2350pqset_06 - YORK UNIVERSITY — ECON2350 — V BARDIS...

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Unformatted text preview: YORK UNIVERSITY — ECON2350 — V. BARDIS PBAQTIQE SET 6 1. Suppose the consumers’ willingnes to pay for Q units of a good is given by WTP(Q) = 12Q — Q2/2. The industry cost of producing Q units is given by C (Q) = Q2. Production of the good generates pollution and results in damages given by the damage function D(Q) = Q2 / 2. (a) Find the the equilibrium price 13 and quantity Q. (b) Calculate society’s welfare (or total surplus) in equilibrium. (c) Find the efficient amount of the good given the pollution externality. Calculate total surplus at this level of output and show that, as expected it is greater than the number you found in part £91 (d) Find the per—unit tax that will yield the efiicient amount of the good in the market equilibrium. 2. Suppose Tom’s benefit from listening to music Q hours a week is given by B (Q) = 12Q — 3Q2 / 2. It can be thought of as the amount of money Tom would be willing to pay to listen to music for Q hours. Jerry is Tom’s roomate. Jerry is annoyed by Tom’s music. He would be willing to pay up to C (Q) = Q2/2 to see Jerry reduce his listening to music from Q to zero hours. In other words, C (Q) is the cost or damage Jerry from Q hours of Tom’s music. (a) If Tom can do as he wishes without any regard for or consultation with Jerry, how many hours will he practice his drums? What will be the benefit to Tom and the cost to Jerry? (b) Argue with the help of a well defined graph that the above number of hours inefficient? What . ] Efi . l f ] 7 (c) Suppose Tom and Jerry get together at the beginning of the week and negotiate a solution. As in part (a), assume that Tom will do what is best for him if the two of them do not come up with a settlement. Jerry will pay Tom S dollars to reduce his music hours. What is the number of hours they will agree on? What is the maximum value of S? What is the minimum value of S? What are the gains from trade between Tom and Jerry? (d) How would the analysis of the Tom and Jerry dispute and its solution change if Jerry has the right to stop Tom from listening to music? 3. Consider the following case of a ‘consumption externality’. Person A and person B are neighboors. Each likes plants and likes gardening in his unfenced garden. If one person adds plants to his own garden the other will also benefit. Let qa and qb be the number of plants grown by A and B respectively. The table below gives what each person would be willing to pay for one more um’t acquired by himself and by the other. For one more plant in A’s garden For one more plant in B’s garden A is willing to pay ll—qa 1 B is willing to pay 1 6% (a) If the price of a plant is p = 1 how many plants will each person buy? (b) Do you think that the amounts you found in part (a) are socially efficient? Explain. (c) Verify your intuition above by calculating the efficient amount of plants in the ‘neighborhood’. 4. Tom is willing to pay 1000 dollars for one unit and 1800 dollars for two or more units. Person B is willing to pay 1300 dollars for one unit and X dollars for two or more units. Suppose it costs 1500 dollars to produce the first unit of the good and 2000 dollars to produce the second unit. For which values of X is one unit the efficient amount of the good? For which values of X is the efficient amount two units? 5. Consider the case of a public good. If (1 units are produced the marginal Willingness to pay of person A and B are given respectively by M WTPA = 4 — q and M WTPB = 8 — 2g. (a) If ‘society’ consists of A and B, find society’s MWTP for the public good and illustrate on a well—defined diagram. (b) What is society’s ‘demand’ for the public good? (C) If this good can be produced at marginal cost M C = 4, What is the efficient amount of the good? (d) Suppose person A provide qA units of this good and a cost per unit of 4. Similarly, person B can provide (13 units of the good a cost of 4 per unit. What is the equilibrium amount of the good in this case? (Hint: Draw each person’s best response curve and identify the intersection.) ...
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