11.8

a. Explain why development of a profit-maximizing model here requires 0 < y < 1.

b. Suppposing y=0.5, calculate the firm's total cost function and profit function.

c. If v 1000, profits? 500, and P = 600, how many students will Acme serve and what are its

d. If the price students are willing to pay rises to P=900, how much will profits change?

e. Graph Acme's supply curve for student slots, and show that the increase in profits calculated in part

(d) can be plotted on that graph. How would you expect an increase in output price, P, to affect the demand for capital and labor inputs?

a. Explain graphically why, if neither input is inferior, it seems clear that a rise in P must not reduce the demand for either factor.

b. Show that the graphical presumption from part

(a) is demonstrated by the input demand functions that can be derived in the Cobb-Douglas case.

c. Use the profit function to show how the presence of inferior inputs would lead to ambiguity in the effect of P on input demand.