Answer to Question #207261 in Microeconomics for bin

Question

5. A company in a purely competitive market has a short run total cost function given by

TC = 50 + 4Q + 1.5 Q². The unit price of the company’s product is Br. 13. A economist working on the efficiency of the company suggested that it has better shut down the business. Do you agree? Explain.

Answer 1

In the perfectly competitive market structure there exists a large number of buyers and sellers of the good in the market and in this market structure every firm produces identical goods and services. Each firm in this market structure produces only a small portion of the total market output and therefore any single firm production decision is not able to affect the market price of the product and as a result, every firm in this market structure act as a price-taking firm.

In the perfectly competitive market structure, there does not exist any kind of entry and exit barriers. The firms in this market structure can earn positive or negative economic profit in the short run but in the long run, every firm in this market structure earns only zero economic profit.

A firm in a perfectly competitive market structure maximizes its profit in the short run by producing an output level where the market price of the product becomes equal to the marginal cost of the good. The firms in the perfectly competitive market structure shut down their production when the market price of the product they are producing becomes less than the average variable cost of producing the output level. When the market price of the product becomes less than the average variable cost of production then the firm is not able to cover even its per-unit cost of production and the firm is going to generate losses by producing every additional unit of output in addition to the loss of the fixed cost of the firm.

The total cost of the firm is given as follows

$TC=50+4Q+1.5Q^2$

The marginal cost refers to the extra cost a firm is required to incur when it produces one more unit of output and the marginal cost of the firm in the question is calculated as follows

$marginal \space cost=\frac{\delta TC}{\delta Q}$

"marginal\\space cost=4+3Q........."1""

The equation "1" above shows the marginal cost of the firm.

As the unit price of the firm's product is Br.13, therefore, the profit-maximizing output level of the firm is calculated by equating the market price of the product with the marginal cost of the firm and it is calculated as follows

$marginal\space cost=market\space price\\4+3Q=13\\Q=3$

The profit-maximizing output level of the firm is equal to 3.

The equation below shows the total variable cost of the firm

$Total \space variable\space cost=4Q+1.5Q^2$

The average variable cost of the firm is calculated as follows

$Average\space variable\space cost=\frac{4Q+1.5Q^2}{Q}$

$Average\space variable\space cost=4+1.5Q$

The average variable cost of the firm when the firm produces 3 units of the firm is calculated as follows

$Average\space variable\space cost=4+1.5Q\\Average\space variable\space cost=4+1.5(3)\\Average\space variable\space cost=9.5$

As the market price of the product produced by the firm is more than the average variable cost of production, therefore, the firm is not going to shut down its operation or business.