A monopolist faces an inverse demand function and a total cost function given by, P(Q) = AQa,A>0 and 0 0 (a) Find the own-price elasticity

A monopolist faces an inverse demand function and a total cost function given by,

P(Q) = AQ"a,A>0 and 0

C(Q) = cQ2,c>0

(a) Find the own-price elasticity of the demand function. What do you observe?

(b) Find the profit-maximizing level of output Q!. Confirm that the second-order condition

for a maximum is satisfied.

(c) Show algebraically (simply the expressions) how an increase in (i) parameter c and (ii) parameter A, aects the profit-maximizing level of output Q!. Do you expect these results?

(d) Now suppose, that the total cost function is C(Q) = c1Q + c2Q2 + c3, where c1, c2, c3 > 0. Find the level of output QC that minimizes average total cost. Confirm that the second-order condition for a minimum is satisfied.