The equimarginal principle of optimality: the rational spending rule and production economics



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CDAE 61: Assignment 6
The EQUIMARGINAL PRINCIPLE OF OPTIMALITY: THE RATIONAL SPENDING RULE and PRODUCTION ECONOMICS
35 points total.
Look at the following pie-chart of discretionary spending by appropriations bill for fiscal year 2008. Discretionary spending is that portion of the federal budget that is not earmarked by law, so it excludes social security, Medicare, Medicaid and so on.

The entire proposed budget is $933 billion. Our fiscal deficit (spending minus revenue) for 2007 is estimated to be about $161 billion. Our national debt is about $9.1 trillion.

Many pie charts would include the bridge fund for Iraq and Afghanistan military operations, Veterans Administration, homeland security and interest payments on defense-related debt as part of defense—in which case defense ads up to about 59% of discretionary spending. Notice that Labor, Health and Human Services, and Education are all lumped together. If you want to get a better idea how these break down, take a look at http://www.truemajorityaction.org/oreos/. This provides more detail for expenditures on k-12 education, world hunger, alternative energy, children’s healthcare, head start, and foreign military budgets. While the site may be partisan, the data is not.


A headline in today’s (Oct. 23) NYT:

Bush’s Request for Wars Increases to $196 Billion



“The Senate majority leader, Harry Reid, criticized the tactic that allowed the White House to pay for the war with emergency spending, keeping the costs off the budget. “The entire war has been paid with borrowed money,” he said in the Senate.”
This means that the real deficit is over twice as large as reported.
1. (15 points) Imagine you are running for office as the candidate of fiscal responsibility. Use the equimarginal principle of optimality (in this case, the rational spending rule) to explain how we should think about cutting expenditures to balance the budget. Your explanation should not use fancy words, and must be understandable to Joe Sixpack. There is no right or wrong answer concerning where you want to target cuts, as long as your explanation makes proper use of economic theory. Since we do not have any actual numbers on utility, this is a subjective assessment on your part. You might want to do some research to see where the current administration is currently targeting its cuts (hint: it’s more likely to health programs for children than subsidies for oil companies).
When the government spends more than it takes in, that money must be paid back. Deficit spending is the same as raising taxes on our children. The US government should spend your children’s tax dollars so that we get as much benefit for the last dollar spent as possible. This means that if we get more benefits from the last dollar spent on education (so our children can get good jobs and afford to pay back our national debt) than the last dollar spent on the military, we should shift funding away from the military and towards education (In technical terms, the equimarginal principle of optimality says that the last dollar spent on any of the slices in the chart should provide the same level of utility.) The US is currently spending more on defense than all other countries in the world combined. If we cut back on defense spending, we will eliminate the least important things we buy, for example, nuclear weapons we won’t use, the $54.6 billion dollar V-22 Osprey aircraft that is fatally flawed (30 deaths even before it has been used in combat) and an anti-ballistic missile shield that won’t work and that will force us to break our ABM treaty with the Russians. One good place to spend the money would be on health care for our children, especially since they are the ones who will have to pay back our debt. The recently vetoed SCHIP plan should be funded for $35 billion over five years, equal to the money budgeted for future production of the defective Osprey. Healthy children become more productive, higher earning adults, so the S-CHIP plan is an investment in our future. Given the problems associated with fossil fuel use (global warming, pollution, dependence on unstable foreign countries for petroleum supplies, etc) and the small amount of money spent on alternative energy technologies, we could get a lot of bang for the buck by spending more here. Energy independence through new technologies and conservation is a far more cost effective approach to secure energy supplies than going to war in the Middle East. A more educated population makes us more productive. It is an investment with high returns. AIDS and other preventable diseases take more human lives every year than war (the 1919 flu epidemic killed more people than all wars ever), so we should put more money into health and human services. With global warming an unavoidable reality, we should spend more money on research into agricultural production. As your candidate, I am not saying that defense is unimportant, merely that the improvement to your well-being from another dollar spent on defense is much less than that from another dollar spent in the other areas. I therefore suggest drastic decreases in our defense budget, to the point where we are only spending twice as much as all countries in the world combined who are not our close allies (i.e. twice as much as all other countries combined except Western Europe, Japan, Canada, and Australia).
You can argue for reductions in any area you want, as long as you claim that the marginal utility of another dollar spent on defense is higher than for those other areas. The current administration has vetoed funding for children’s health care and in recent years has slashed money spent on the environment, basic research, student loans, and a number of other areas. Deficit spending allows the government to put off more serious budget cuts for the future, but to pay off the deficit, we will eventually need to raise taxes.
8 points for a good explanation of the rational spending rule, 7 points for explaining why marginal utility is lowest in the areas you are cutting, and highest in the areas where you are not cutting expenditures.

2. (FROM F&B, Second edition, p. 163) (20 points)

The Paducah Slugger Company makes baseball bats out of lumber supplied to it by Acme Sporting Goods, which pays Paducah $10 for each finished bat. Paducah’s only factors of production are lathe operators and a small building with a lathe. The number of bats per day it produces depends on the number of employee-hours per day, as shown in the table below.

Number of bats per day

Number of employee-hours per day

0

5

10



15

20

25



30

35


0

1

2



4

7

11



16

22


Q

(bats/day)



Total Revenue

($/day)


Total labor cost

($/day)



Marginal cost /bat


Total cost

($/day)


Profit

($/day)


0

0

0




60

-60

5

50

15

$3

75

-25

10

100

30

$3

90

10

15

150

60

$6

120

30

20

200

105

$9

165

35

25

250

165

$12

225

25

30

300

240

$15

300

0

35

350

330

$18

390

-40

a. (5) If the wage is $15 per hour and Paducah’s daily fixed cost for the lathe and building is $60, what is the profit-maximizing quantity of bats?

The rule for profit maximization is MC<=MB. MC is given in the table. MB = $10, the price of a bat. As indicated by the entries in the last column of the table below, the profit-maximizing quantity of bats for Paducah is 20/day, which yields daily profit of $35.
b. (5) What would be the profit-maximizing number of bats if the firm’s fixed cost were not $60/day but only $30?

Same quantity as in part a, but now profit is $65, or $30 more than before.


c. (5) How would Paducah’s profit-maximizing level of output be affected if the government imposed a tax of $10/day on the company?(Hint: Think of this tax as equivalent to a $10 increase in fixed cost).

A tax of $10 per day would decrease Paducah’s profit by $10 per day at every level of output. But the company would still maximize its profit by producing 20 bats per day. A tax that is independent of output does not change marginal cost, and hence does not change the profit-maximizing level of output.



d. (5) What would Paducah’s profit-maximizing level of output be if the government imposed a tax of $2 per bat? (Hint: Think of this tax as a $2/bat increase in the firm’s marginal cost.) Why do these two taxes have such different effects?
A tax of $2 per bat has exactly the same effect as any other $2 increase in the marginal cost of making each bat. As we see in the last column of the table below, the company’s profit-maximizing level of output now falls to 15 bats per day. At that level it earns exactly 0 profit, but at any other level of output it would sustain a loss.


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