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Profit Maximization

Chapter 8

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PERFECTLY COMPETITIVE MARKETS

• The model of perfect competition rests on three basic assumptions:

(1) price taking,(2) product homogeneity, and (3) free entry and exit.

Price Taking

Because each individual firm sells a sufficiently small proportion of total market output, its decisions have no impact on market price.

price taker Firm that has no influence over market price

and thus takes the price as given.

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Product Homogeneity

When the products of all of the firms in a market are perfectly substitutable with one another—that is, when they are homogeneous—no firm can raise the price of its product above the price of other firms without losing most or all of its business.

free entry (or exit) Condition under which there are no special costs that make it difficult for a firm to enter (or exit) an industry.When Is a Market Highly Competitive?

Because firms can implicitly or explicitly collude in setting prices, the presence of many firms is not sufficient for an industry to approximate perfect competition.

Conversely, the presence of only a few firms in a market does not rule out competitive behavior.

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Profit Maximization

• Do firms maximize profits?– Managers in firms may be concerned with other

objectives• Revenue maximization• Revenue growth• Dividend maximization• Short-run profit maximization (due to bonus or

promotion incentive)– Could be at expense of long run profits

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Marginal Revenue, Marginal Cost, and Profit Maximization

• We can study profit maximizing output for any firm whether perfectly competitive or not– Profit () = Total Revenue - Total Cost– If q is output of the firm, then total revenue is price of the

good times quantity– Total Revenue (R) = P*q

Costs of production depends on outputTotal Cost (C) = C*q

Profit for the firm, , is difference between revenue and costs

)()()( qCqRq

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MARGINAL REVENUE, MARGINAL COST,AND PROFIT MAXIMIZATION

• Revenue is curved showing that a firm can only sell more if it lowers its price

• Slope in revenue curve is the marginal revenue– Change in revenue resulting from a one-unit increase in

output• Slope of total cost curve is marginal cost

– Additional cost of producing an additional unit of output

Δπ/Δq = ΔR/Δq − ΔC/Δq = 0

MR(q) = MC(q)

Profit Maximization by a Competitive Firm

MC(q) = MR = P

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Profit Maximization – Short Run

Profits are maximized where MR (slope at A) and MC (slope at B) are equal

Profits are maximized where R(q) – C(q) is maximizedR(q)

C(q)

(q)

Cost,Revenue,

Profit($s per

year)

Output q*q0

A

B

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Marginal Revenue, Marginal Cost, and Profit Maximization

• Profit is maximized at the point at which an additional increment to output leaves profit unchanged

MCMR

MCMR

q

C

q

R

q

CR

0

0

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The Competitive Firm

• The Competitive Firm– Price taker – market price and output determined from

total market demand and supply– Market output (Q) and firm output (q)– Market demand (D) and firm demand (d)

• Demand curve faced by an individual firm is a horizontal line– Firm’s sales have no effect on market price

• Demand curve faced by whole market is downward sloping– Shows amount of good all consumers will purchase at

different prices

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The Competitive Firm• Demand curve faced by an individual firm is a horizontal line

– Firm’s sales have no effect on market price• Demand curve faced by whole market is downward sloping

– Shows amount of good all consumers will purchase at different prices

The competitive firm’s demand

Individual producer sells all units for $4 regardless of that producer’s level of output.

MR = P with the horizontal demand curve

For a perfectly competitive firm, profit maximizing output occurs when

ARPMRqMC )(

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A Competitive Firm

10

20

30

40

Price

50

0 1 2 3 4 5 6 7 8 9 10 11Output

AR=MR=P

MC

q*q1 q2

AVC

ATC

Lost Profit for q2>q*Lost Profit

for q2>q*

q1 : MR > MCq2: MC > MRq0: MC = MR

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A Competitive Firm – Positive Profits

q2

MC

AVC

ATC

q*

AR=MR=PA

q1

10

20

30

40

Price

50

0 1 2 3 4 5 6 7 8 9 10 11Output

Total Profit = ABCD

Profits are determined by output per unit times

quantity

Profit per unit

= P-AC(q) = A to B

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A Competitive Firm – Positive Profits

• A firm does not have to make profits• It is possible a firm will incur losses if the P < AC for

the profit maximizing quantity– Still measured by profit per unit times quantity– Profit per unit is negative (P – AC < 0)

Summary of Production Decisions

Profit is maximized when MC = MR

If P > ATC the firm is making profits.

If P < ATC the firm is making losses

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A Competitive Firm – Losses

BC

AVC

ATCMC

P = MRD

q*

A

Output

Price

At q*: MR = MC and P <

ATCLosses =

(P- AC) x q* or ABCD

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Competitive Firm – Short Run Supply

• When should the firm shut down?– If AVC < P < ATC the firm should continue producing in

the short run• Can cover some of its variable costs and all of its

fixed costs– If AVC > P < ATC the firm should shut-down.

• Can not cover even its fixed costs

Supply curve tells how much output will be produced at different pricesCompetitive firms determine quantity to produce where P = MC

Firm shuts down when P < AVCCompetitive firms supply curve is portion of the marginal cost curve above the AVC curve

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A Competitive Firm’s Short-Run Supply Curve

AVC

ATC

S

P = AVC

P1

q1

P2

q2

MC

Price($ per

unit)

Output

Supply is MC above AVC

The firm chooses theoutput level where P = MR = MC,

as long as P > AVC.

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Elasticity of Market Supply

• Elasticity of Market Supply– Measures the sensitivity of industry output to

market price– The percentage change in quantity supplied, Q, in

response to 1-percent change in price

)//()/( PPQQEs

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Producer Surplus versus Profit

• Profit is revenue minus total cost (not just variable cost)

• When fixed cost is positive, producer surplus is greater than profit

VC- R PS Surplus Producer

FC - VC- R - Profit

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Output Choice in the Short Run

q1

BC

AD

Output

SACSMC

q3q2

$30

LAC

LMC

P = MR$40

Price

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Output Choice in the Long Run

Price

Outputq1

BC

ADP = MR$40

SACSMC

q3q2

$30

LAC

LMC

FG

In the long run, the plant size will be increased and output increased to q3.

Long-run profit, EFGD > short runprofit ABCD.

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long-run competitive equilibrium• Accounting profit

– Difference between firm’s revenues and direct costs

• Economic profit– Difference between firm’s revenues and direct

and indirect costs– Takes into account opportunity costs

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long-run competitive equilibrium• Firm uses labor (L) and capital (K) with purchased

capital• Accounting Profit & Economic Profit

– Accounting profit: = R - wL– Economic profit: = R = wL - rK

• wl = labor cost• rk = opportunity cost of capital

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Long-Run Competitive Equilibrium

1. All firms in industry are maximizing profits– MR = MC

2. No firm has incentive to enter or exit industry– Earning zero economic profits

3. Market is in equilibrium– QD = QD

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Firms Earn Zero Profit in Long-Run Equilibrium

$10$10

Economic Rent

$7.20$7.20A team with the samecost in a larger citysells tickets for $10.

Season TicketsSales (millions)

LACLMC

TicketPrice

1.31.3

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The Industry’s Long-Run Supply Curve

• To analyze long-run industry supply, will need to distinguish between three different types of industries1.Constant-Cost2.Increasing-Cost3.Decreasing-Cost

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Constant-Cost Industry

Industry whose long-run supply curve is horizontal

Assume a firm is initially in equilibrium

Demand increases causing price to increaseIndividual firms increase supply

Causes firms to earn positive profits in short-runSupply increases causing market price to decrease

Long run equilibrium – zero economic profits

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Increasing-Cost Industry

• Prices of some or all inputs rises as production is expanded when demand of inputs increases

• When demand increases causing prices to increase and production to increase– Firms enter the market increasing demand for

inputs– Costs increase causing an upward shift in supply

curves– Market supply increases but not as much

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Decreasing-Cost Industry

• Industry whose long-run supply curve is downward sloping

• Increase in demand causes production to increase– Increase in size allows firm to take advantage

of size to get inputs cheaper– Increased production may lead to better

efficiencies or quantity discounts– Costs shift down and market price falls