A competitive firm's cost of production is C(Q) = 16Q - Q^2 + 4Q^3.
(a) Calculate and draw the firm's average and marginal cost functions. The firm's problem is to choose the quantity that maximizes profit, given an exogenous market price P.
(b) Does this problem satisfy the global second order condition?
For parts (c) and (d), assume that the market price is P=26.
(c) Calculate the quantities that satisfy the firm's first-order condition. Which of these quantities
satisfies the local SOC?
(d) Calculate the firm's profit-maximizing quantity. Justify your answer carefully. Calculate the
firm's highest attainable profit.
(e) Carefully draw the firm's supply curve. What is the lowest price at which the firm is willing to
produce? You should show the exact coordinates of the supply curve at that price and the exact
coordinates of the supply curve at the points where P=10 and P=26.
(f) In what circumstances should the firm choose Q=1/10?
(g) Calculate the firm's inverse supply function, for the range of quantities where the firm has
A competitive firm's cost of production is C(Q) = 16Q - Q^2 + 4Q^3.
(a) Calculate and draw the firm's average and marginal cost functions. The firm's problem is to choose the quantity that maximizes profit, given an exogenous market price P.
(b) Does this problem satisfy the global second order condition?
For parts (c) and (d), assume that the market price is P=26.
(c) Calculate the quantities that satisfy the firm's first-order condition. Which of these quantities
satisfies the local SOC?
(d) Calculate the firm's profit-maximizing quantity. Justify your answer carefully. Calculate the
firm's highest attainable profit.
(e) Carefully draw the firm's supply curve. What is the lowest price at which the firm is willing to
produce? You should show the exact coordinates of the supply curve at that price and the exact
coordinates of the supply curve at the points where P=10 and P=26.
(f) In what circumstances should the firm choose Q=1/10?
(g) Calculate the firm's inverse supply function, for the range of quantities where the firm has
