Answer to Question #127010 in Macroeconomics for Humphrey

Question

A firm in a perfectly competitive market in the short run, faces a price of $20 per unit of its output. It is producing 200 units per week and employing 40 workers. The last unit of output takes 32 percent of one worker's week to produce. The wage rate is $50 per week and fixed costs (per week) are $1000.

i) Calculate MC, AC and profit at the present level of output.

ii) Is the firm maximizing its profit?

iii) Suppose that the price falls to $16 and fixed costs rise to $1,500, should the firm close down?

Answer 1

i)

Answers

$MC = \$16$

$AC = \$15 \space per \space unit$

$\pi = \$1,000 \space per \space week$

Workings

MC is short for marginal cost. Marginal cost is the additional cost arising from increasing output by one more unit. It is the cost of an additional output.

The last unit being referred to in the question is the marginal unit whose cost is the marginal cost.

Therefore,

MC = 32% of one worker's weekly wage rate

= $50 × 32%

= $50 × 0.32

= $16

Hence, MC = $16

AC is short for average cost (Average Total Cost), and it is also written ATC.

$ATC = \dfrac {TC} {Q}$

Where, TC represents Total Costs and Q represents output level.

$TC = Fixed \space production \space Costs + Variable \space production \space costs$

$TC = FC + VC$

FC = $1,000 per week

VC = 40 workers × $50 weekly wage rate

= $2,000 per week.

TC = $1,000 + $2,000

= $3,000 per week.

Q = 200 units per week.

Therefore, $AC = \dfrac {\$3,000}{200units}$

$AC = \$15 \space per \space unit$

Profit = Total Revenue - Total Cost

π = TR - TC

TR = price per unit × number of units produced

= P × Q

= $20 × 200 units

= $4,000 per week.

Therefore,

Profit = $4,000 - $3,000

π = $1,000 per week.

ii)

Answer

The firm is not maximizing profit. Profit is undermined.

Explanation

Firms maximize profit if they produce at the point where,

MR = MC

The firm in question is in perfect competition. All firms in perfect completion face a horizontal demand curve and a linear total revenue curve. Because TR is linear, MR is constant and is equal to AR.

Thus, under perfectly competitive conditions,

MR = AR = Price

As a result, since P = $20, it implies that MR = $20.

MC was calculated and is $16.

Now, comparing MR and MC it is found that $20 > $16

Thus, MR > MC

This condition violets the profit maximization rule MR = MC, and hence the firm is not maximizing profits.

The firm is foregoing profits by underproducing. If output is increased, profit will increase as well. Any condition where MR > MC represents underproduction and foregone profits.

iii)

Answer

No. The firm should not shut down; it is producing above the shut down point.

explanation

In the short run, the shutdown decision is influenced by variable costs. Fixed Costs do not influence shutdown decisions; they are not affected by output level and unavoidable in the short run.

The short run shut down point is P = AVC, where AVC is the average variable costs. As long as $P \geq AVC$ even if $P < ATC$ , firms should continue operating. If $P < AVC$ then the firm should close down for it could not cover both fixed costs and some variable costs.

In this case,

P = AR = $16

$AVC = \dfrac {VC} {Q}$

$AVC = \dfrac {\$2,000} {200 \space units}$

= $10 per unit

Since $16 > $10

AR > AVC,

Hence the firm is producing above its shutdown point. So, the firm should continue operating. By shutting down it will be worse off for it will suffer a total loss equal to the whole fixed costs part of which it is able to meet when in operation.