Answer to Question #192489 in Microeconomics for Narendra

Question

State the decision for each case to supply positive amounts of output in a competitive market in both the short - run and the long run.

Solve it mathematically.

Answer 1

Solution:

The decision to supply positive amounts of output in a competitive market is based on profit maximization in both the short-run and long run. Profit maximization will help a firm to determine the price, input, and output levels that lead to the highest profit.

In determining how much output to supply, the firm’s goal is to maximize profits subject to the consumer's demand for the firm’s product and the firm's cost of production. The firm’s profits are the difference between its total revenues and total costs.

In the short run, a firm maximizes its profits by choosing to supply the level of output where its marginal revenue (MR) equals its marginal cost (MC). When MR exceeds MC, the firm can earn greater profits by increasing its output.

Mathematically it can be presented as follows:

First, derive TR:

TR = P x Q

Get the derivative of the TR to get MR

= $\frac{\partial TR} {\partial Q} = MR$

Derive MC from the TC.

MC = $\frac{\partial TC} {\partial Q} = MC$

Set MR = MC, to determine the profit-maximizing output, which the firm will supply to the competitive market. If MR>MC, then the firm can increase the supply of its output to the market to earn more profits.

In the long run, the profit-maximizing level of output will be at the point where MC = MR. Since the firm’s long-run average total cost (ATC) per unit equals the firm’s MR per unit, the firm will be earning zero economic profits. The firm will, therefore, make some adjustments and will seek to minimize its long-run average total cost.

Mathematically it can be depicted as follows:

First, derive TR:

TR = P $\times$ Q

Get the derivative of the TR to get MR

= $\frac{\partial TR} {\partial Q} = MR$

Derive MC from the TC.

MC = $\frac{\partial TC} {\partial Q} = MC$

Set MR = MC, to determine the profit-maximizing output, which the firm will supply to the competitive market. Since the firm’s long-run ATC = MR, the firm should produce at that point which is the minimum point of its long-run ATC, at the minimum efficient scale level of output.