisse de l’investissement et des charges de la dette budgétisée1 de 34,2% et de 11,1%
respectivement.

So basically the government has put a lot of money to stabilize prices -but at the same time transfers generous sums back to the privileged few- and to recruit many more civil servants – that might not be needed or do not have what it takes- the result is indeed a stimulus package, and it might as well be working by providing the boost for GDP growth, but it will not last long, and the benefits of such an overkill are not that obvious.

          |σ       |σj/σy  |Corr(y,j)|
----------+--------+-------+----------
Y_GDP     |0,08030 |1       |1       |
----------+--------+-------+---------+
Con       |0,07013 |0,87339|0,82150  |
----------+--------+-------+---------+
Investment|0,24127 |3,00463|0,83690  |
----------+--------+-------+---------+
Government|0,22035 |2,74415|0,49970  |
--------------------------------------

$\sigma =\left (\sum_{i=1955}^{2011}\left ( \mu -x_{i} \right )^{2} \right )^{1/2}\\ \rho _{x,y}=\frac{\sigma_{xy}}{\sigma_{y}\sigma_{x}}$

The table above shows some evidence that government expenditure does not necessarily influence GDP the way other aggregates do, and the effects can be random indeed: government expenditure is just as volatile as the most volatile aggregate in an economy (Investment) yet it is also the least correlated to GDP. The only way that generous increase in government expenditure can pick up growth is through the subsidy to household consumption. In an ideal world, the Finance Ministry would provide us with a technical note to explain and illustrate the model they are using to forecast growth, and more importantly, the contribution to growth per aggregate. One thing is sure though, the present increase in expenditure doesn’t help, and the boomerang effect will be painful.

## Get Some! Get Some! Comments on the 2012 Budget Bill

Posted in Dismal Economics, Flash News, Morocco, Read & Heard by Zouhair ABH on March 15, 2012

And finally, the Finance Ministry has gone to Parliament House with the new budget. Ministers Nizar Baraka (PI) and Driss Azami Idrissi (PJD) have both taken turns to deliver their Budget Statement before parliament, and though I did not listen to it live, but from the figures I came across, I can predict a few things and/or comment on others;

[Exclusively, you will find on this link the Budget Bill].

A raw assessment for this new budget is that the fresh whiff of new government has been squashed by the hard, cold reality of, well, old government; on all the major investment plans, on fiscal policy, on the whole business of government, this new coalition has proven to be conservative in its choices, à contre-temps with the defiant and hopeful tone set by Head of Government Abdelilah Benkirane. So this not an earth-shattering budget, it is simply business as usual.

The budget goes 346Bn dirhams, that is 44.3% of GDP, for a 5% deficit. There is no way the government will reach the 3% deficit limit they have pledged to in their manifesto. Istiqlal and PJD have lost in terms of fiscal responsibility; in absolute and relative terms, a similar level of deficit dates back to 2001: 34Bn deficit, 8% GDP. But 2001 was the light at the end of the tunnel, and privatization revenues turned the deficit into a small surplus of 500 Million dirhams. This year is full of uncertainty, even the language both ministers adopted in their respective statement was cautious: spendings are there to guarantee social balances; the truth is, the sole development policy any government in the past two decades has ever implemented was to make sure growth was high; when the cycle is expansionary, that is of no particular problem; but now that we are heading toward a mild downturn, there is pressure to keep people happy, and the fact no major changes have been introduced in taxation paints quite a picture: the trade-off obviously favours the immediate present to the expenses of future stability.

Bad news for PJD: current expenditure has been projected for 187Bn, 16Bn up from the initial 171Bn appropriated in the initial Budget bill. For the life of me I can’t figure out where the 16Bn came from, and I for one would not hesitate to draw an interesting parallel between the gung-ho, austere approach PJD ministers boast on newspapers, about how they will squash unnecessary expenses; I particularly enjoyed digging up some Lahcen Daoudi quotes:

Well, the biggest increase in expenses has been without a doubt on current expenditure: 23.8% in paywage, stationary requisitions and other administrative expenses, while public investment increased only 11.3% year-on-year, quite a first step coming from a government bent on showing their toughness on waste and unnecessary bureaucracy. The 2012 fiscal year has blown PJD’s economic credibility right out of the gate, in my opinion.

What worries me though is not the budget breakdown per categories of expenses; According to the figures Minister Azami laid before Parliament, there is no substantial increase -and by that, I mean at least a dozen Billions- in fiscal receipts, and I surmise from the figures Public Borrowing Requirements will jump from an initial 61Bn to 65Bn, while repayments will remain unchanged, some 42Bn including interests. Not only has the government failed to keep its word on the 3% deficit limit, it has planned to over-borrow this year. For sure, domestic debt alleviates the danger of default and wards off potential threats on Morocco’s foreign currency reserves, but only up to a point; let us not forget that liquidities are drying up; such a large increase in PSBR will inevitably push yields higher – a scenario a lot of businesses and individuals dread; as a matter of fact, the generous fiscal exemptions this government and the governments before are providing Real Estate developers might turn against them and kill off an essential component of economic growth in Morocco.

And finally, there’s a disturbing news embedded in the Budget statement: it projects  2.5% inflation rate for 2012. To go from 1.1% inflation in 2011 to 2.5% in 2012 shows that subsidies, the Compensation Fund in fact, can do only so much, before the harsh reality of facts catches up with a well-meaning government: subsidies do not work; the measures proposed by the government do not work, and the inflation rate testifies to that matter: the Compensation Fund does not reward hard-working families by protecting their purchasing power, it secures established businesses good and generous rents; 2.5% is a moderate rate of inflation however, but I would very much like to hear Ministers Baraka, Azami or Boulif spin it to justify a 40Bn boondoggle that benefits only the 1.3 Million wealthiest households.

## When Fiscal Conservatism can Actually Do Better

Posted in Dismal Economics, Moroccan Politics & Economics, Morocco, Read & Heard by Zouhair ABH on March 11, 2012

The level of prices in Morocco is perhaps the most important economic issue that can rally Moroccans around; Debt doesn’t seem to matter much, nor does the deficit. Even taxes do not seem to matter much. Since no particular (and reliable) polls are being carried out, I take it media coverage of these issues speaks for itself: public opinion does not seem to care about public debt and deficit, and public policy ensures level of prices are low, a good indicator of how priorities are ranked with a relatively popular government: stabilize prices at all costs.

By now, the major aspects of the new 2012 Budget have been made public: a big push in social sectors, education, health, housing and industrial relations, not to mention the appropriation for the Compensation Fund – around 40 Billion dirhams, and the deficit does not seem to be a priority, the trade-off in public debt and fiscal receipts has been pretty clear and favour immediate stabilization. It seems to me – but I might be mistaken- there is no Budget Policy for the next 5 years, only a year-to-year management of public finances. Sure, CST funds and Budget-allocated Public investment do contribute one way or the other to some long-term vision, but I doubt the government has fully endorsed, or even grasped the implications of, the spirit of past investment plans, like Plan Maroc Vert, Haleutis or the High-Speed train.

BKAM Core inflation doesn't take into account some elements that might be blamed for a rise in inflation

Though the government has pledged to spend its way to stabilize prices, it seems they have already overlooked the impact of their policies on future inflation as well as on the prospects of growth itself. Inflation is going to be a problem later on, perhaps sooner than what they might expect; so far, latest reports on inflation (core and total) state the following:

Selon le Haut commissariat au plan (HCP), l’Indice des prix à la consommation (IPC) a enregistré une hausse mensuelle de 0,2% en janvier 2012, après le recul de 0,5% observé en décembre dernier. Cette évolution reflète principalement l’accroissement des prix des produits alimentaires volatils de 0,9% après les baisses successives enregistrées durant les trois mois précédents. La progression des prix de cette catégorie tient à celle des prix des volailles et lapin et des légumes frais de 1,3% et 2,1% respectivement, qui a plus que compensé la baisse des prix des poissons et des fruits. Pour leur part, les prix des produits réglementés ont connu une légère hausse de 0,1%. Abstraction faite des prix des produits volatils et de ceux réglementés, l’inflation sous-jacente de Bank Al-Maghrib (BAM) ressort en hausse de 0,1% après 0,2% le mois précédent.

En glissement annuel, l’inflation s’est établie à 0,9% en janvier, inchangée par rapport à décembre 2011. Cette évolution résulte essentiellement de la poursuite de la baisse des prix des produits alimentaires volatils (-1,3% au lieu de -1,4%). Pour sa part, l’inflation sous-jacente est ressortie à 1,6%, après 1,7% en décembre.

The efforts put in stabilizing prices have brought overall inflation down, it is effectively a deflation of sorts: food prices are notoriously volatile, and the methodology makes sure they are not taken into account in core inflation computation. Bank Al Maghrib puts the 2012 trend for core inflation at 1.6%; yet HCP projects:

Concernant l’évolution de l’inflation, l’accélération attendue de la demande intérieure, associée à la persistance de la hausse des prix à l’importation, exercerait, en dépit du niveau élevé des dépenses de compensation, une légère pression sur les prix intérieurs.

L’inflation, mesurée par le prix implicite du PIB, passerait de 1,6% en 2011 à 2,5% en 2012.

that is to say, GDP deflator will rise moderately above BKAM’s core inflation 2%, which will amount to the same thing, since the last decade observed a 1.9% average GDP Deflator inflation rate, and BKAM policy rates haven’t change significantly on that period, and were much more responsive to GDP deflator fluctuations than they have been to regular ICV/IPC inflation rate. And so by postponing inflation shocks with subsidies, the budget only makes it harder to sustain future, compounded inflationary pressures that will come mainly from the crowding-out effect.

Bank Al Maghrib has only two alternatives: either support government policy and intervene a lot more on monetary markets to supplement flailing M3 and make up for the effect of government bond issues on available liquidities: as of late February 2012, the amount of liquidities BKAM serves amounted on average to 29.75 Bn dirhams, up to 238Bn since January 2012. up from 67Bn served last year at the same time by the Central Bank, an average intervention of a little less of 10Bn.

BKAM is more responsive to Deflator than the regular ICV rate. (1998 does not take into account a 50bps hike in policy rates from 5% to 5.5% then back to 5%)

My point is, government expenditure to stabilize prices will backfire, and I argue the price to pay for an inflation freeze on food prices is not worth it, since it also takes deviates liquidities from potential growth, and it pressures the Central Bank in going in with a hike in interest rates to sustain its other equally important target: sustain the Dirham’s value and manage foreign currency reserves.

Since I am getting more and more alarmist about this whole business, how come no major rating agency has produced a document about it so far? How come S&P didn’t change its outlook on Morocco? Last time they published any Moroccan-related news was July 2011, and the Outlook was Stable – and thus unlikely to change. So from a financial standpoint, the debt is manageable, not because Morocco’s economic prospects are going to improve, but because as far as its capabilities to mobilize foreign resources go, Morocco can count on generous creditors. And there goes the historic lesson: Morocco got into trouble in the early 1980s because it has borrowed too much from abroad. Foreign debt now stands at around 20% GDP; perhaps that level is considered to be sustainable; as long as the dices roll, take your chances, domestic debt doesn’t matter, does it?

Why fiscal conservatism, then?

Well, why not? It’s all a matter of trade-off, that is, a political decision that favours delaying deficit reduction and bringing debt under control because it values immediate price stability. I guess a 40Bn expenditure in compensation fund that benefits at least 75% to the top 20% affluent households. A subsidy that is likely to worsen trade deficit and weaken the level of foreign reserves accordingly. It looks as though as long as Morocco is assured of generous foreign financing -from the Gulf or the EU- its public finances aren’t much of a problem. On the other hand, if the assumption the business cycle has reached its peak holds, then it is dangerous to pursue the foreign debt path; it looks as though Real Estate is likely to be the main growth booster, and foreign, ‘hot money’ inflows do not mix well with tangible asset acquisition.

Budget rebalancing means the following: yes, overall inflation will rise moderately within the 2% BKAM target rate, and probably so would unemployment, but not above the 9% limit; but capping PSBR and spending would allow available liquidities to be channelled into private expenditure, thus boosting economic growth. Simultaneously, fiscal policy has to be rebalanced in favour of less indirect taxes and broader tax base; this means many of the existing loopholes, temporary and permanent exemptions and moratorium would be closed or ended, or at least directed in favour of actual contributors to growth: small and innovative businesses, agricultural cooperatives, higher education and research. What this government is doing is basically the worse of two worlds: social spending with no immediate repercussions on growth (domestic expenditure has a lower contribution to growth when heavily subsidized, and improving the livelihoods of 400,000 public servants out of a workforce of 11,8 Million people isn’t really going to make it happen) rolling up large deficits and mounting debt that crowd out liquidities.

## Subsidized Pass the parcel: Compensation Fund

Posted in Dismal Economics, Moroccan Politics & Economics, Morocco by Zouhair ABH on February 12, 2012

As per the latest Treasury survey figures, the Compensation Fund stands at about 41Bn – although the initial 2012 Budget bill provides for 45Bn; that represents 5.7% of GDP, 14% of total budget. It also represents 80% of total public investments for 2012. And finally, it seems all public subsidies equate total expenditure en education. And yet every annual budget statement pushes for a Compensation Fund reform:

L’accent sera mis, notamment, sur des questions liées à la réforme fiscale, à la masse salariale, à la réforme de la compensation… pour s’assurer de la soutenabilité des finances publiques à la lumière des exigences de développement économique et social auquel le Maroc est en droit d’aspirer.

But is the compensation fund worth the money? After all, the total resources allocated to the most important expense – or shall we say the most politically sensitive- remains wheat and sugar; According to the addendum on special funds to the Budget bill (Comptes Spéciaux du Trésor) the designated “Fonds de Soutien des Prix de certains Produits Alimentaires” is allocated with some 880 Million dirhams – and even that amount of money can be halved; either by targeting those subsidies (which hasn’t really been the case ever since subsidies were enforced) or by by setting up a task force within the Exchange Office or the Finance Ministry to trade in those commodities the Moroccan authorities consider to be valuable.

I’m looking at some of the ministry’s own figures regarding the observed average traded prices of sugar on international markets,  and they list traded average prices:

Les cours moyen du sucre brut et du blé tendre au titre du premier semestre 2011 s’élèvent respectivement à près de 652 $/t et 352$/t contre respectivement 444 $/t et 172$/t au titre de la même période de l’année 2010.

It is a bit strange the Sugar Index prices do not match MINEFI figures. Or perhaps looking for the cheaper alternative isn't a priority down there. (Bloomberg)

But it seems to me this is not true; not for sugar anyway. I have looked up two indexes for sugar, and the maximal value did not top up $360/ton – March 2011, if our government was wise enough to cover imports with futures. As for wheat, it seems the market price did not go beyond$350/ton since 2008; that  \$ 20 doesn’t make a difference, and for the specific category of wheat, total cost to import was about MAD 6 Bn for 2010; that means each household had to shoulder 896 dirhams of direct expenses incurred from wheat imports. Total cost for imported sugar (of all kinds) would have been 3.3Bn, that is 511 dirhams per household

896 dirhams of basic cost computed from raw imported wheat; assuming negligible additional costs, and based on the regulated price of one loaf of bread, that means one household would have consumed an annual set of 690 loafs of bread; same computations for sugar based on an average price of 6 dirhams/kg would yield a theoretical consumption of 85kg per household. Gee-whiz statistics perhaps, but it paints a picture; international prices have only limited impact on purchasing power; as far as I can tell, domestic interactions account for a lot more, perhaps because of the strait-jacketing of specific prices and oligopolistic markets for goods such as wheat storage, sugar and distribution.

Now 2010 yielded an average annual income per household of about MAD 106,751, and based on HCP 2006/2007 household consumption survey, consume 41.3%, thus spending MAD 1812 in sugar and MAD 7847 in wheat (bread and otherwise) That’s a lot more than the raw cost for these imported goods.

This comparison suffers from major flaws however: it does not take into account other costs factored in the final product, and second, computing expenditure in average term tends to produce bias; indeed, compensation subsidies are not mean-tested; furthermore, figures are not that reassuring when one looks into the median expenditure, let alone the fact that average household does not take into account its intrinsic size. Median annual income has been MAD 77,000 and thus consume MAD 5288 in wheat and MAD 1244 in sugar per annum.

But the argument is basically sound: raw cost per household is too low to justify what might come to be a MAD 7,800 subsidy per household. Actually, that argument is strengthened by the disparities in consumption distribution; in fact, because the top 10% households (that’s 2 Million individuals, give or take) capture a third of total household consumption, they get more than their theoretical 10% share in subsidies -since those are indiscriminate- in fact they get three times more than average, and they get to benefit from 3/4 of total subsidies – this is derived from the fact that subsidies are distributed uniformly across population deciles.

I would argue it is too high a price to pay for an arcane system that may have been working when income dispersion was not that high: with a widening income, wealth and consumption gaps within the economy, an indiscriminate subsidy on food and other essential goods tends to favour those who capture the largest proportion of household consumption, i.e. the top 10%, or as one would like to label them, those who do not need the subsidy.

Furthermore, the compensation also encompasses the following:

à la compensation des produits de base, en l’occurrence le sucre et la farine. Le montant réglé dans ce cadre par prélèvement sur le compte intitulé “Fonds de soutien des prix de certains produits alimentaires” se monte à 880 MDH, auquel s’ajoutent des dépenses de 14.987 MDH prises en charge par le budget général (Chapitre des Charges Communes), dont 2.357 MDH au titre de la compensation des denrées alimentaires de base et 12.630 MDH destinés à couvrir la charge de compensation des produits pétroliers.

So as far as identified compensation-related items go, the industrial subsidy is 4 times larger than the more important matter of subsidizing food and edible goods. A call has been made by government officials to maintain an industrial status-quo that might not, after all, benefit the domestic economy; what if the cost of subsidizing oil-intensive industries was actually much higher than any transitional loss to alternative industries? And how come oil-related imports benefit from a 12.6Bn subsidy when the immediate household consumption of Butane is only 15%? Unless Butane is sold for a symbolic price (which is not the case as long as I can recall the commercial price of one butane cylinders) that subsidy goes primarily into business oil consumption;

So total expenses for subsidizing food is at most 3.2Bn, that’s less than 1% of total budget and 13% of projected deficit – which is so far quite a sustainable subsidy and an expenses ceiling for future mean-tested programs for targeted subsidies. As for oil-related subsidies, the same observations can be made regarding income/consumption gaps: on households’ sides, who owns/drives cars? on business’ side, which industries are hungry for oil? A valid counter-argument can be made for the poorer household deciles; how will they cook and keep their family warm? Well, given the fact that these account for 10%, and since HCP reports the following:

En 2007, 54,6% des ménages marocains disposaient d’une cuisinière à gaz. Selon le milieu de résidence, ce taux passe de 42,9% dans les campagnes à 61,6% dans les villes. Selon la classe de dépense, ce taux passe de 67,4% pour les ménages les plus favorisés à 37,1% pour les moins nantis.

[…] Au niveau national, 20% des ménages disposent d’un chauffe-eau à gaz. Ce taux varie de 1,2% pour les 20% les moins aisés à 45,9% pour les 20% les plus riches. En milieu urbain, le taux d’équipement est 10 fois supérieur à celui enregistré en milieu rural (30,3% contre 3,0%).

Furthermore, the bottom 20% households are twice less likely than the top 20% to own a gaz-based stove, and only 1.2% of those households own a gaz-based heaters.

This is to say that an inflated compensation fund, in all its individual components, is not due to the international hike in prices – only 4Bn out of the 45 have a direct impact on the livelihoods of Moroccan households;A willing (and strong-willed) finance minister can gradually start reforming the fund by first setting up a team to supervise pricing on international markets -by using commodity futures, since Morocco’s own demand is unlikely to tip futures’ valuation one way or the other- and get prices down by as much as 6% per annum for wheat for instance. Second, there must be a way to mobilize the services of the Inland Revenues (Direction des Impôts) HCP and the whole Finances ministry to design mean-tested tax deductions and breaks, as well as cash relief schemes to support as many as 661,000 households, about 5.3Mln individuals who do not have the means to sustain themselves; so far, a 7,000 annual relief (that’s a 23% boost on average income of the bottom decile) would cost about 4.7Bn and still be a relatively low burden on the budget, plus subsidy would go to those it can actually help. Third, subsidies to businesses cannot go on indefinitely; first because it skews Morocco’s industrial structure, and would give an unfair advantage to what might be obsolete and rent-seeking industries; subsidized fuel only boost the value of a taxi license, when the money can be used to improve public transportation.

The thing is, there is a way to halve subsidies gradually, though it means taking on many powerful lobbies. The only essential condition for such a scheme to succeed is political courage. I doubt Mr Baraka or his sidekick Mr Azami Idrissi, or even Mr Benkirane have what it takes to take the fight where it is necessary: suppressing rent, promoting innovation to boost growth.

format: plain


text:
Lemma 33.20.2. Let $k$ be a field. Let $X$ be a locally algebraic $k$-scheme of dimension $0$. Then $X$ is a disjoint union of spectra of local Artinian $k$-algebras $A$ with $\dim _ k(A) < \infty$. If $X$ is an algebraic $k$-scheme of dimension $0$, then in addition $X$ is affine and the morphism $X \to \mathop{\mathrm{Spec}}(k)$ is finite.

Proof. Let $X$ be a locally algebraic $k$-scheme of dimension $0$. Let $U = \mathop{\mathrm{Spec}}(A) \subset X$ be an affine open subscheme. Since $\dim (X) = 0$ we see that $\dim (A) = 0$. By Noether normalization, see Algebra, Lemma 10.115.4 we see that there exists a finite injection $k \to A$, i.e., $\dim _ k(A) < \infty$. Hence $A$ is Artinian, see Algebra, Lemma 10.53.2. This implies that $A = A_1 \times \ldots \times A_ r$ is a product of finitely many Artinian local rings, see Algebra, Lemma 10.53.6. Of course $\dim _ k(A_ i) < \infty$ for each $i$ as the sum of these dimensions equals $\dim _ k(A)$.

The arguments above show that $X$ has an open covering whose members are finite discrete topological spaces. Hence $X$ is a discrete topological space. It follows that $X$ is isomorphic to the disjoint union of its connected components each of which is a singleton. Since a singleton scheme is affine we conclude (by the results of the paragraph above) that each of these singletons is the spectrum of a local Artinian $k$-algebra $A$ with $\dim _ k(A) < \infty$.

Finally, if $X$ is an algebraic $k$-scheme of dimension $0$, then $X$ is quasi-compact hence is a finite disjoint union $X = \mathop{\mathrm{Spec}}(A_1) \amalg \ldots \amalg \mathop{\mathrm{Spec}}(A_ r)$ hence affine (see Schemes, Lemma 26.6.8) and we have seen the finiteness of $X \to \mathop{\mathrm{Spec}}(k)$ in the first paragraph of the proof. $\square$

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).


text:
Coax Cylinders End Faces - MapleSim Help

Coax Cylinders End Faces

The Coax Cylinders End Faces component models the leakage flux through between the end-planes of a solid inner cylinder and a coaxial outer hollow cylinder.  The equations are

 ${V}_{m}=\mathrm{Φ}\cdot {R}_{m}$ ${V}_{m}\equiv {V}_{{m}_{p}}-{V}_{{m}_{n}}$ ${\mathrm{Φ}}_{p}+{\mathrm{Φ}}_{n}=0$ ${R}_{m}=\frac{1}{{G}_{m}}$ ${G}_{m}=2\cdot {\mathrm{μ}}_{0}\cdot \left({r}_{0}+\frac{{l}_{g}}{2}\right)\cdot \left\{\begin{array}{cc}1+\frac{2\cdot t}{{l}_{g}}& t\le {r}_{0}\\ 1+\frac{2\cdot {r}_{0}}{{l}_{g}}& \mathrm{otherwise}\end{array}\right\$

Connections

 Name Description Color ${\mathrm{port}}_{p}$ Positive magnetic port Solid orange ${\mathrm{port}}_{n}$ Negative magnetic port Open orange

Variables

 Symbol Units Description Modelica ID ${V}_{m}$ $A$ Magnetic potential across component V_m ${V}_{{m}_{x}}$ $A$ Magnetic potential at port_x.V_m ${\mathrm{Φ}}_{x}$ $\mathrm{Wb}$ Magnetic flux into ${\mathrm{port}}_{x}$, port_x.Phi $\mathrm{Φ}$ $\mathrm{Wb}$ Magnetic flux through component Phi ${R}_{m}$ ${H}^{-1}$ Magnetic reluctance Rm ${G}_{m}$ $H$ Magnetic permeance Gm ${l}_{g}$ $m$ Radial gap length between cylinders l_g $t$ $m$ Radial thickness of outer hollow cylinder t

Parameters

 Symbol Default Units Description Modelica ID ${r}_{0}$ $0.01$ $m$ Radius of inner solid cylinder r_0 ${r}_{1}$ 0.017 $m$ Inner radius of outer hollow cylinder r_1 ${r}_{2}$ 0.020 $m$ Outer radius of outer hollow cylinder r_2

Initial Conditions

 Symbol Units Description Modelica ID ${V}_{\mathrm{m0}}$ $A$ Magnetic potential across component V_m ${\mathrm{Φ}}_{0}$ $\mathrm{Wb}$ Magnetic flux through component Phi ${R}_{\mathrm{m0}}$ ${H}^{-1}$ Magnetic reluctance Rm ${G}_{\mathrm{m0}}$ $H$ Magnetic permeance Gm