Marginal Revenue, Marginal Cost, and Profit Maximization

Chapter 8 1©2005 Pearson Education, Inc.

Marginal Revenue, Marginal Cost,and Profit Maximization pp. 262-8

�We can study profit maximizing output forany firm, whether perfectly competitive ornot�Profit (π) = Total Revenue - Total Cost

�If q is output of the firm, then total revenue isprice of the good times quantity

�Total Revenue (R) = Pq



�Costs of production depends on output, q�Total Cost (C) = C(q)

�Profit for the firm, π, is differencebetween revenue and costs

)()()( qCqRq −=π



� Firm selects output to maximize thedifference between revenue and cost

�We can graph the total revenue and totalcost curves to show maximizing profitsfor the firm

�Distance between revenues and costsshow profits



� Revenue is a curve, showing that a firm canonly sell more if it lowers its price

� Slope of the revenue curve is the marginalrevenue�Change in revenue resulting from a one-unit increase

in output

� Slope of the total cost curve is marginal cost�Additional cost of producing an additional unit of

output


Profit Maximization – Short Run pp.262-8

0

Cost,Revenue,

Profit($s per

year)

Output

C(q)

R(q)A

B

π(q)q0 q*

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

Profits aremaximizedwhere R(q) –C(q) ismaximized



� If the producer tries to raise price, sales arezero

� Profit is negative to begin with, since revenue isnot large enough to cover fixed and variablecosts

� As output rises, revenue rises faster than costsincreasing profit

� Profit increases until it is maxed at q*� Profit is maximized where MR = MC or where

slopes of the R(q) and C(q) curves are equal



�Profit is maximized at the point at whichan additional increment to output leavesprofit unchanged

π = R −C

ΔπΔq

=ΔRΔq

−ΔCΔq

= 0

MR − MC = 0

MR = MC



� The Competitive Firm�Price taker – market price and output

determined from total market demand andsupply

�Market output (Q) and firm output (q)

�Market demand (D) and firm demand (d)


The Competitive Firm pp. 262-8

�Demand curve faced by an individual firmis a horizontal line� Each firm is so small that its sales have no

effect on market price. As a result, eachregards market price as given.

�Demand curve faced by whole market isdownward sloping�Shows amount of goods all consumers will

purchase at different prices



d$4

Output (bushels)

Price$ per bushel

100 200

Firm Industry

D

$4

S

Price$ per bushel

Output (millions of bushels)

100



� 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, profitmaximizing output occurs when

ARPMRqMC ===)(


Profit Maximization – Short Run pp.262-8

0

Cost,Revenue,

Profit($s per

year)

Output

C(q)

π(q)

q*

Profits are maximized where MR=p andMC are equal

Profits aremaximizedwhere R(q) –C(q) ismaximized

R(q)=pq


Choosing Output: Short Run pp. 268-73

� In the short run, capital is fixed and a firmmust choose levels of variable inputs tomaximize profits

�We can look at the graph of MR, MC,ATC and AVC to determine profits


q2

A Competitive Firm pp. 268-73

10

20

30

40

Price

50

MC

AVC

ATC

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

AR=MR=PA

q1 : MR > MCq2: MC > MRq*: MC = MR

q1

Lost Profitfor q2>q*Lost Profit

for q2>q*


Choosing Output: Short Run pp. 268-73

� The point where MR = MC, the profitmaximizing output is chosen�MR = MC at quantity, q*, of 8

�At a quantity less than 8, MR > MC, so moreprofit can be gained by increasing output

�At a quantity greater than 8, MC > MR,increasing output will decrease profits

See also Fig. 8-8 on p. 275 of the text for anexample of actual MC curve.


A Competitive Firm – PositiveProfits pp. 268-73

10

20

30

40

Price

50

0 1 2 3 4 5 6 7 8 9 10 11Outputq2

MC

AVC

ATC

q*

AR=MR=PA

q1

D

C B Profits aredetermined

by output perunit timesquantity

Profit perunit = P-AC(q) =A to B

TotalProfit =ABCD



�A firm does not have to make profits

� It is possible a firm will incur losses if theP < AC for the profit maximizing quantity�Still measured by profit per unit times

quantity

�Profit per unit is negative (P – AC < 0)


A Competitive Firm – Losses pp. 268-73

Price

Output

MC

AVC

ATC

P = MRD

At q*: MR =MC and P <ATCLosses =(P- AC) x q*

or ABCD

q*

A

BC


Short Run Production pp. 268-73

�Why would a firm produce at a loss?Leave as your exercise!�Might think price will increase in near future�Shutting down and starting up could be

costly

� Firm has two choices in short run�Continue producing�Shut down temporarily�Will compare profitability of both choices


Short Run Production pp. 268-73

�When should the firm shut down?�If AVC < P < ATC, the firm should continue

producing in the short run� Can cover all of its variable costs and some of

its fixed costs

�If P< AVC< ATC, the firm should shut down� Cannot cover its variable costs or any of its

fixed costs


A Competitive Firm – Losses pp. 268-73

Price

Output

P < ATC but�AVC sofirm willcontinue toproduce inshort run

MC

AVC

ATC

P = MRD

q*

A

BC

Losses

EF


Competitive Firm – Short RunSupply pp. 273-6

�Supply curve tells how much output willbe produced at different prices

�Competitive firms determine quantity toproduce where P = MC�Firm shuts down when P < AVC

�Competitive firms’ supply curve is portionof the marginal cost curve above theAVC curve


A Competitive Firm’sShort-Run Supply Curve pp. 273-6

Price($ perunit)

Output

MC

AVC

ATC

P = AVC

P2

q2

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

as long as P > AVC.

P1

q1

S

Supply is MCabove AVC



�Supply is upward sloping due todiminishing returns

�Higher price compensates the firm for thehigher cost of additional output andincreases total profit because it applies toall units



�Over time, prices of product and inputscan change

�How does the firm’s output change inresponse to a change in the price of aninput?�We can show an increase in marginal costs

and the change in the firm’s output decisions


MC2

q2

Input cost increases and MC shifts to MC2

and q falls to q2.

MC1

q1

The Response of a Firm toa Change in Input Price pp. 273-6

Price($ perunit)

Output

$5

Savings to the firmfrom reducing output


Short-Run Market Supply Curve pp. 276-81

�Shows the amount of product the wholemarket will produce at given prices

� Is the sum of all the individual producersin the market

�We can show graphically how we cansum the supply curves of individualproducers


MC3

Industry Supply in the ShortRun pp. 276-81

$ perunit

MC1

SSThe short-runindustry supply curve

is the horizontalsummation of the supply

curves of the firms.

Q

MC2

15 21

P1

P3

P2

1082 4 75


ProducerProducerSurplusSurplus

Producer surplusis area above MC

to the price

Producer Surplus for a Firm pp. 276-81

Price($ per

unit ofoutput)

Output

AVCAVCMCMC

AABB

PP

qq**

At q* MC = MR.Between 0 and q,

MR > MC for all units.


Producer Surplus in the ShortRun pp. 276-81

� Price is greater than MC on all but the last unit ofoutput

� Therefore, surplus is earned on all but the last unit

� The producer surplus is the sum over all unitsproduced of the difference between the marketprice of the good and the marginal cost ofproduction ( It indicates a firm’s gains fromtrade.)

� Area above supply curve to the market price


The Short-Run Market SupplyCurve pp. 276-81

�Sum of MC from 0 to q*, it is the sum ofthe total variable cost of producing q*

�Producer Surplus can be defined as thedifference between the firm’s revenueand its total variable cost

�We can show this graphically by therectangle ABCD�Revenue (0ABq*) minus variable cost

(0DCq*)


Producer surplusis also ABCD =Revenue minusvariable costs

Producer Surplus for a Firm pp. 276-81

Price($ per

unit ofoutput)

Output


AVCAVCMCMC

AABB

PP

qq**

CCDD


DD

PP**

QQ**


Market producer surplus isthe difference between P*

and S from 0 to Q*.

Producer Surplus for a Market pp. 276-81

Price($ per

unit ofoutput)

Output

SS


Choosing Output in the LongRun pp. 281-7

� In short run, one or more inputs are fixed�Depending on the time, it may limit the

flexibility of the firm

� In the long run, a firm can alter all itsinputs, including the size of the plant

�We assume free entry and free exit�No legal restrictions or extra costs


Choosing Output in the LongRun pp. 281-7

� In the short run, a firm faces a horizontal demandcurve

�Take market price as given

� The short-run average cost curve (SAC) andshort-run marginal cost curve (SMC) are lowenough for firm to make positive profits (ABCD)

� The long-run average cost curve (LRAC)

�Economies of scale to q2

�Diseconomies of scale after q2


q1

BC

AD

In the short run, thefirm is faced with fixedinputs. P = $40 > ATC.Profit is equal to ABCD.

Output Choice in the Long Run pp. 281-7

Price

Output

P = MR$40

SACSMC

q3q2

$30

LAC

LMC


Output Choice in the Long Run pp. 281-7

Price

Outputq1

BC

ADP = MR$40

SACSMC

q3q2

$30

LAC

LMC

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

Long-run profit, EFGD > short runprofit ABCD.

FG


Long-Run CompetitiveEquilibrium pp. 281-7

� For long run equilibrium, firms must haveno desire to enter or leave the industry

�We can relate economic profit to theincentive to enter and exit the market



� Firm uses labor (L) and capital (K) withpurchased capital

�Accounting Profit and Economic Profit�Accounting profit: π = R - wL

�Economic profit: π = R = wL - rK� wl = labor cost

� rk = opportunity cost of capital



� Zero-Profit�A firm is earning a normal return on its

investment

�Doing as well as it could by investing itsmoney elsewhere

�Normal return is firm’s opportunity cost ofusing money to buy capital instead ofinvesting elsewhere

�Competitive market long run equilibrium



�Entry and Exit�The long-run response to short-run profits is

to increase output and profits

�Profits will attract other producers

�More producers increase industry supply,which lowers the market price

�This continues until there are no more profitsto be gained in the market – zero economicprofits


Long-Run CompetitiveEquilibrium – Profits pp. 281-7

S1

Output Output

$ per unit ofoutput

$ per unit ofoutput

LAC

LMC

D

S2

$40 P1

Q1

Firm Industry

Q2

P2

q2

$30

•Profit attracts firms: New entrants•Supply increases until profit = 0


Long-Run CompetitiveEquilibrium – Losses pp. 281-7

S2

Output Output

$ per unit ofoutput

$ per unit ofoutput

LAC

LMC

D

S1

P2

Q2

Firm Industry

Q1

P1

q2

$20

$30

•Losses causeexisting firms to leave•Supply decreases until profit = 0



1. All firms in industry are maximizingprofits� p = MC

2. No firm has incentive to enter or exitindustry� Earning zero economic profits

3. Market is in equilibrium� QD = QS


Firms Earn Zero Profit inLong-Run Equilibrium pp. 281-7

TicketPrice

Season TicketsSales (millions)

$7$7

1.01.0

A baseball teamin a moderate-sized city

sells enough tickets so that price is equal to marginal

and average cost(profit = 0).

LACLMC

Marginal Revenue, Marginal Cost, and Profit Maximization

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