A: Suppose you have a homothetic production technology and you face output price p and input prices (w,r).

(a) On a graph with labor „“ on the horizontal and capital k on the vertical axis, draw an isoquant and label a point on that isoquant as ().

(b) Suppose that the point in your graph represents a profit maximizing production plan. What has to be true at this point?

(c) In your graph, illustrate the slice along which the firm must operate in the short run.

(d) Suppose that the production technology has decreasing returns to scale throughout. If p falls, can you illustrate all the possible points in your graph where the new profit maximizing production plan will lie in the long run? What about the short run?

(e) What condition that is satisfied in the long run will typically not be satisfied in the short run?

(f) What qualification would you have to make to your answer in (d) if the production process had initially increasing but eventually decreasing returns to scale?

B: Consider the Cobb-Douglas production function x = f („“,k) = A„“^αk^β.

(a) For input prices (w,r) and output price p, calculate the long run input demand and output supply functions assuming 0 < α,β ‰¤ 1 and α + β < 1.

(b) How would your answer change if a + β ‰¥ 1?

(d) What has to be true about a and β for these short run functions to be correct?

(c) Suppose that capital is fixed at in the short run. Calculate the short run input demand and output supply functions.

(e) Suppose = (w,r,p) (where k(w,r,p) is the long run capital demand function you calculated in part (a).) What is your optimal short run labor demand and output supply in that case?

(f) How do your answers compare to the long run labor demand function „“(w,r,p) and the long run supply function x(w,r,p) you calculated in part (a)? Can you make intuitive sense of this?

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