2.7 Suppose a firm’s total revenues depend on the amount produced (q) according to the function TR
70q  q 2

.

Total costs also depend on q:

TC
q 2  30q  100

a. What level of output should the firm produce in order to maximize profits (TR TC)?

What will profits be?

b. Show that the second-order conditions for a maximum are satisfied at the output level found in part (a).

c. Does the solution calculated here obey the “marginal revenue equals marginal cost”

rule? Explain.