Question 1

Suppose that the production function for widgets is given by Q(K, L) = KL 0.8K2 0.2L2,

where Q is the annually produced quantity of widgets, K is the annually used capital, and L is the annually employed quantity of labor. (a) Suppose that K = 10. Draw the total and average product of labor curves. Which is the level of labor that maximizes the average product of labor? How many widgets are produced at that point?

(b) Again assume that K = 10. Draw the marginal product of labor curve. For which level of labor do we obtain PML = 0? (c) Suppose now that K = 20. How do the answers to items (a) and (b) change? (d) More generally, if the amount of inputs double, does the quantity of produced widgets change more than, less than, or proportionally to the change of inputs?

Question 2

Suppose the production function for cakes is Q = LK where Q is the quantity of cakes produced per year, L is the quantity of labor (man-hours) and K is the quantity of capital (machine-hours). 1. Sketch the isoquant corresponding to a quantity of Q = 100?

2. What is the general equation for the isoquant corresponding to any level of output Q?

For questions 3 and 4, select your answer and motivate it with a short comment.

Question 3

If the marginal rate of technical substitution for a firm doesn't vary along its isoquant curve, being always equal to 1, then its inputs are perfect substitutes.

Question 4

When labor is the only input to the production function, it must be that when the marginal product of labor is greater than the average product of labor, the average product of labor is increasing (and vice-versa).