A firm has the exogenous cost function C(Q) = 354Q-30Q^2 + Q^3.
(a) Compute the marginal cost function.
(b) Use calculus to find the value of Q at which marginal cost is minimized.
(c) Compute the average cost function.
(d) Use calculus to find the value of Q at which average cost is minimized.
(e) Does this cost function satisfy the three assumptions made in class concerning the cost function?
For the remaining parts, assume that the demand for the firm’s product is D(P) = 25- √P
(f) Calculate the inverse demand function.
(g) Calculate the slope of the demand curve at the point where P=100.
(h) Calculate the elasticity of demand at the point where P=100.
(i) If the firm produces Q=16, then calculate its average cost and profit.
(j) If the firm sets price P=144, then calculate its average cost and profit.