Question

ea, but it we need to close some apps. update now Consider a firm with a production function Q = Q(L), a total revenue function TR = TR(Q), and total cost function TC = TC(Q). (a) Suppose the firm's goal is to maximize profit. Find and interpret the first- and second-order conditions for the firm's problem. Draw a picture of the result in terms of the marginal conditions that are applied by first- and second-order conditions. (b) Suppose the firm's goal is to maximize sales (total revenue). Find and interpret the first- and second- order conditions for the firm's problem. Draw a picture of the result in terms of the marginal conditions that are applied by first- and second-order conditions. (c) Suppose the firm's goal is to maximize output. Find and interpret the first- and second-order conditions for the firm's problem. Draw a picture of the result in terms of the marginal conditions that are applied by first- and second-order conditions. (d) Based on b) and c), under what condition(s) is output maximization equivalent to revenue maximization? Explain carefully and defend your answer mathematically. Support you answer by a graph.

Answer 1

a) Profit Maximization:

Profit (Π) = TR(Q) – TC(Q)

First order condition to maximize profits is when marginal revenue (dTR/dQ) is equal to marginal cost (dTC/dQ).

Second Order Condition is d²Π/dQ² < 0

or, d/dQ(MR) < d/dQ(MC)

This implies that if price falls below Average variable cost, the firm will earn a loss.

МС О ре MR q* Q.

b) Sales Revenue maximisation: This indicates the highest possible sales volume, without making a loss. Revenue is maximised where MR = 0.

Costs & Revenue МC АТС P MR Output AR

c) Maximizing Output:

When AC = AR, output is maximized.

Cost MC AC P MR AR 0 Quantity

d) Output maximization is not equivalent to revenue maximization because average cost can never be zero. Output is maximized when AC = AR. Whereas, revenue is maximized at MR = 0

Cost MC AC P MR AR 0 Quantity

In the above graph, you can see that AC can not be zero at any point as fixed cost of a firm can never be zero. Even if a factory is closed and not producing, there will be some fixed cost such as cost of land, machinery cost etc.