1. Profit maximization by firms
ECO61
Muhammad Farhan Javed

2. Revenues and costs
• A firm’s costs (C) were discussed in the previous
chapter
• A firm’s revenue is R = P × Q
– Where P is the price charged by the firm for the
commodity it sells and Q is the quantity of the firm’s
output that people buy
– We discussed the link between price and quantity
consumed – the demand curve – earlier
• Now it is time to bring revenues and costs
together to study a firm’s behavior

3. Profit-Maximizing
Prices and Quantities
• A firm’s profit, Π, is equal to its revenue R less its
cost C
– Π = R – C
• We assume that a firm’s actions are aimed at
maximizing profit
• 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,
– Π = R(Q) – C(Q) = P(Q)Q – C(Q)
9-3

4. 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

5. Profit-Maximization: An Example
)]50[50(2
])50250[50(2
])10050[50(2
)1005050(2)100(2
2200200
)200(
22
222
222
2222
222
2
Q
QQ
QQ
QQQQ
QQQQQ
QQQ
CQPCR
−−=Π
+××−−=Π
+−−=Π
−+−=−=Π
−=−−=Π
−×−=Π
−×=−=Π
Note that [50 – Q]2
is always a positive number. Therefore,
to maximize profit one must minimize [50 – Q]2
. Therefore,
to maximize profit, Noah and Naomi must produce Q = 50
units. This is their profit-maximizing output.
When Q = 50, π = 2 × 502
= 5000. this is
the biggest profit Noah and Naomi can
achieve.

6. Figure 9.2: A Profit-Maximization Example
9-6

7. Choice requires balance at the margin
• 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

8. Example

9. Marginal Revenue
• Here the firm’s marginal benefit is its marginal
revenue: the extra revenue produced by the ∆Q
marginal units sold, measured on a per unit basis
9-9

10. Marginal Revenue and Price
• An increase in sales quantity (∆Q) changes revenue
in two ways:
– Firm sells ∆Q additional units of output, each at a price
of P(Q). This is the output expansion effect: P∆Q
– Firm also has to lower price as dictated by the demand
curve; reduces revenue earned from the original Q units
of output. This is the price reduction effect: Q∆P
9-10

11. Figure 9.4: Marginal Revenue and
Price
9-11
Output expansion effect: P∆Q
Price reduction
effect of output
expansion: Q∆P.
Non-existent
when demand is
horizontal

12. Marginal Revenue and Price
• The output expansion effect is P∆Q
• The price reduction effect is Q∆P
• Therefore the additional revenue per unit of
additional output is MR = (P∆Q + Q∆P)/∆Q = P +
Q∆P/∆Q
• When demand is negatively sloped, ∆P/∆Q < 0. So,
MR < P.
• When demand is horizontal, ∆P/∆Q = 0. So, MR = P.
9-12

13. Demand and marginal revenue

14. Profit-Maximizing Sales Quantity
• Two-step procedure for finding the profit-maximizing
sales quantity
• Step 1: Quantity Rule
– Identify positive sales quantities at which MR=MC
– If more than one, find one with highest Π
• Step 2: Shut-Down Rule
– Check whether the quantity from Step 1 yields higher
profit than shutting down
9-14

15. Profit
• Profit equals total revenue minus total costs.
– Profit = R – C
– Profit/Q = R/Q – C/Q
– Profit = (R/Q - C/Q) × Q
– Profit = (PQ/Q - C/Q) × Q
– Profit = (P - AC) × Q

16. Profit: downward-sloping demand of price-setting firm
profit
Average
cost
Quantity
Profit-
maximizing
price
QMAX0
Costs and
Revenue
Demand
Marginal cost
Marginal revenue
Average cost
B
C
E
D

17. Profit: downward-sloping demand of price-
setting firm
• Recall that profit = (P - AC) × Q
• Therefore, the firm will stay in business as
long as price (P) is greater than average cost
(AC).

18. Shut down because P < AC at all Q: downward-sloping demand of
price-setting firm
Quantity0
Costs and
Revenue
Demand
Average total cost

19. Profit Maximization: horizontal demand for a price taking firm
Quantity0
Costs
and
Revenue
MC
AC
MC1
Q1
MC2
Q2
The firm maximizes
profit by producing
the quantity at which
marginal cost equals
marginal revenue.
QMAX
P = MR1 = MR2 P = AR = MR

20. Shut down because P < AC at all Q: horizontal demand for a price
taking firm
Quantity0
Costs
and
Revenue
MC
AC
P = AR = MR
ACmin

21. 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
• not subject to the price reduction effect
– Firms in perfectly competitive markets, e.g.
– MR = P for price takers
• Use P=MC in the quantity rule to find the profit-maximizing
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.
9-21

22. Price determination
• We have seen how the price is determined in the
case of price setting firms that have downward
sloping demand curves
• But how is the price that price taking firms use to
guide their production determined?
– For now think of it as determined by trial and error.
Pick a random price. See what quantity is demanded
by buyers and what quantity is supplied by producers.
Keep trying different prices whenever the two
quantities are unequal
– The market equilibrium price is the price at which the
quantities supplied and demanded are equal