1. There are a lot of mosquitoes in island of Liholiho. Only two people live in this island, Robinson Crusoe and Man Friday. Their respective demand curves for the mosquito control are given by P_{c} = 120 - 2Q_{c} and P_{f} = 260 - 4Q_{f}, where c stands for Crusoe, f stands for Friday, and Q and P are quantity and price of mosquito control. Assume that mosquito control is a public good.
(a) What is optimal level of provision of this good if it can be produced at the constant marginal cost of $80 per unit?
(b) What would it cost Government of Liholiho to offer the optimal amount of mosquito control?
(c) How should the tax bill be assigned between the two individuals if they are to share it in proportion to total benefits from mosquito control received by each individual?
(d) If mosquito control were left to private market, how much would be provided? Does your answer depend on what each person assumes the other would do? describe.
2. Assume that a public park is visited by people living in five concentric zones around the park. Each zone has a population of 5000, and the total travel cost for a visit to the park from zone i is given by TC_{i} = 4 (i -1), where i = 1 , ... , 5. For each zone, the estimated relationship between visitation rate V (defined as annual number of visits/1000) and total travel cost (TC) is given by
V = 100 - 5 TC.
(a) For each zone, obtain an equation relating total number of visits from that zone to different levels of a hypothetical fee charged per visit.
(b) prepare down in the equation form (and also depict in a diagram) aggregate demand curve for the park and use this curve to compute the annual user value of the park.
(c) Assume that the annual maintenance cost of the park is 30,000 and the local government is under considerable pressure to sell the park to urban developers. What would you advise in this case? Use the information obtained in 2(b) and lists any additional factors that might need to be investigated before arriving at the correct decision.
3. The inhabitants of Fantasia live for two periods, 0 and 1. They consume a non renewable resource called Fantasium in each period. Fantasium has to be extracted from ground and the (constant) marginal cost of extraction is $4/unit. The total available supply of Fantasium in ground is 22 units and you must suppose that the complete amount will be consumed over the two periods. The market demand curve for Fantasium in period 0 is given by P0 = 10 - Q0 + M and in period 1 this demand curve is given by P1 = 10 - Q_{1} + M, where Pi is price in period i, Qi is quantity demanded in period i (i = 0, 1), and M is Fantasia's national income in each period. Assume that there are many identical firms extracting Fantasium in every period, each firm has perfect foresight about prices, each firm discounts profits at the rate of 50%, and M = 20.
(a) Use Hotelling's Rule to get an equation which relates the equilibrium price in period 0 (i.e., P_{0}) to the equilibrium price in period 1 (i.e., P_{1}).
(b) Use the market demand curve in each period and your answer to 3(a) to get an equation which relates the equilibrium quantities Q0 and
Q1. Use this equation and the constraint on total accessible supply of Fantasium to solve for the equilibrium quantities of Q_{0} and Q_{1}.
(c) Use your answers to 3(b) in the demand curve for each period to get equilibrium values of P_{0} and P_{1}.
(d) What would be the equilibrium values of Q_{0} and Q_{1} if the rate of discount was 100% instead of 50%?
(e) What would be the equilibrium values of Q_{0} and Q_{1} if the rate of discount was 50% but the marginal cost of extraction of Fantasium was $14/unit instead of $4/unit?
(f) What would be the equilibrium values of Q_{0} and Q_{1 } if the rate of discount was 50%, the marginal cost of extraction of Fantasium was $4/unit, but M was 40 instead of 20 ?