Question 1

A manufacturer of soda cans has a Cobb-Douglas production function:

Y = 10KL

where Y is output, K is capital (machines) and L is labor (workers).

(a) What is the output created by K = 4 and L = 10? Draw the isoquant (IsoQ) for this level of output (put L on the x-axis).

(b) Calculate (using the standard formula) the Technical Rate of Substitution of Labor at the bundle (K = 4, L = 10). [You can use the MRS formula, but you may have to rearrange the equation to line up the unknowns properly.]

(c) The wage is w = 15 and the rent is r = 150. What is the total cost of the firm when it uses 4 machines and 10 workers?

(d) On the same diagram as part a), draw the isocost line (IsoC) containing the combination (K = 4, L = 10). Pay attention to the relative slope of isocost and isoquant at this combination. Label the intercepts of the isocost line.

Question 2

Consider the same soda can manufacturer, with the same production function as in the previous question.

(a) At the wage of w = 15 and the rent of r = 150, write down an equation relating relating K and L that comes from the tangency condition.

(b) Suppose that the firm has to make 100 soda cans. Write down an equation relating K and L that comes from the production function.

(c) Based on your previous work, solve for the cost-minimizing combination K and L .

(d) If C(Q) is the cost function for the firm, what is C(100)?

[This is the long-run cost, since we are assuming that firms can freely optimize all quantities of inputs]