Note: This practice exam does not cover everything, but it does cover a lot of the basic  concepts. For the actual exam I’ll put more care into the difficulty level and will attempt to make it so that most students can finish on time.

1.   Consider the production function f (L, K ) = L2  + L3 K 3  . For parts (a) – (c) assume the level of capital is fixed at K .

a.   What is the marginal product of labor?

b.   Is the marginal product of labor diminishing?

c.   What is the average product of labor?

d.   What is the MRTS?

e.   Is the MRTS diminishing?

f.    Doesf(L, K) have constant, increasing or decreasing returns to scale?

g.   Isf(L, K) homogeneous? If so, to what degree. If not, briefly explain why not.

2.   Consider a generic Cobb-Douglas production function f (L, K ) = LaK  with α    and β > 0. Is it possible thatf(L, K) has an increasing marginal product of labor     and decreasing returns to scale? If so, state values of α and β that will do so. If it’s not possible, demonstrate why not.

3.   For each graph given below is it possible that the solid curve is the short-run     average cost curve and the dashed curve is the short-run marginal cost curve for the same production function. Briefly explain why or why not.

(b)

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4.   Consider the production function f (L, K ) = L3 K 3   where K is fixed at 8.