Perfect competition: Key concepts

A. Equilibrium in the short run

1. Choosing output

    Firms try to maximize profits (p) = TR - TC
        TC = TC(Q) => MC = DTC/DQ
        TR = TR(Q) =>  MR = DTR/DQ
            TR(Q) = P(Q)^.Q. For a PC firm, P = a constant => MR = P

    2-step process to choosing profit-maximizing output (Q*):
        Step 1: Expand production as long as MR > MC (the upward-sloping portion of MC).
        Step 2: If profits are < 0, check to be sure that TR > TVC (=> P > AVC). If not, shut down.

    The shutdown option:
    Q=0 => TR = 0, TC = TFC, p = -TFC
    => better to operate at Q* if
    p > -TFC =>
    TR - TC  > -TFC =>
    TR > TC - TFC =>
    TR > TVC =>
    TR/Q* > TVC/Q* =>
    P > AVC at Q*

2. Calculating and illustrating profits

B. equilibrium in the long run

    Profits > 0 => entry until profits = 0 again
    Profits < 0 =>exit until profits = 0 again

Firm supply decisions under perfect competition

Suppose you have a costume firm with the cost structure given in the table below. You are a perfectly competitive firm, so you can sell as many Halloween costumes as you want at the going market price.
Part 1: Suppose that the price = $13, and the following table summarizes your revenue and cost situation:
	(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Q P TR TC TVC TFC Profit MR MC MRvsMC (>,<,=) 0 13 0 13   0 13 -13 --- --- --- 1 13 13 22 9 13 -9 13 9 > 2 13 26 27 14 13 -1 13 5 > 3 13 39 33 20 13 +6 13 6 > 4 13 52 40 27 13 +12 13 7 > 5 13 65 50 37 13 +15 13 10 > 6 13 78 63 50 13 +15 13 13 = 7 13 91 80 67 13 +11 13 17 <
	How much output should the firm produce to maximize profits? Q* = ________
Part 2: Marginal analysis helps determine the firm's profit-maximizing output (Q*) for any possible market prices:
	2.1: Expand production as long as MR > MC (the upward-sloping portion of MC). 2.2: If profits are < 0, check to be sure that TR > TVC (=> P > AVC). If not, shut down.
	(1) (2) (3) (4) (5) (6) (7) (8) (9) P=MR Q* TR TC Profit TVC AVC MC PvsAVC $17 7 119 80 +39 67 9.57 17 > 13 6 78 63 +15 50  8.33 13 > 10 5 50 50 0 37  7.40 10 > 8 4? 32 40 -8 27 6.75 7 > 7 4? 28 40 -12 27  6.75 7 > 6 3? 18 33 -15 20  6.67 6 <
	Key lesson: The firm's supply curve = its upward-sloping MC curve above its minimum AVC (for price < minimum AVC, Qs = 0).

Output and shutdown decisions
Palm Desert resort hotel

Suppose you own a resort hotel in the perfectly competitive tourist market of Palm Desert. The lefthand panel above depicts the hotel industry in Palm Desert for each of the four seasons: W=winter, Sp=spring, Su=summer, and F=fall.
Your task is to illustrate your profit-loss situation for each season in the two righthand panels above, which depict your hotel's cost curves, (assumed to be the same for each season). Use the center panel for the winter and summer seasons, and the the righthand panel for the spring and fall seasons.
For each season:
	1. Draw your marginal revenue curve.
	2. Indicate your most profitable output level if you operate.
	3. Indicate the size of your profits or losses if you operate.
Complete the following table:
Season Profits (>,<,=) 0? Operate or shutdown? Winter     Spring     Summer     Fall

Perfect competition: Review exercise

1.	Suppose the market price is $10. Use "Q1" to label the firm's profit-maximizing output in the diagram to the right. How did you decide?
2.	Suppose the market price is $4. Use "Q2" to label the firm's profit-maximizing output if the firm continues to operate.
3.	Indicate in the diagram the firm's profits/losses at the output level you chose for question 2.
4.	Should the firm operate or shut down if the price is $4? How did you decide?