Question

Auctio sells sprockets in a perfectly competitive market. Below are its short-run total variable costs at different output levels. The firm's fixed cost is $5. The market price of one sprocket is $8.

Units	Total Variable Cost
0	$0
1	$12
2	$18
3	$22
4	$28
5	$35
6	$43

1. What is the average total cost of the 5th unit?
2. What is the first unit of output where diminishing marginal returns have begun?
3. What profit or loss would Auctio earn at its profit maximum? Show your work.
4. Would Auctio operate in the short run? Explain.
5. Would Auctio stay in the market in the long run? Explain.

Answer 1

A) When Q = 5, Total cost = TVC + TFC = $35+ $5 = $40

Average total cost of the 5th unit = TC/Q = $40/5 = $8.

B) The law of diminishing marginal returns states that after some optimal level of capacity is reached, adding one additional factors of production will decrease the marginal product. When marginal product starts to decrease, MC starts to increase.

MC = (change in total cost / change in output)

When Q = 1, TC = $12+$5 = $17

When Q = 2, TC = $18 + $5 = $23. Therefore, When Q = 2, MC = ($23 - $17)/(2-1) = $6

When Q = 3, TC = $22 + $5 = $27. Therefore, when Q = 3, MC = ($27 - $23)/(3-2) = $4

When Q = 4, TC = $28+$5 = $33. Therefore, at Q = 4, MC = ($33 - $27)/(4-3) = $6

When Q = 5, TC = $35+$5 = $40. MC = $7

When Q = 6, TC = $43+$5 = $48. MC = $8

Therefore, you can see that at Q = 4, MC starts to increase. Diminishing marginal returns have begun at 4th unit of output.

C) A profit maximizing perfectly competitive firm produces at the point where market price = MC. If price = $8, then the firm will produce 6 units of output in order to maximize profit.

Profit = Total Revenue - total cost

Or, Profit = (price*quantity) - total cost

Or, profit = $(8*6) - $48 = $0

D) A profit maximizing perfectly competitive firm will produce in the short run if the market price is greater than it's average variable cost of production at the profit maximizing level of output.

At Q = 6, total variable cost = $43. Therefore, average variable cost = $43/6 = $7.2. This value is less than the market price of $8. Therefore, the firm will operate in the short run.

E) We already have calculated that the firm earns zero economic profit in the short run at profit maximizing output level. As it doesn't make any loss in the short run, therefore it will stay in the market in the long run.