Answer to Question #153839 in Microeconomics for Mar

Question

The company operates in a fully competitive market. The following numbers provides 
information on the company's production volume and costs.

Q 1; 2; 3; 4; 5; 6;

AFC 5; 2,5; 1,6; 1,25; 1; 0,83

AVC 5; 3; 2; 5; 10; 13

MC 4; 2; 4; 6; 8; 12;

Determine:
1) How many units does it take to maximize profit if the market price is 4 EUR?
2) Determine -  if the market price is 6 EUR,  company will stay in business?  and if so, how much it will produce?
3) Determine - if the market price is 8 EUR,  company will stay in business?  and if so, how much it will produce?

Answer 1

ANSWER

The first step

We should to find the numbers that provide information on the company's Average total costs (denoted by ATC). It is easy to see that $ATC=TC/Q=(VC+FC)/Q=AVC+AFC$

Hence, when Q=1 the ATC = 10,

when Q=2 the ATC = 5,5;

when Q=3 the ATC = 3,6;

when Q=4 the ATC = 6,25;

when Q=5 the ATC = 11;

when Q=6 the ATC = 13,83.

The calculations and a cost diagram are depicted in the picture below.

The second step

The cost diagram allows to see that MC is greater (upper) than ATC only when Q=3. The quantity Q=3 allows to make a positive economic profit when the market price is equal to 4 per unit (according to rule that market price should be equal to MC in a perfect market). If the market price is greater than 4 the company can not make a positive economic profit and should cover its variable costs in short run period.

Based on the explanition written in the first and the second steps we can answer to the questions (a), (b), and (c).

Answer to the question (a).

When the market price is 4 the avarage profit is equal to 0,4 EUR per unit and number of units (denoted by Q) is equal to 3 (according to the value of MC and rule for the highest profit in perfect market). Hence, the total profit is equal to the 1,2 EUR.

Answer to the question (b).

When the market price is 6 the avarage profit is equal to -0,26 EUR per unit and Q is equal to 4 (according to the value of MC and rule for the highest profit in perfect market). The total profit will not be positive (total profit is equal to -1 EUR when Q=4). However, the MC (and price) will be greater than AVC when Q=4. The difference between MC and AVC is positive. Hence, the company will stay in business and produce 4 units (not more because when Q=5 the AVC is greater than MC).

Answer to the question (c).

When the market price is 8 the avarage profit is equal to -3 EUR per unit and Q is equal to5 (according to the value of MC and rule for the highest profit in perfect market). The total profit will not be positive (total profit is equal to -15 EUR when Q=5). However, the MC (and price) will not be greater than AVC when Q=5. Hence, the company will not stay in business and can not produce more than 4 units.