School Evans of Public Affairs, Mark Long PBAF 516: Microeconomic Policy Analysis
Problem Set 3 -- Answers Costs and Producer Behavior 1. In 1998 the price of energy increased dramatically. Before the price surge, Kaiser Aluminum (in Spokane) had purchased the rights to buy electricity at a fixed rate. After the price surge, Kaiser still owned these rights so they were able to buy their electricity at a much lower price than the rest of the city. (Note: these rights can be bought and sold at any time) a. What happened to Kaisers cost of producing aluminum when the price of electricity went up? (Remember, they didnt have to pay the higher price for electricity.) The cost of producing aluminum went up because the opportunity cost of using the electricity (rather than selling it) increased. b. Imagine there was another aluminum plant, Alcoa, that didnt have the rights to buy electricity at a low price. After the price of electricity went up how did production costs for Alcoa compare to production costs for Kaiser? We would expect it to be equally costly for Alcoa and Kaiser to produce aluminum: By producing aluminum, Kaiser is still missing out on the money it could earn if it were to sell the electricity instead. c. As it turns out, when the price of electricity was very high Kaiser stopped producing aluminum. Does this surprise you? Why or why not? That is not surprising since aluminum is more costly to produce with high electricity prices, even if it is only the opportunity cost of selling the aluminum. It is not surprising that Kaiser decided to sell the electricity rather than use it to produce aluminum.
2.
A firm has two plants, each with different costs of production. Plant 1: Cost = 100 + 9Q + Q2 (MC=9+2Q) Plant 2: Cost = Q + 5Q2 (MC=1+10Q) The firm wants to produce 200 units of the good at the lowest cost. How much should it produce at each plant? First, note that we want total production to be equal to 200: Q1 + Q2 = 200 Q2 = 200 - Q1 If the MC of one plant was higher than the other plant, the firm could lower its total costs by shifting production towards the plant with the lower marginal cost. Thus, the firm will produce where marginal costs are equal across plants. MC1 = MC2 9+2Q1 = 1+ 10Q2 9+2Q1 = 1+ 10(200 - Q1) 9+2Q1 = 1+ 2000 -10 Q1 12Q1 = 2001 - 9 Q1 = 1992 / 12 Q1 = 166 Q2 = 34
Evans School of Public Affairs, Mark Long PBAF 516: Microeconomic Policy Analysis
3.
Fill in the following table assuming computers are a fixed input that costs $30 per unit to rent and labor is a variable input that costs $12 per unit:
Labor 0 1 2 3 4 5 6 Q 0 200 500 600 650 680 700 APL -200 250 200 162.5 136 116.7 MPL -200 300 100 50 30 20 TFC 300 300 300 300 300 300 300 TVC 0 12 24 36 48 60 72 TC 300 312 324 336 348 360 372 MC -0.060 0.040 0.120 0.240 0.400 0.600 AFC -1.500 0.600 0.500 0.462 0.441 0.429 AVC -0.060 0.048 0.060 0.074 0.088 0.103 ATC -1.560 0.648 0.560 0.535 0.529 0.531
Computers 10 10 10 10 10 10 10
a. Graph the APL and MPL curves with Units of Labor on the horizontal axis and Units of Output per Worker on the vertical axis.
350
300
Units of Output per Worker
250
200 APL -MPL -150
100
50
0 1 2 3 4 5 6 Units of Labor
b. Graph the AVC and MC curves with Output (Q) on the horizontal axis and Dollars per Unit on the vertical axis.
0.700
0.600
0.500 Dollars per Unit
0.400 MC AVC 0.300
0.200
0.100
0.000 0 100 200 300 400 Output (Q) 500 600 700 800
Evans School of Public Affairs, Mark Long PBAF 516: Microeconomic Policy Analysis
c. What is relationship between APL and AVC? What is relationship between MPL and MC? AVC MC 4. = w / APL = w / MPL
Sketch on one diagram the short run AVC, ATC, and MC curves for a firm with a fixed capital stock (assume a typical production function as shown in the bottom panel of Figure 8-2 on page 205).
$ MC ATC AVC
Q
a. Suppose the town in which this firm is located passed a law requiring every business, no matter what its size, purchase to a $500 business permit. Which of the curves would be affected by the new law? ATC would shift up by $500; AVC and MC would be unaffected. b. Repeat part (a) assuming the wage rate for labor rose instead of a new law. Now, all three curves would shift up because the cost of a variable input has risen. c. Repeat again assuming instead that a tax on all capital equipment equal to 5% of its value is enacted. In the long-run this might shift the firm toward using more labor and less capital (depending on their flexibility). However, since capital generally cant be changed in the short-run, the firms short-run supply curve and AVC and MC curves would be unaffected. The ATC curve, however, would shift up.
5.
Suppose w=$6, r=$10, TC=$1200. Suppose the MRTS = 3K/4L. a. Graph the Isocost line. 6L + 10K = 1200
Evans School of Public Affairs, Mark Long PBAF 516: Microeconomic Policy Analysis
160 140 120 100 Capital
Expansion Path
80 60 40 20 0 0 50 100 150 Labor 200 250 300
K K (with $1500)
b)
Find and graph the optimal choice of K and L.
Optimal choice: 3K/4L = 6/10 30K = 24L K=0.8L Plug into isocost: 6L + 10(0.8L) = 1200 14L = 1200 L = 1200/14 = 85.7 K = 0.8* 85.7 = 68.6 c) On the same graph, redo a) and b) for TC=$1500. 14L = 1500 L = 1500/14 = 107.1 K = 0.8* 107.1 = 85.7 d) e) Add the expansion path to your graph. With TC=$1200, compute the optimal choice of K and L if r rises to $15
Optimal choice: 3K/4L = 6/15 45K = 24L K=(24/45)L Plug into isocost: 6L + 15((24/45)L) = 1200 14L = 1200 L = 1200/14 = 85.7 K = (24/45)* 85.7 = 45.7
Evans School of Public Affairs, Mark Long PBAF 516: Microeconomic Policy Analysis
Browning and Zupan Problems: 8.8 This firm could produce more output at the same total cost if it shifted to point c. The firm has hired too much labor and not enough capital. Thus, MPK/r > MPL/w. Alternatively, we can see this by noting that the slope of the isoquant (MRTS = MPL/MPK) is less than the slope of the isocost line (w/r). Thus: MPL / MPK < w/r MPL / w < MPK / r 8.14 The minimum efficient scale of operations is much larger for automobiles than for textiles. Given the position of the demand curve for automobiles, there may be simply no room for profitable entry by a fourth automobile firm. If a fourth did enter, all four firms would earn negative profits until one of them gives up and exits...