Midterm Preparation EconS 330 Instructor: Ana Espinola, Hulbert 111C, anaespinola@wsu.edu This midterm preparation is a guide that will help you to study for Midterm #1. It does not imply that you will face the same questions during the exam. The midterm will be mainly focused on Chapters #2, 3, 4, 5, 6 and 7. Exercises 1) Assume that the inverse demand function for the depletable resource is P = 10 0.2q and the marginal cost of supplying it is $8. a. If 30 units are to be allocated between two periods, in a dynamic efficient allocation how much would be allocated to the first period and how much to the second period when the interest rate is 0.15? b. What would be the efficient price in the two periods? c. What would be the marginal user cost in each period? 2) Suppose the inverse demand function of a product is P= 40-5q, and the marginal cost of producing it is MC = 2q+3, where P is the price of the good and q is the quantity demanded and/or supplied. a. Draw a graph showing the demand curve and the marginal cost curve. b. How much would be supplied in a static efficient allocation? c. What would be the magnitude of the net benefits 3) A chemical producer dumps toxic waste into a river. The waste reduces the population of fish, reducing profits for the local fishing industry by $100,000 per year. The firm could eliminate the waste at a cost of $60,000 per year. The local fishing industry consists of many small firms. Using the Coase Theorem, explain how costless bargaining will lead to a socially efficient outcome, regardless of whether the property rights are owned by the chemical firm or the fishing industry. Why bargaining not be costless? How would your answer to part (a) change if the waste reduces the profits for the fishing industry by $40,000? (Assume, as before, that the firm could eliminate the waste at a cost of $60,000 per year) 4) There are three consumers of a public good. The demands for the consumers are as follows: Consumer 1: P1 = 60 Q Consumer 2: P2 = 100 Q Consumer 3: P3 = 140 - Q Where Q measures the number of units of the good and P is the price in dollars. The Marginal Cost of the public good is $180. What is the economically efficient level of production of the good? Illustrate your answer on a clearly labeled graph 1
5) Consider a variation of the chemical manufacturing example. Suppose the inverse demand curve for the chemical (which is also a marginal benefit curve) is P d = 30 Q, where Q is the quantity consumed (in millions of tons per year) when the price is P d (in dollars per ton). The inverse supply curve (also the marginal private cost curve) is MC P = 0.5 Q, where MC P is the private marginal cost when the industry produces Q. The industry emits one unit of pollutant for each ton of chemical it produces The external marginal cost is: MC E =4+3Q where MC E is the external marginal cost in dollars per unit of pollutant, when Q units of pollutant are released. a. Draw a graph showing the demand curve, MC S, MC P and the MEC. b. Find the optimal Tax (or optimal emission fee) c. Construct a table comparing the equilibria with and without the emission fee. 6) Consider an industry consisting of a given number of profit maximizing firms, each having free access to an exogenously fixed common property resource (fishing ground). The size of fishing ground is fixed and the cost of catching fish is related to the total number of fishing vessels. Each vessel can potentially capture F(f)=-f 2 +100f, where f denote fish. The price of a fish is given and equal to $1. Assume that the cost of catching a fish is. Identify the optimal number of fish when the fishing ground is privately owned and compare this result to the case where the fishing ground is not privately owned. [Hint: ] 7) What is the Coase theorem, and when is it likely to be helpful in leading a market with externalities to provide the socially efficient level of output? 8) What is the public good? How can one determine the optimal level of provision of provision of a public good? 9) Explain why cigarette smoking is often described as a good with negative externalities. (b) Why might a tax on cigarettes induce the market for cigarettes to perform more efficiently? (c) How would you evaluate a proposal to ban cigarette smoking? Would a ban on smoking necessarily be economically efficient? 10) Summarize the Theory of Justice develop by John Rawls (1971) 11) Why does an otherwise competitive market with a negative externality produce more output than would be economically efficient? 2
Question (1) (a) Answer Key Equalizing equation (1) and (2): From the above equation q 1 can be expressed as follows, (B) Substituting (B) into (3), and (b) In order to obtain prices in period 1 and 2 you need to substitute the optimal quantities (q 1 and q 2 ) into the demand function: Next, we need to determine the Marginal User Cost in period 1. From equation (1) we know that: = And in period 2 the MUC is: = (c) The MUC in period 1 is -0.93 and The MUC in period 2 is -0.93 PLEASE CONSTRUCT THE GRAPH! (2) 3
a. Graph Price 40 Marginal Cost Marginal Cost = Demand 13.55 3 Demand 5.29 8 Quantity b. The static efficient allocation is when MC=D P=MC 40 5q = 2q + 3-7q = -37 q = 5.29 Substituting 5.29 into the demand function: P=40 5x5.29=13.55 c. The magnitude of the benefit is: =97.865 Analyze what happens with the efficient allocation obtained in part (b) if we assume that the Marginal External Cost is equal to: MEC=2q!!!! (3) (a) If property rights are assigned to the chemical producer, the fisherman will pay $60,000 to the firm to eliminate the toxic waste. If property rights are assigned to the fisherman, the chemical producer will clean up the waste since this is cheaper than compensating the fisherman. This, regardless of who property rights are assigned to, the toxic waste gets cleaned up because this is less costly than the damage. (b) Because the waste harms many fishermen, it may not be easy to organize them to bargain about compensation. Organizing the fishermen may be costly. In addition, if fishermen and the firm have different perception regarding the cost of the externality, they might not reach an efficient solution. (c) If the fishermen s profits were reduced by $40,000 rather than $100,000, then if property rights were assigned to the chemical producer, the fishermen would not find it worthwhile to pay for cleanup. The fishermen will receive no 4
compensation. If property rights are assigned to the fishermen, the chemical producer would compensate the fishermen $40,000 rather than paying the cleanup cost. Thus, regardless of whom property rights are assigned to, the waste will not get cleaned up. This is economically efficient because cleanup costs more than the damage. (4) The demands for the consumers are as follows: Consumer 1: P1 = 60 Q Consumer 2: P2 = 100 Q Consumer 3: P3 = 140 - Q Marginal Cost: $180 We know that the MSB = Demand 1 + Demand 2 + Demand 3. Therefore: MSB = 60 Q + 100 Q + 140 Q MSB = 300 3Q The economically efficient level of output occurs where MSB = MC. Since this occurs where all three consumers are in the market we have: 300 3Q = 180 Q = 120/3 Q = 40 Question #5 P = MPC 30 Q = 0.5Q -1.5Q = -30 Q = 20 If Q = 20 then the price (using demand curve) is: P= 30 20 = 10 The social Optimal quantity is : P = MSC. Therefore we need to identify the MSC curve: 5
MSC = MEC + MPC = [4+3Q] + [0.5Q] MSC = 4+3.5Q 30 Q = 4 + 3.5Q -4.5Q = -26 Q = 5.77 Substituting Q=5.77 into the demand function we have that Pc=24.22 (30-7.43) Finally, when the quantity produced is 5.77 then the MPC is (substituting 5.77 into MPC equation): P f =MPC = 0.5x5.77= 2.888 Therefore the optimal tax is TAX=Pc- P f =24.22-2.888=21.33 c) b) Without Tax Tax CS (30-10)x20/2=200 (30-24.22)x5.77/2=16.67 PS (10-0)x20/2=100 (2.88-0) x5.77/2=8.37 CE Class Class GTR - (21.333)x5.77=123.25 DWL (74-10)x(20-5.77)/2=455.36 0 6