Does your answer to part b violate the rule describing the relationship between average and marginal values? Explain.

Problem Set #3
1. Suppose that the hourly output of chili at a barbecue  is characterized by q = 20√KL
where K is the number of large pots used each hour and L is the number of worker hours employed.
a. Graph the q = 2000 pounds per hour isoquant.
b. The point K = 100, L = 100 is one point on the q = 2000 isoquant. What value of K
corresponds to L = 101 on that isoquant? What is the approximate value for the MRTS at K = 100, L = 100?
c. The point K = 25, L = 400 also lies on the q = 2000 isoquant. If L = 401, what must K be for this input combination to lie on the q = 2000 isoquant? What is the approximate value of the
MRTS at K = 25, L = 400?
d. For this production function, the MRTS is
MRTS = K/L.
Compare the results from applying this formula to those you calculated in part b and part c. To convince yourself further, perform a similar calculation for the point K = 200, L = 50.
e. If technical progress shifted the production function to
q = 40√KL all of the input combinations identified earlier can now produce q = 4000 pounds per hour.
Would the various values calculated for the MRTS be changed as a result of this technical progress, assuming now that the MRTS is measured along the q = 4000 isoquant?
2. Consider the production function f (L, K) = L + K. Suppose K is fixed at 2. For this function, the marginal product of labor, MP(L), is 1. (a) Find the algebraic expression for the average product of labor AP(L). (b) Graph the total product of labor function TP(L), the average product of labor AP(L), and the marginal product of labor MP(L). Does your answer to part b violate the rule describing the relationship between average and marginal values? Explain.
3. For each of the following production functions, determine if the technology exhibits increasing, decreasing, or constant returns to scale.
a. f (L, K) = 2L + K
b. f (L, K) = √L + √K
c. f (L, K) = L2 + K
d. f (L, K) = √LK + L + K