EconS 330, Fall 2013 Homework #1: Due September 13th ANSWER KEY

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1 EconS 330, Fall 013 Homework #1: Due September 13th ANSWER KEY Instructor: Ana Espinola, O ce hours: Tuesdays pm, or by appointment 1 Question #1-15 Points Serious problems have arisen as a result of timber harvesting, grazing, oil exploration, mining, and reservoir operations in the Rockies Mountains. Logging and oil exploration have been responsible for accelerated slope erosion, both from the operations themselves and from the access roads built to reach them. Erosion has stripped away the often thin soil cover and caused serious silting of streams. Trace quantities of harmful metals have been released into streams and groundwater from mining operations, particularly from the leaching of mill tailings. Reservoir operations have disrupted sheries by altering the temperature and ow patterns of streams and by disrupting riparian (streamside) vegetation communities. Wildlife habitat has been lost through the development of lands for agriculture and livestock grazing. Thus, the degree to which land in the Rocky Mountains remains natural generally declines as elevation decreases. a. Discuss this problem using the circular economy approach and identify which variables are negatively a ecting natural resources and consumers utility. The Rockies Mountains is a natural resource that contains renewable (RR) and non-renewable resources (NR). Those resources are being used in the production process of several goods that are consumed in our economy. One of the main problems described in question #1 is related to the harvesting rate. The rate at which the RR and NR are harvested exceeds the natural regenerative capacity, h > g. This negatively a ects the wildlife habitat, the production process, consumers utility (negative amenities) and, nally, the entire economy. Question # - 15 Points Assume that a regulatory authority is interested in the preservation of the Rockies Mountains. The marginal cost (MC) of preserving it can be represented by the following function: MC = 1q, where q denotes the 1 quantity preserved in miles. The demand function is P = 5 q, where P denotes price. a. Draw a graph representing these two functions. 1

2 Price 5 MC 4 D 50 Quantity preserved (miles) Figure 1 b. What is the e cient number of miles preserved and the net bene t? [Static E ciency] MC = Demand 1q = 5 1 q = 4q = 50 q q = The e cient number of miles is and the price is 4 [substitute q = into the demand, P = 5 1 = 4] In addition, the net bene t is represented by the shaded area in gure 1. That is, NB = 5. Note that the net bene t can also be represented by the di erence between the total willingness to pay and the total cost, NB = T W P T C. Using the graph, we know that T W P is represented by the area below the demand curve until q =, (5 4) T W P =. + 4 = 49 The TC is represented by the area below the MC curve until q =, T C = 4 = 4. Hence, NB = T W P T C NB = 49 4 = 5 c. What is the net bene t of preserving 5 miles? Is it e cient? The net bene t of preserving q = 5 is obtained using NB = T W P T C. In order to obtain the T W P we need to identify the price, using the demand function we know that when q = 5, p = :5. Hence, T W P = (5 :5)5 + :5 5 = 118:75. The marginal cost of preserving 5 miles is MC = 60, hence the T C = 605 = 150. Therefore, T W P = 118: = 31:5 is negative. We can conclude that preserving 5 miles is not e cient since the net bene ts are negative. 3 Question #3-15 Points Three mutually exclusive projects are being considered for a remote river valley: Project R, a recreational facility, has estimated bene ts of $10 million and costs of $8 million; project F, a forest preserve with some recreational facilities, has estimated bene ts of $13 million and costs of $10 million; project W, a wilderness area with restricted public access, has estimated bene ts of $5 million and costs of $1 million. In addition, a road could be built for a cost of 4 million that would increase the bene ts of project R by $8 million, increase the bene ts of project F by $5 million, and reduce the be ts of project W by 1 million. Even in the absence of any of the other projects, the road has estimated bene ts of $ million.

3 a. Calculate the net bene ts for each possible alternative to the status quo. Note that there are seven possible alternatives to the status quo: R, F, and W with and without the road, and the road alone. Without With R F W R F W Road Benefit Additional Benefit Costs Road cost Net Benefits b. If only one of the seven alternatives can be selected, which should be selected according the Cost-Bene t Analysis decision rule? Alternative R, since it has the highest net bene t. c. Calculate the net present value of alternative R with the road. Assume a period of time equal to 4 years (include year 0, part a) and an interest rate of 5%. Bene ts decrease by $1 million each year and costs are constant after year 0 and equal to $ million. The NPV is t=0 t=1 t= t=3 t=4 Benefit Additional Benefit Costs 8 Road cost Net Benefits Question #4-5 Points Wheat is an important agricultural commodity, and the wheat market has been studied extensively by economists. From statistical studies, we know that for 1981 the supply curve for wheat was approximately Q S = P, where price P is measured in nominal dollars per bushel and quantities (Q) in millions of bushels per year. These studies also indicate that in 1981, the demand curve for wheat was Q D = P. a. Draw a graph showing the demand curve and the marginal cost curve. Price (per bushel) Q D Quantity (million bushels) b. How much would be supplied in a static e cient allocation? (Illustrate the quantity on your graph) 3

4 Price (per bushel) Q S 3.46 Q D Quantity (million bushels) Q D = Q S P = P 506P = 1750 P = $3:46 To nd the market-clearing quantity, substitute this price of $3.46 into either the supply curve equation or the demand curve equation. Substituting into the supply curve equation, we get Q S = :46 = 630 million bushels c. What would be the magnitude of the net bene ts? (Illustrate the net bene ts on your graph) the NB = (13:35 ( 7:5))630 = 7; 417:75 5 Question #5-30 Points Suppose the inverse demand curve for the chemical (which is also a marginal bene t curve) is P d = 1 0:5Q, where Q is the quantity consumed (in millions of tons per year) when the price consumer pay is P d (in dollars per ton). The inverse supply curve (also the marginal private cost curve) is MP C = 1 + 0:5Q, where MP C is the marginal private cost when the industry produces Q. The industry emits one unit of pollutant for each ton of chemical it produces. As long as there are fewer than 1 million units of pollutant emitted each year, the external cost is zero. But when the pollutant exceeds million units, the marginal cost is positive. The marginal external cost, M EC, is: 0 when Q 1 MEC = 1 + 0:5Q when Q > 1 where MEC is marginal external cost in dollars per unit of pollutant when Q units of pollutant are released. Also supposed the government wants to use an emissions fee of $6 per unit of emissions to induce the market to produce the economically e cient amount of chemical. a. Draw a graph showing the demand curve, the MPC, MEC and MSC. 4

5 Price 1 MSC MPC Tax $ MEC 3 Demand Q b. Construct a graph and a table comparing the equilibria with and without the emission fee. Identify in your table the CS, PS, GTR, CE and DWL. Without Tax With Tax CS PS CE GTR DWL 6.75 P = MP C 1 0:5Q = 1 + 0:5Q Q = 11 Q = 11 If Q = 11 then the price (using demand curve) is: P = 1 0:5 11 = 6:5 The social Optimal quantity is : P = MSC. Therefore, we need to identify the MSC curve: MSC = MEC + MP C MSC = [1 + 0:5Q] + [ 1 + 0:5Q] MSC = Q Therefore, P = MSC 1 0:5Q = Q Q = 8 5

6 Substituting Q = 8 into the demand function we have that P = (1 0:5 8) = 8 Finally, when the quantity produced is 8 then the MP C is (substituting 8 into MPC equation): Note that DW L(without taxes) = (4:53) = 6:75 MP C = :5 = 5 c. Discuss why the value of DWL is di erent when the government sets an emission fee. The DWL with an emission fee is zero, since all the negative externality produced by the chemical rm is internalized. 6