Transcript Chapter 9 - Academic Csuohio

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
9-2
Profit-Maximizing
Prices and Quantities
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) = P(Q)Q – C(Q)
9-3
Profit-Maximization: An Example
Noah and Naomi face 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
9-4
Figure 9.2: A Profit-Maximization
Example
9-5
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
9-6
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; reduces revenue earned from
the original (Q-DQ) units of output, the price
reduction effect
Price-taking firm faces a horizontal demand
curve and is not subject to the price reduction
effect
9-7
Figure 9.4: Marginal Revenue and
Price
9-8
Sample Problem 1 (9.1):
If the demand function for Noah and
Naomi’s garden benches is Qd = D(P) =
1,000/P1/2, what is their inverse demand
function?
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
9-10
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.
9-11
Figure 9.6: Profit-Maximizing
Quantity of a Price-Taking Firm
9-12
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
9-13
Figure 9.7: Supply Curve of a
Price-Taking Firm
9-14
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
9-15
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
9-16
Figure 9.10: Change in Input Price
and the Supply Function
9-17
Figure 9.11: Change in Avoidable
Fixed Cost
9-18
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
9-19
Figure 9.13(a): Quantity Rule
Firm’s best positive
quantity:
Q*SR in short run
Q*LR in long run, a
larger amount
9-20
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
9-21
Producer Surplus
A firm’s producer surplus equals its revenue
less its avoidable costs
P = producer surplus – sunk cost
Represented by the area between firm’s price level
and the supply curve
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
9-22
Figure 9.16: Producer Surplus
9-23
Sample Problem 2 (9.8)
Suppose Dan’s cost of making a pizza is
C(Q) = 4Q + Q2/40), and his marginal cost
is MC = 4 + (Q/20). Dan is a price taker.
What is Dan’s supply function? What if
Dan has an avoidable fixed cost of $10?