Department of Economics ECO 431 FINAL EXAM KEY. This question asks you to apply the Weitzman model of policy choice under uncertainty.

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1 Department of Economics ECO 431 Cal Poly State University Steve Hamilton Fall Semester, 2004 Question 1. Taxes or Standards (30 points) FINAL EXAM KEY This question asks you to apply the Weitzman model of policy choice under uncertainty. Part 1 (5 points). You can get 5 points for either answer (elastic or inelastic) as long as you justify it. SO 2 demand is fairly elastic, because there are fairly good substitutes available for high-sulfur coal (e.g., utilities can burn low-sulfur coal or switch to natural gas). Part 2 (25 points). Graph and discuss. When demand is elastic, standards perform better than taxes. Under Elastic Demand $ MSC t 1 D 1 t 2 D T D 2 X 1 T X 2 S X* X 1 S X 2 T Pollution (X) Suppose true demand for SO 2 is given by D T. The regulator, not knowing this, is just as likely to overestimate pollution demand as D 1 as to underestimate it as D 2. If the regulator believes demand to be D 1, she will set the pollution standard at X S 1. If the regulator believes pollution demand to be D 2, she will set the pollution standard at X S 2. Both policies miss the mark. X S 2 is less than X*, while X S 1 is greater than X*. Under a tax, if the regulator believes demand to be D 1, she will set the pollution tax at t 1 (the price that satisfies D 1 = MSC). Since the true demand

2 of firms is D T, firms cut back pollution to X 1 T under a tax of t 1. If the regulator believes demand to be D 2, she will set the pollution tax at t 2. Since the true pollution demand of firms is D T, firms cut back pollution to X 2 T. Either way, the outcome of regulation is always closer to X* under a standard than under a tax. Similarly, When demand is inelastic, taxes perform better than standards. Question 2. Think (30 points) When resources are owned by "all the people", this results in a common property problem. Individuals fail to account for the effect of their resource use on the well-being of others (as in the 'give-to-the-group' game we played in class). Common property resources are nonexcludable, and this leads to free-riding behavior, much as in the case of public good problems. Privatization is one way to resolve the common property problem, because privatizing resources creates property rights. Question 3. Salty Water (30 points) Dominant strategies (10 points): U.S. cheat; Mexico comply Outcome of the game (5 points): Mexico complies and the U.S. cheats. Efficiency (10 points): The outcome is inefficient. The efficient outcome is where the sum of the payoffs is highest, and this is mutual compliance Does it make sense? (5 points): Sure. The flow of the river is from the U.S. to Mexico, so Mexico has nothing to lose from compliance. Compliance can be costly to the U.S., because of pollution controls. Question 4. Honeybees (35 points) A. (5 points). MPB = 50 - Q; MPC = 2 + 3Q Competitive equilibrium: 50 - Q = 2 + 3Q => 48 = 4Q => Qc = 12 Pc = = $38.00 B. (10 points). MEB = Q, so MSB = MPB + MEB = Q MEC = Q, so MSC = MPC + MEC = Q Socially optimal outcome: Q = Q => 70 = 5Q => Q* = 14 Q* > Qc, so the external benefits outweigh the external costs on the margin.

3 C. (10 points). Graph. DWL is from under-production and is the difference between MSB and MSC for all the units the private market fails to produce (Q* - Qc). $ MSC P* MPC Pc DWL MSB MPB Qc Q* D. (10 points). The optimal policy in this case will be a subsidy, because the private market does not produce enough. We can conceive the policy to be the sum of an externality tax, t = MEC(Q*), and an externality subsidy, s = MEB(Q*). If we did this, the tax that internalized the negative externality would be, t* = (14) = 29. The subsidy that internalized the negative externality would be, s* = (14) = 37. So, in total, a subsidy of S* = s* - t* = 8 would induce the private market to provide Q* = 14 units. Verify. The private market sets MPB + S* = MPC, or 50 - Q + 8 = 2 + 3Q => 4Q = 56 Qc = Q* = 14 Question 5. Bauxite Extraction A. (5 points). Graph. Royalty = MB MC = 16 2Q. Q 1 * is shown, and Q 2 * = 10 - Q 1 *. $/Q 1 $/Q 2 16 R R 1 (1/(1.1))R Q 14.6 P 1 = λ* P 2 λ* 0 Q 1 * 10 Q 1

4 B. (5 points). Calculate. R 1 = (1/(1+r))R 2. And, Q 2 = 10 - Q Q 1 = (1/1.1)[16-2(10 - Q 1 )] = 0.909[2Q 1-4] = 3.818Q 1 => Q 1 * = 5.14 Q2 = 10 - Q1 Q 2 * = 4.86 C. (5 points). User cost is a dynamic opportunity cost. Use of a unit of a resource today precludes use of the unit in the following period, and user cost is the value of this lost opportunity. User cost is shown as λ* on the graph. Notice that R 1 = λ*. R 1 = λ* = 16-2(5.14) = $5.71. D. (10 points). The effect of a decrease in the discount rate to 0% is shown on the above graph. In this case, the quantity extracted in each period is 5 units, and the user cost rises to λ* = 16-2(5) = $6. In general, a decrease in the discount rate increases future values, increasing the user cost. This means less will be extracted in the current period and more will be extracted in the future period. E. (5 points). Under open access, Q 1 OA = 8 (where R = 0 in the current period). This is inefficient, because total value would be greater by extracting as calculated in part B. (You can show the DWL on the figure to be more concrete about this.) F. (5 points). The optimal tax under open access would be t* =λ* = 16-2(5.14) = $5.71. Question 6. Queuingistan A. (5 points). Farmers will adopt the cheapest technology available, which is the traditional technology. This is because senior rights holders do not pay for water and the return to a larger fixed investment in modern technology is the value of the water saved, which is zero. B. (5 points). A senior rights-holder maximizes profits, which are given by π s = 250[12e - e 2 ] FOC: dπ s /de = 250[12-2e] = 0 => e* = 6 With traditional technology, a = 2e, so a* = 12 acre feet of water. This implies the water on the island is enough to irrigate L* = 24,000 / 12 = 2,000 acres. C. (5 points). Output per acre is y* = 12(6) - (6) 2 = 36 π s * = 250(36) = $8,500. GNP = (2,000 acres)($8,500 / acre) = $17 million D. (5 points). Under a market allocation, allocative efficiency requires equating the marginal benefit of water use across all users. This implies that water should be distributed equally across all acres. So a* = 24,000 / 4,000 = 6

5 E. (5 points). Old technology. At 50% efficiency, e* = 3 => y* = 12(3) - (3) 2 = 27 New technology. At 80% efficiency, e* = 4.8 => y* = 12(4.8) - (4.8) 2 = F. (5 points). Water price is given by: v = VMP = 250[12-2e*]h Old technology. v = 250[12-6]0.5 = $750 New technology. v = 250[12-2(4.8)]0.8 = $480 G. (5 points). If senior rights-holders sell water to junior rights-holders, each senior rights holder will receive a property right for 12 units of water and sell 6 units of water to junior holders: Old technology. π s * = 250(27) + 750(6) = $10,700 π j * = 250(27) - 750(6) = $1,700 GNP = 2000(π s *) (π j *) = 2,000[12,400] = $24.8 million New technology. π s * = 250(34.56) + 480(6) = $9,470 π j * = 250(34.56) - 480(6) = $3,710 GNP = 2000(π s *) (π j *) = 2,000[13,180] = $26.36 million Senior rights holders will not willingly adopt the modern technology, because their profit is lower by doing so. (Note: this is true even is you recalculate the case where junior rights holders adopt and senior rights holders do not.) H. (5 points). If the King sells water permits to everyone, then all islanders face profit incentives identical to those calculated above for junior rights holders. (The King is now the only senior rights holder of water.) Now all islanders adopt the modern technology. Whether the king sells the water permits or the islanders sell the permits makes no difference to GNP. The revenue from the sale of water permits is a pure transfer that has no implications on the total value of pineapple output on the island. So, GNP = $26.36 million.