Transcript Chapter 9

Chapter 9
Profit Maximization
McGraw-Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All Rights Reserved.
Main Topics
Profit-maximizing quantities and prices
Marginal revenue, marginal cost, and
profit maximization
Supply decisions by price-taking firms
Short-run versus long-run supply
Producer surplus
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Profit-Maximizing
Prices and Quantities
In previous chapters, we have looked at:
How many units can be sold
Sales price per unit.
In Ch. 2, the product’s demand function
states how many units buyers will
demand at each price.
Quantity Demanded=D(Price)
Holding all other factors, ie. taste, income,
etc. fixed
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Profit-Maximizing
Prices and Quantities
In addition to a product’s demand
function, we can work from the inverse
demand function.
This function states how much a firm
must charge to sell any given quantity of
its product.
Price = P(Quantity Demanded )
Holding all other factors, ie. taste, income,
etc. fixed
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Profit-Maximizing
Prices and Quantities
The primary goal of a firm is not to make
money but to maximize its profit!
A firm’s profit, P, is equal to its revenue R less
its cost C
P = R – C
Maximizing profit is another example of finding
a best choice by balancing benefits and costs
Benefit of selling output is firm’s revenue, R(Q) =
P(Q)Q
Cost of selling that quantity is the firm’s cost of
production, C(Q)
Overall,
P = R(Q) – C(Q) or P(Q)Q – C(Q)
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Profit-Maximization: An Example
Noah and Naomi face a weekly inverse
demand function P(Q) = 200-Q for their
garden benches
Weekly cost function is C(Q)=Q2
Suppose they produce in batches of 10
To maximize profit, they need to find the
production level with the greatest
difference between revenue and cost
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Figure 9.2: A Profit-Maximization
Example
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Marginal Revenue
In general, marginal benefit must equal
marginal cost at a decision-maker’s best
choice whenever a small increase or
decrease in her action is possible
Here the firm’s marginal benefit is its
marginal revenue: the extra revenue
produced by the DQ marginal units sold,
measured on a per unit basis
DR R(Q)  R(Q  DQ)
MR 

DQ
DQ
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Marginal Revenue and Price
An increase in sales quantity (DQ) changes
revenue in two ways
Firm sells DQ additional units of output, each at
a price of P(Q), the output expansion effect
Firm also has to lower price as dictated by the
demand curve. This reduces revenue earned
from the original (Q-DQ) (inframarginal) units of
output, the price reduction effect
Price-taking firm faces a horizontal demand
curve and is not subject to the price reduction
effect
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Marginal Revenue and Price
The green shaded area is due to the output expansion effect.
The yellow shaded area is due to the inframarginal
unit/price reduction effect because it must lower its price to
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sell the extra units.
Marginal Revenue and Price
In this curve, the firm is
a price taker in a
perfectly competitive
market. If you
remember from our
Principles course, p.
comp. mkts allow a firm
to sell as much as it
wants at price P. In this
case, only the outward
expansion effect occurs.
Why is the curve flat? Why cant we raise/lower the price?
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Profit Max. for a Competitive Firm
Costs
and
Revenue
The firm maximizes
profit by producing
the quantity at which
marginal cost equals
marginal revenue.
Suppose the market price is P.
MC
If the firm produces
Q2, marginal cost is
MC2.
ATC
MC2
P = MR1 = MR2
P = AR = MR
AVC
If the firm
produces Q1,
marginal cost is
MC1.
MC1
0
Q1
QMAX
Q2
Quantity
Marginal Revenue and Price
In this curve, the
demand curve slopes
downwards. Any
additional unit sold must
be sold at a reduced
price.
What kind of market would this be for?
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Profit Max. for a Monopoly
Costs and
Revenue
2. . . . and then the demand
curve shows the price
consistent with this quantity.
B
Monopoly
price
1. The intersection of the
marginal-revenue curve
and the marginal-cost
curve determines the
profit-maximizing
quantity . . .
Average total cost
A
Demand
Marginal
cost
Marginal revenue
0
Q
QMAX
Q
Quantity
Profit-Maximizing Sales Quantity
Two-step procedure for finding the profitmaximizing sales quantity
Step 1: Quantity Rule
Identify positive sales quantities at which MR=MC
If more than one, find one with highest P
Step 2: Shut-Down Rule
Check whether the quantity from Step 1 yields
higher profit than shutting down
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Supply Decisions
 Price takers are firms that can sell as much as they want
at some price P, but nothing at any higher price
 Face a perfectly horizontal demand curve
 Firms in perfectly competitive markets, e.g.
 MR = P for price takers
 Use P=MC in the quantity rule to find the profitmaximizing sales quantity for a price-taking firm
 Shut-Down Rule:
 If P>ACmin, the best positive sales quantity maximizes profit.
 If P<ACmin, shutting down maximizes profit.
 If P=ACmin, then both shutting down and the best positive sales
quantity yield zero profit, which is the best the firm can do.
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Figure 9.6: Profit-Maximizing
Quantity of a Price-Taking Firm
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Comp. Firm’s S-R Supply Curve
Costs
If P > ATC, the firm
will continue to
produce at a profit.
Firm’s short-run
supply curve
MC
ATC
If P > AVC, firm will
continue to produce
in the short run.
AVC
Firm
shuts
down if
P < AVC
0
Quantity
Supply Function of a
Price-Taking Firm
A firm’s supply function shows how much it
wants to sell at each possible price: Quantity
supplied = S(Price)
To find a firm’s supply function, apply the
quantity and shut-down rules
At each price above ACmin, the firm’s profitmaximizing quantity is positive and satisfies P=MC
At each price below ACmin, the firm supplies nothing
When price equals ACmin, the firm is indifferent
between producing nothing and producing at its
efficient scale (why?)
What about firms with sunk costs? Does the
above rule apply?
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Supply Curve of a Price-Taking Firm
Where is the most efficient place to produce in each
graph? Why?
Where is the minimum place of production? Why?
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Figure 9.9: Law of Supply
 Law of Supply: when
market price increases,
the profit-maximizing sales
quantity for a price-taking
firm never decreases.
 If Q* is the rev. max point
before the price increase,
can we sell any less after
the price increase?
 Note: This doesn’t nec.
work though in regards to
the final quantity supplied.
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Change in Input Price and the
Supply Function
How does a change in an input price affect a
firm’s supply function?
Increase in price of an input that raises the per
unit cost of production
AC, MC curves shift up
Supply curve shifts up
Increase in an unavoidable fixed cost
AC shifts upward
MC unaffected
Supply curve does not shift
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Figure 9.10: Change in Input Price
and the Supply Function
b. The curve has shifted by $5 and essentially, if the
farmer receives exactly $5 more per bushel, he is willing
to supply the same amount of wheat.
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Change in Avoidable Fixed Cost
B. As the only increase is in avoidable fixed costs, the MC and
AC curves have not changed. Therefore the supply curve
hasn’t changed. The only real change in this situation is that
with the rise in avoidable fixed cost, the producer has to
receive a higher price to stay in business.
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Short-Run versus
Long-Run Supply
Firm’s marginal and average costs may differ in
the long and short run
This affects firm response over time to a
change in the price it faces for its product
Suppose the price rises suddenly and remains
at that new high level
Use the quantity and shut-down rules to
analyze the long-run and short-run effects of
the price increase on the firm’s output
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Figure 9.13(a): Quantity Rule
Firm’s best positive
quantity:
Q*SR in short run
Q*LR in long run, a
larger amount
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Figure 9.13(b): Shut-Down Rule
New price is above
the avoidable shortrun average cost at
Q*SR and the long-run
average cost at Q*LR
Firm prefers to
operate in both the
short and long run
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Producer Surplus
A firm’s producer surplus equals its
revenue less its sunk costs
P = producer surplus – sunk cost
Sunk Fixed costs are no considered as they
are incurred no matter what, so can be
ignored in making economic decisions.
Avoidable fixed costs though are considered.
Represented by the area between firm’s
price level and the supply curve
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Figure 9.16: Producer Surplus
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Producer Surplus
Common application: investigate welfare
implications of various policies
Can focus on producer surplus instead of
profit because the policies can’t have any
effects on sunk costs
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Supply by Multi-Product Price
Taking Firms
When a firm’s marginal cost of
production for one product changes with
the quantity of a second product it
produces, an increase in the price of the
second product can change the firm’s
supply of the first product.
Why?
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