The Maxwell School

Syracuse University

Syracuse University

The Maxwell School

Syracuse University

Syracuse University

Here are notes on the solution. This is not a complete answer to the exercise but it will let you check your work.

- The initial equilibria in the L and H markets are shown below.

The agency's extra revenue in the L market is ($100-$80)*10,000 = $200,000. The agency's overall net position on the policy is equal to the total surplus it raises in L less the total subsidy it provides in H. Using that to find the total subsidy and the subsidy per unit:

Surplus in L - Subsidy in H = Net

Inserting the current $200,000 surplus in L and overall net -$100,000 gives:

$200,000 - Subsidy in H = -$100,000

Solving for the subsidy in H gives $300,000. Dividing that by the number of customers gives the subsidy per unit: $300,000/5,000 = $60. Since customers are being charged `P^d`=$100 and the government is providing a $60 subsidy, `P^s` is $160 and thus `WTA_H` must be $160 as well. - The new quantities can be calculated using the demand elasticities for the two markets. In both cases, the price rises by 10%. For the L market:

`{%\Delta Q_L}/{%\Delta P} = -0.5 => {%\Delta Q_L}/{10%} = -0.5 => %\Delta Q_L = -5% => Q_L`=9,500

For the H market:

`{%\Delta Q_H}/{%\Delta P} = -1 => {%\Delta Q_H}/{10%} = -1 => %\Delta Q_H = -10% => Q_H`=4,500

The new price and quantities are shown in the diagram below, which also shows the new surplus raised in the L market, area A, and the new subsidy paid out in the H market, area B:

The revised surplus in the L market (A) is ($110-$80)*9,500 = $285k. The revised subsidy in the H market (B) is ($160-$110)*4,500 = $225k. The program overall now produces a net surplus of $285k - $225k = $60k. The price increase is more than enough to eliminate the deficit. - The policy decreases CS for both types of customer since each group sees a $10 price increase. The diagram and calculations are shown below:

`\Delta CS_L` = -$10*(10,000+9,500)/2 = -$97.5k.

`\Delta CS_H` = -$10*(5,000+4,500)/2 = -$47.5k.

There are a couple of approaches to computing the overall change in SS. The quickest way is to treat the full surplus in the L market and the full subsidy in the H market as PS (that is, treating the agency and the government as one overall entity). The overall change in PS would be computed like this:

`\Delta PS_L` = $285k - $200k = +$85k (extra revenue)

`\Delta PS_H` = (-$225k) - (-$300k) = +$75k (savings in reduced subsidy)

`\Delta PS` = `\Delta PS_L` + `\Delta PS_H` = $85k + $75k = $160k.

The overall change in SS is thus:

`\Delta SS` = - $97.5k - $47.5k + $160k = $15k.

An alternative and equally valid approach is to treat the agency as always having an overall PS of zero (that is, it puts exactly as much into the H market as it collects in the L market) and then having the government pick up the difference. In that case, the initial situation has PS=$0 and Rev=-$100k and the revised situation has PS=$0 and Rev=+$60k. Computing the changes gives `\Delta PS`=$0 and `\Delta Rev`=$60k-(-$100k)=$160k. The overall change in SS would then be the following:

`\Delta SS` = `\Delta CS_L` + `\Delta CS_H` + `\Delta PS` + `\Delta Rev`

`\Delta SS` = - $97.5k - $47.5k + $0 + $160k = $15k. - The increase in revenue in L contributes $85k toward solving the problem (`\Delta PS_L`) and the reduction in the subsidy in H contributes another $75k (`\Delta PS_H`). Together they move the overall budget in the positive direction by $160k: more than enough to eliminate the initial $100k deficit. Also, the two components are pretty similar to one another: the extra revenue in L is pretty close to the reduction in spending in H.

Since setting the price to $110 is more than enough to eliminate the deficit you might wonder what price would just bring it into balance. To the nearest cent, the answer turns out to be $106.11. Determining that requires solving a nonlinear equation, however, and was not a required part of the problem.

- The overall market without a hurricane looks like the diagram below. The price is $5, total consumption is 95, firm A supplies 18, and firm B supplies 77.
- After the hurricane hits and firm B is knocked off line, the market equilibrium would look like the graph below. The price would rise to $12, total consumption would fall to 60, and firm A's output would rise to 60.
- A price ceiling imposed at the original $5 price would cause the quantity to drop back to firm A's original quantity: 18. Relative to the post-hurricane equilibrium in 2, the change in PS would be a loss of areas A and B in the diagram below. The change in CS would be a gain of A and a loss of C.

The value of X is the WTP when Q is 18, which is $20.40. Computing the areas:

A = $7*18 = $126

B = 0.5*$7*(60-18) = $147

C = 0.5*($20.40-$12)*(60-18) = $176.40

Calculating the changes in PS, CS and SS:

`\Delta PS` = -($126 + $147) = -$273

`\Delta CS` = $126 - $176.40 = -$50.40

`\Delta SS` = -$273 - $50.40 = -$323.40

As expected, the price control reduces social surplus. - Interestingly, this particular policy makes
*both*suppliers*and*consumers worse off overall: consumers, who are the intended beneficiaries of the policy, see their CS*fall*under the control.

With that said, consumers who are able to buy gasoline are better off under the price control. However, MUCH less gasoline is available (60 down to 18, a drop of 70%), so many consumers will be hurt by being unable to buy gas. On balance, the harm suffered by people unable to buy gas exceeds the benefits to those who can.

- `MRS = (200-170)/(20-22) = -15 "hp"/"mpg"`
- Yes, although his preferences are unusual (he dislikes horsepower and fuel efficiency), they are complete (ranks all cars) and transitive (C>A>D>B>E>F).
- The graphs are shown below. For some of the people, too little information is given to determine the slopes of their indifference curves precisely.
Person 1 regards hp and mpg as perfect substitutes at a 15:1 ratio; Person 2 cares only (or mostly) about mpg; and person 3 cares only (or mostly) about hp. Person 4's preferences are odd: he basically likes poor quality cars: low hp and low mpg. Because 4's preferences are complete and transitive, however, they are rational.

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URL: https://wilcoxen.maxwell.insightworks.com/pages/4909.html

Peter J Wilcoxen, The Maxwell School, Syracuse University

Revised 10/21/2019

URL: https://wilcoxen.maxwell.insightworks.com/pages/4909.html

Peter J Wilcoxen, The Maxwell School, Syracuse University

Revised 10/21/2019