Assume the market demand curve faced by a monopolist is and its short-run total cost function is (a) Derive the inverse demand curve for the monopolist.

(a) Derive the inverse demand curve for the monopolist.
(b) Using the result obtained in part (a), derive the monopolist’s total revenue curve as a function of Q. Compute the corresponding marginal revenue function.
(c) Compute the firm’s short run marginal cost curve.
(d) Using the results obtained in part (b) and part (c), derive the monopolist’s short-run profit-maximizing level of output.
(e) Determine the price charged by the profit-maximizing monopolist and the amount of profit earned.

QUESTION 2
Consider a broking firm that supplies consulting services. The corresponding demand relation and cost functions are and , respectively.

(a) Derive the first-order condition for the firms profit maximization. Determine the profit maximizing level of Q.
(b) Verify that, at the point of maximum profit that the second-order sufficient condition holds.
(c) Check that marginal revenue is equal to marginal cost at the profit-maximizing level of output determined in (b).

QUESTION 3
A firm’s production function is given by.

Find the value of L which maximizes the average product of labour. Ensure you have found the value of L that maximizes the average product.

QUESTION 4
A firm produces three products—leather, cardboard and string—denoted and respectively. The corresponding total revenue function has the form

At what combination of outputs will the marginal revenues of all three products be simultaneously equal zero?