Answer to Question #313042 in Microeconomics for Kathy

Question

) A firm has the production function: , and sells its output in two separate markets with demand functions:

;

(i) Find the profit-maximizing output and sales in each market [8 marks]

(ii) Use the Hessian matrix to check if the second-order conditions for a maximum are met.

Answer 1

1) Monopolist market

The monopolist determines its profit-maximizing level of output by choosing the quantity. The monopolist decides what price to charge and identifies its profit. A monopolist isn't the price taker since it decides on the quantity it produces. Its total revenue is relatively low at low quantities of output since there are not many sales. Total revenue is also relatively low at very high quantities of output because very high quantities will sell only at low prices. The monopolist will select the profit-maximizing level of output where MR=MC then prices are charged as determined by the market demand curve.

2) Perfect competitive markets have a major role in determining the quantity to produce. It accepts the price for its output as determined by the product's market demand and supply since it can not change the price. However, it can choose to sell any quantity of output at the same price, thus the market prevalence for the product determines the firm's total revenue, total costs, and level of profits.

ii) Profit maximization arises with regards to an input when the value of the marginal product is equal to the input cost. Hessian is the rate of change of the function. The second-order condition is met since the second characteristic of a maximum is that the second derivative is negative.