Suppose two upstream agricultural producers divert some water from a stream to irrigate their crops. This water diversion leaves less water for downstream water users, imposing a cost on those users. Consider the optimal level of total water use for the upstream producers. The two farmers' aggregate marginal profits from using the water are Mr = 20 - (1/5), where q represents the aggregate amount of water used. Marginal external costs to downstream users are MEC = (1/5). Calculate the efficient aggregate level of water use and the efficient level of marginal external costs. Now consider the allocation of water use between the two farms. Farm 1 uses q units of water and farm 2 uses q2 units. Farm l's marginal profits from water use are given by M.7. =150- 34 Farm 2's marginal profits from water use are given by M.7, 5100 - 29 Suppose a regulator implements a tradable permit system to regulate water use. a. If the regulator sets the total number of permits efficiently (i.e., the solution to problem 1), i. What will be the equilibrium permit allocation and permit price in the market for water rights? ii. Is this allocation efficient? Why or why not? If the regulator initially gave all the permits to farm 1 (and that farm did not act as a monopolist for permits), use a graph to explain how each farm could gain from trade. Label the net gains on a graph. b. Suppose two upstream agricultural producers divert some water from a stream to irrigate their crops. This water diversion leaves less water for downstream water users, imposing a cost on those users. Consider the optimal level of total water use for the upstream producers. The two farmers' aggregate marginal profits from using the water are Mr = 20 - (1/5), where q represents the aggregate amount of water used. Marginal external costs to downstream users are MEC = (1/5). Calculate the efficient aggregate level of water use and the efficient level of marginal external costs. Now consider the allocation of water use between the two farms. Farm 1 uses q units of water and farm 2 uses q2 units. Farm l's marginal profits from water use are given by M.7. =150- 34 Farm 2's marginal profits from water use are given by M.7, 5100 - 29 Suppose a regulator implements a tradable permit system to regulate water use. a. If the regulator sets the total number of permits efficiently (i.e., the solution to problem 1), i. What will be the equilibrium permit allocation and permit price in the market for water rights? ii. Is this allocation efficient? Why or why not? If the regulator initially gave all the permits to farm 1 (and that farm did not act as a monopolist for permits), use a graph to explain how each farm could gain from trade. Label the net gains on a graph. b
