Use the following as a reference. Do NOT answer though. Use the above picture to

Question

Use the following as a reference. Do NOT answer though.

Use the above picture to answer the questions below. The question below is the ones I need answered. NOT the ones above. Also - no work needed. Thank you!

Part A:

Question 1 part (b) (i), what is the firm's short-run total cost function?

Part B:

Question 1 part (b) (ii), what is the firm's short-run marginal cost function?

Part C:

Question 1 part (b) (ii), what is the firm's short-run average cost function?

Part D:

In Part II (Producer Theory) Question 1 part (c) (ii), what are the firm's conditional demands for capital and for labor?

Part E:

Question 1 part (c) (iii), what is the firm's long-run total cost function?

Part F:

Question 1 part (c) (iv), what is the firm's long-run marginal cost function?

A.

B.

C.

D.

Question 1 (Technology and cost) A firm has a production function Input prices are wK$3/hr and wL-$6/hr. a) Graph the firm's isoquant corresponding to its output of y = 100, what is the technical rate of substitution (TRS) at the point (L, K)-(5.4)? Is L-5, K = 4, a cost-minimizing choice of inputs to produce y- 100? Answer this question without yet solving for the cost minimizing bundle. Explain your answer using in your argument the TRS b) The short run problem The firm rents its capital on a weekly basis from Capital-R-Us®, but signs annual contracts with the labor union that represents its employees. These contracts both specify the wage that the firm pays (wL- $6/hr) and preclude the firm from firing any current employees (or hiring any new employees) until the next round of contract negotiations. Thus, in this problem in the short run labor is fixed. Denote the fixed quantity of labor by L (i) As a function of L and y what is the firm's short-run total cost function? (ii) What is its short-run marginal cost function? What is its short-run average cost function? c) Now consider the firm's long-run problem. Use (i) In this problem, what is the time-frame in which the firm makes long-run decisions? some level of output y cost LRC(v) cost function? (ii) Calculate the firm's conditional demands for capital and for labor, given that it produces (iii) Use your answer for part (ii) to derive the firm's long-run total cost function, long run (iv) What is the firm's long-run marginal cost function? What is the firm's long-run average (vi) What amount of inputs would the firm choose in the long run if it wanted to produce 50 units of output? d) Comparing short run and long run (i) What is the firm's long-run average cost when y - 50? What is the firm's short-run average cost when y50 and L is fixed at the level of input you found in part c(vi) [i.e. the labor that is optimal in the long run for producing y-50)? How are they related? Why? ii) Suppose the firm chooses to increase output to 75 units, but is stuck using the same amount of labor that you found in part c(vi) [i.e. the labor that is optimal in the long run for producing y-501. What would its short-run average cost of producing y = 75 be? What is its long-run average cost of producing y -75 be? Which is greater and why?

Explanation / Answer

Part-A

Consider the given problem, here on the basis of the given information the SR cost function is given by “C(Y) = 6L + (3*Y/L^2)”, so “C” be the right option.

Part-B.

The MC is given by “MC = (3/L^2), so the right option is “A”.

Part-C.

The AC is given by “AC =( 6L/Y) + (3/L^2)”, so the correct option is “C”.

Part-D.

The conditional demand for labour and capital is given by “L(Y) = K(Y) = Y^(1/3)”, so the correct option is “A”.

Part-E.

The LR cost function is given by “C(Y) = 9*Y^(1/3)”, so the correct option is “B”.

Part-F.

The LR MC is given by “MC = 3*y^(-2/3)”, so the correct option is, “C”.

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