Long Run We make a lot of similar assumptions with the production function that

Question

Long Run We make a lot of similar assumptions with the production function that we same and a production isoquant is similar to an indifference curve in the made with the utility function. They look the role it plays in the model. 9. Amalgamated SteelWorks has the following production function: The wage rate a. What is the firm's short run total cost function (in terms o is $60 and the rental rate on capital is $200. In the short run, the firm has 0.25-KL rented 400 units of K b. What are the firm's average total cost function (ATC), average variable cost function (C function (AFC), and marginal cost function (MC)? f Q)? . average variable cost function (AVC), average fixed cost 10. Suppose you are hired capital. Assume the price of labor i $100 and the price of Table 1. as a new manager of a firm producing 20 units of output with 10 units of labor and 5 units of capital is $100 Along the isoquant, the MRTSx is as noted in Table 1 Between MRTS a and b500 b and c c and d 600 750 d and e 1.00 Q-20 7 8 9 1011 L. Given the above graph and table: a. In detail, explain the optimizing decisions for minimize cost (Hint: think about the MC and MB of changing L) b. To minimize cost, you should use integer units of capital) c. How much total cost will you be able to save by changing the input combination? -laborers and units of capital. (It is possible to hire non- 11. A firm discovers that when it uses K units of capital and L units of labor it is able to produce K L units of output, Q. a. Draw the isoquants for Q 2, 3, 4 b. Suppose the firm produces 10 units of output with 20 units of K and 5 units of L. What is the MPL, MPK and MRTS.u c. On the basis of your answer in "b." is the equation MRTS MPL/MPK about right?

Explanation / Answer

Ans 9)

Q=sqrt(0.25KL)=sqrt(0.25(400)L)=sqrt(100L)=10sqrt(L)

w=$60, r=$200 and K=$400

C=wL+rK

C=60(L)+200(400)=60L+80000

C=60(Q^2/100)+80000

C=0.6Q^2+80000

ATC=C/Q=0.6Q+(80000/Q)

AVC=0.6

FC=80000

AFC=80000/Q

MC=dC/dQ=1.2Q

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