profit maximization, firm supply and market supply under perfect competition dr. jennifer p. wissink...

Profit Maximization, Firm Supply And Market Supply

Under Perfect Competition

Dr. Jennifer P. Wissink©2011 John M. Abowd and Jennifer P. Wissink, all rights reserved.

Short Run Profit Maximization In A Perfectly Competitive Output Market Consider

– Structure, then– Conduct, then– Performance.

Structure for Perfectly Competitive Markets– Many firms, and– Homogeneous output, and– Free entry and exit, and– Full and symmetric information.

THINK: Apples market, Cortland variety and Jonathan’s apple orchard

Short Run Profit Maximization In A Perfectly Competitive Output Market

Introduce some “new” notation. Jonathan’s output: q The aggregate output of the

entire apple market: Q The market price for apples: P

– Jonathan is a “price taker”.– Jonathan’s perceived demand for

HIS apples (δ) will be the prevailing market price P.

– So… for Jonathan, or any other price taking firm…

» Total revenue = tr = P•q» So marginal revenue = mr = P» δ = P = marginal revenue.

Q

$ D=Demand

$

q

mr = δP

S=Supply

P

Jonathan’s Economic Profit and Loss when P=$528

Just follow the rules for profit maximization:– 1) Set mr=mc, 2) make sure at a max and not min, 3) check profit level– Note: since Jonathan is a price taker, if P=$528 mr=$528

At mr=$528, the profit maximizing apple production is the highlighted line.

Apple Farm Profits (detail)

Apples (tons/year) Total Cost

Total Revenue

Marginal Cost

Marginal Revenue = Market

PriceEconomic

Profits200 80,000 105,600 25,600210 84,160 110,880 440 528 26,720220 88,800 116,160 484 528 27,360230 93,840 121,440 528 528 27,600240 99,360 126,720 588 528 27,360250 105,600 132,000 632 528 26,400260 112,000 137,280 25,280

Economic Profits Economic profits are the difference

between total revenue and total costs.

Economic total costs include the opportunity costs of all inputs to the production process–in particular, the opportunity costs of the owner’s time and physical capital (equipment and space).

Accounting Profits Accounting profits are defined as total sales

revenue (the same as total revenue in the economic profits definition) minus operating costs (costs of goods sold + administrative and sales costs for those who know some accounting).

Accounting Profits = Sales Revenue - Accounting Costs

Did Jonathan Make Accounting Profits?

The blue line in the table illustrates that Jonathan makes an accounting profit of $40,800 when the apple price is $528/ton.

Accounting Profits vs. Economic Profits (detail)

Apples (tons/year)

Total Revenue

Accounting Costs

Accounting Profits Total Costs

Economic Profits

200 105,600 66,800 38,800 80,000 25,600210 110,880 70,960 39,920 84,160 26,720220 116,160 75,600 40,560 88,800 27,360230 121,440 80,640 40,800 93,840 27,600240 126,720 86,160 40,560 99,360 27,360250 132,000 92,400 39,600 105,600 26,400260 137,280 98,800 38,480 112,000 25,280

Reconciling Economic and Accounting Profits

The table to the right shows that Jonathan’s economic profits equal his accounting profits minus the opportunity cost of his time.

Thus, when the price of apples is $528/ton and 230 tons/year are sold, economic profits = $27,600

Reconciling Accounting and Economic Profits (detail)

Apples (tons/year)

Accounting Profits

- Opportunity Cost of

Jonathan's Time

= Economic Profits

200 38,800 13,200 25,600210 39,920 13,200 26,720220 40,560 13,200 27,360230 40,800 13,200 27,600240 40,560 13,200 27,360250 39,600 13,200 26,400260 38,480 13,200 25,280

Question 1 At a market price of $484/ton for apples, what is the

optimal annual production of apples?

Marginal revenue = marginal cost at a production level of 220 tons/year.

This is the profit maximizing level of output when the market price is $484/ton.

Apples (tons/year) Land

Hired Labor

Proprietor's time Total Cost

Average Cost

Marginal Cost

(midpoint formula)

200 12,400 54,400 13,200 80,000 400 400210 12,400 58,560 13,200 84,160 401 440220 12,400 63,200 13,200 88,800 404 484230 12,400 68,240 13,200 93,840 408 528240 12,400 73,760 13,200 99,360 414 588250 12,400 80,000 13,200 105,600 422 632260 12,400 86,400 13,200 112,000 431

Jonathan's Apple Farm Costs (detail)






Hired Labor


Average Cost

Marginal Cost

(midpoint formula)

200 12,400 54,400 13,200 80,000 400 400210 12,400 58,560 13,200 84,160 401 440220 12,400 63,200 13,200 88,800 404 484230 12,400 68,240 13,200 93,840 408 528240 12,400 73,760 13,200 99,360 414 588250 12,400 80,000 13,200 105,600 422 632260 12,400 86,400 13,200 112,000 431


Question 4

Should Jonathan continue to operate the apple farm if the market price of apples is $400/ton?

Answer 4

Jonathan’s economic profits are zero when the market price of apples is $400/ton ($0.20/pound, about the current wholesale price for first quality fresh apples).

Jonathan just recovers the opportunity cost of his time ($13,200), so he is indifferent between producing apples and taking a job at $12/hour.

Question 5

Should Jonathan continue to operate the apple farm if the market price of apples is LESS THAN $400/ton?

Answer 5 Depends on if we are talking long run or short run.

In the long run, Jonathan should not stay in the apple business if profits will continue to be negative.

In the short run, however, Jonathan must consider a little more.

– Jonathan’s economic profits are negative if he operates and does the best that he can.

– If Jonathan shuts down in the short run his economic loses will be ALL THOSE COSTS HE CAN NOT AVOID by shutting down, i.e., frequently called his sunk costs.

– So, Jonathan must compare his (negative) profits from operating versus shutting down.

– π(q*>0) = TR – avoidable costs – sunk costs.– π(q*=0) = -sunk costs– π(q*>0) > π(q*=0) when [TR - avoidable costs - sunk costs > - sunk costs]

[TR - avoidable costs > 0] [TR > avoidable costs] [price > average avoidable costs]

Jonathan’s Cost Curves

Assume Land and Proprietor’s time are FIXED COSTS = $25,600 Assume Hired Labor is the only VARIABLE COST

Jonathan's Apple Farm Costs


Hired Labor


Average Cost

Marginal Cost

(midpoint formula)

0 12,400 0 13,200 25,60050 12,400 20,000 13,200 45,600 912 296

100 12,400 29,600 13,200 55,200 552 200150 12,400 40,000 13,200 65,600 437 248200 12,400 54,400 13,200 80,000 400 400250 12,400 80,000 13,200 105,600 422 656300 12,400 120,000 13,200 145,600 485 1,360350 12,400 216,000 13,200 241,600 690

Jonathan’s Costs So Land and Proprietor’s time are FIXED COSTS = $25,600

– If Q>0 no need for more discussion– If Q=0, then need to differentiate between

» avoidable fixed costs» unavoidable fixed costs, a.k.a sunk costs

Assume Hired Labor is the only VARIABLE COST– Regardless of Q>0 or Q=0, all variable costs are avoidable, by definition

So when choosing to either operate or shut down with loses in the short run the rule is: – operate if revenues cover variable costs + avoidable fixed costs– otherwise shut down and see what happens

NOTE: most of the time books assume that ALL fixed costs are sunk.

Jonathan’s Short Run Supply Curve So, in general, for a

perfectly competitive firm, the srsfirm = srmcfirm for all points where srmc ≥ sravc (assuming all fixed costs are sunk).

For a perfectly competitive firm, choosing the output at which market price equals marginal cost maximizes profits.

Remember, it’s really mr=mc at q*, but since the firm is a price taker, P=mr all the time, so P=mc at q*.

$P1

$P2

$P3

$P4

q4 q3 q2 q1

Individual Producer’s Surplus Recall: Producer’s surplus measures the gain to the firm

from selling all units at the market price. Marginal Producer’s Surplus on a given unit (the qth) is:

Price – Marginal Cost for that unit. Producer’s Surplus on all units supplied (q units) is:

Total Revenue – Variable Costs. Producer’s Surplus is:

the area above the short run firm supply curve and below the market price

Producer’s Surplus is: Economic Profit + Fixed Costs.

Jonathan’s Producer Surplus Jonathan’s

individual producer’s surplus, when the market price is $528, is the sum of his economic profits ($27,600) and his fixed costs ($25,600) = $53,200.

Jonathan's Producer Surplus

0

200

400

600

800

1,000

1,200

1,400

1,600

0 100 200 300 400

Apples (tons/year)

Pri

ce

($

/to

n)

Market Price = $528

Producer surplus = area above the marginal cost curve, below the market price = $53,200

The Short RunMarket Supply Curve The market supply curve is the sum of

the quantities supplied by each seller at each market price.

Market supply, thus reflects the marginal costs of each of the producers in the market.

Short Run Market Supply Curve: Horizontal Summation

Farm A’s Supply of Apples

0

200

400

600

800

1,000

1,200

1,400

1,600

0 100 200 300 400

Apples (tons/year)

Pri

ce (

$/to

n)

Farm B’s Supply of Apples

0

200

400

600

800

1,000

1,200

1,400

1,600

0 100 200 300 400

Apples (tons/year)

Pri

ce (

$/to

n)

At a price of $1000/ton, add Farm A’s supply to Farm B’s supply to get market supply (about 560 tons/year). Add over all farms.

The market supply curve is the horizontal summation of the firms’ supply curves.

Producers’ Surplus To get market producers’ surplus we simply

sum the producer’s surplus over all the producers in the market.

So once we have the short run market supply curve, which reflects the marginal cost of each of the producers in the market, we have producers’ surplus as the area between the market price and above the short run market supply curve.

Producers’ surplus will still be total revenue – variable cost, aggregated over all producers.

Recall the supply function for X = CD players:QS = g(PX, Pfop, Poc, S&T, N)Where:QS = maximum quantity that producers are willing and able to sell

PX = X’s pricePfop = the price of factors of productionPoc = the opportunity costsS&T = science and technologyN = number of firms in the market

Short Run Market Supply - Reprised

How does our scratch supply curve compare to the one we bought off the shelf?

profit maximization, firm supply and market supply under perfect competition dr. jennifer p. wissink...

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