PAI 723 Economics for Public Decisions > Exercise 5


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

Part A

  1. 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.
  2. 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.
  3. 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.
  4. 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.

Part B

  1. 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.
  2. 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.
  3. 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.
  4. 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.

Part C

  1. `MRS = (200-170)/(20-22) = -15 "hp"/"mpg"`
  2. 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).
  3. 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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Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 10/21/2019