Question

3) Perfect Competition (5 points) 

The data in the table below are the monthly average variable costs (AVC), average total costs (ATC), and marginal costs (MC) for Alpacky, a typical alpaca wool-manufacturing firm in Peru. The alpaca wool industry is competitive.

For each market price given below, give the profit-maximizing output level and state whether Alpacky's profits are positive, negative, or zero. Also state whether Alpacky should produce or shut down in the short run.

 a. If the market price is $22...

 i. what is the firm's profit-maximizing output level?

 ii. Will the firm's profit at this output level be positive, negative, or zero?

 iii. Will the firm produce in the short-run? Why/why not?

 iv. If the firm will produce in the short-run, what is the firm's profit (or loss) per unit of output? [If the firm will not produce in the short-run, answer “N/A”]

 b. Now imagine a price of $18. Answer questions (i)-(iv) from above.

 c. Do the same for a price of $16.

 d. If firms in this perfectly competitive market are earning economic profits, what can we predict will happen to the industry in the long-run? Explain briefly.

Answer 1

a)

Output(units of wool)	Price($)	AVC($)	ATC($)	MC($)
0	---	---	--	---
1	22	20.00	30.00	20.00
2	22	17.00	22.00	14.00
3	22	16.70	20.00	16.00
4	22	17.00	19.50	18.00
5	22	18.00	20.00	22.00
6	22	22.33	24.00	44.00

i) The firm maximize its profit by producing a quantity where its MC=MR. The profit maximizing output is 5 units where its MC is $22 and MR (price)=$22.

ii) The profit per unit is the difference between unit cost (ATC) and average revenue(AR or price). At the level of output at 5 units, the cost per unit is $20 but the revenue from per unit is $22. Thus the firm earns a per unit profit = $2. The profit at this level of positive. Any profit above the ATC is the positive profit earning situation.

iii) The firm will produce in shortrun because it earns positive profit. Any price below the AVC is the shutdown point.

iv) The firm will earn a profit of $2 per unit. The firm will produce in shortrun thus shutdown is not applicable.

b)      

Output(units of wool)	Price($)	AVC($)	ATC($)	MC($)
0	---	---	--	---
1	18	20.00	30.00	20.00
2	18	17.00	22.00	14.00
3	18	16.70	20.00	16.00
4	18	17.00	19.50	18.00
5	18	18.00	20.00	22.00
6	18	22.33	24.00	44.00

i) When the price falls to $18, the firm will set an output at a level where its MC equates with new price. When it produce 4 units it MC equals MR at $18. Then the optimum output of the firm is 4 units.

ii) The profit at this level of output is negative since MR or AR =$18 but the ATC= $19.50. Thus the firm incur a per unit loss equal to $1.50.

iii) At a price of $18, the firm can cover its average variable cost ($17) and a part of fixed cost. Thus the firm will continue to produce in shortrun.

iv) If the firm produces in shortrun it per unit loss is $1.50. If the firm will not produce it will lose its fixed cost in shortrun. The shutdown is not applicable at this price.

c                 

Output(units of wool)	Price($)	AVC($)	ATC($)	MC($)
0	---	---	--	---
1	16	20.00	30.00	20.00
2	16	17.00	22.00	14.00
3	16	16.70	20.00	16.00
4	16	17.00	19.50	18.00
5	16	18.00	20.00	22.00
6	16	22.33	24.00	44.00

i) At a price of $16, the equilibrium output is 3 units where it’s MC=$16 and MR=$16.

ii) The profit is negative since its ATC is $20 but MR or AR(price) = $16. The ATC =$20.

iii) The price is below the AVC ($16.70). Thus the firm is losing it fixed cost and variable cost fully. Thus the firm will shut down.

iv) The firm will shutdown. The profit or loss is not applicable.

d. If the firms are earning positive profit in shortrun, the new firms will enter into the industry. The industry supply increase and the price fall and the positive profit disappears and all firms will earn zero economic profit in longrun.