Final 1 - Mortimer PART II MULTIPART QUESTIONS(a total of...

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Mortimer 5 PART II: MULTIPART QUESTIONS (a total of 140 pts) 1. COST MINIMIZATION (32 pts) Consider a firm that has production function q = 50(KL) 1/2 . The price of labor w is $5 per unit and the price of capital r is $20 per unit. a. minimizing amount of labor for a given q? (4 pts) q=50(4L) 1/2 = 50(2)L 1/2 = 100 L 1/2 . L=q 2 /10,000 b. -run total cost curve? (4 pts) STC = wL+rK = 5 (q 2 /10,000) + 20(4) = (1/2,000)q 2 + 80 . c. Now consider the long- the cost minimizing amount of labor for a given q? What is the cost minimizing amount of capital for a given q? (Hint: MP L =25(K/L) 1/2 and MP K =25(L/K) 1/2 ) (8 pts) The tangency condition is MP L /MP K =w/r or K/L=5/20=1/4. K=(1/4)L or L=4K. Thus, the production function can be expressed as q=50(4K 2 ) 1/2 =50(2)K = 100K. K = (1/100)q. Similarly, q=50(KL) 1/2 =50((1/4)L 2 ) 1/2 = 50(1/2)L=25L. L=(1/25)q.
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Mortimer 6 d. -run total cost curve? (4 pts) LTC = wL+rK = 5 (1/25)q+ 20(1/100)q = (1/5)q + (1/5)q = (2/5)q =0.4q . e. Does this cost function exhibit diseconomies of scale or economies of scale? (4 pts). Neither. The long-run average cost curve (and the long-run marginal cost curve) is flat at 0.4. The LAC curve is neither increasing nor decreasing. Also, the LTC curve shows that C(2q 0 )=2C(q 0 ) when the output doubles, then the cost doubles. f. Suppose the firm wants to produce q=1,000 units. Using the results you found above, fill in the following table: Quantity of K Quantity of L Total Cost ($) Short-run 4 100 580 Long-run 10 40 400
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Mortimer 7 Compare the short-run and long-run costs and explain why this result is surprising or not surprising. Draw a graph of isoquants and isocost lines to support your argument. (8 pts) Short-run: L=1,000,000/10,000=100. STC = (1/2,000)q 2 + 80 = (1/2,000)(1,000,000)+80=500+80=580. Long-run: L=(1/25)1,000=40. K=(1/100)(1,000)=10. LTC=0.4(1,000)=400. The fact that the short-run cost is higher than the long-run cost for producing 1,000 units is not surprising. In the short-run, this firm is stuck with the level of capital that is not the most efficient for producing 1,000 units of output. See the graph below. GRAPH
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Mortimer 8 2. THE AGRECULTURAL SECTOR (22 pts) Price support programs are common in the agricultural sector. We studied two types of programs in this class. a. Briefly describe what acreage limitation programs and government purchase programs are and how they work. (4 pts) Both programs are designed to support a price higher than the free-market price for farmers. In the acreage limitation program, the government gives farmers an incentive to hold production below the free-market level by paying farms not to plant. The limitation on output elevates the price for farmers. In the government purchase program, the government supports a price above the free-
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Final 1 - Mortimer PART II MULTIPART QUESTIONS(a total of...

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