Intermediate Microeconomics chapter 8 slides

Walter Nicholson
Amherst College
Christopher Snyder
Dartmouth College
PowerPoint Slide Presentation | Philip Heap, James Madison University
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1

©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
2
Profit
Maximization
and Supply
CHAPTER
8

• In the last two chapters:
– Production: relationship between inputs and output.
– Costs: relationship between output and costs.
• In this chapter, we want to study a firm’s output decision.
– How much should the firm produce to maximize profits?
Chapter Preview
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Ch. 8 • 3

The Nature of the Firm
• Why do firms exist?
– If they did not, how would goods be produced?
– The role of transaction costs.
• Contracts within Firms
– Formal vs. informal contracts
• Contract Incentives
– Relationship between incentives and efficiency
• Firms’ Goals and Profit Maximization

Profit Maximization
• Economic profit is the difference between revenue and economic
cost.
– Economic cost includes all relevant opportunity costs.
– Owner’s return on her investment and normal rate of return.
– Economic profit (loss) and entry (exit).
• Marginalism
– How much profit can I make from making one more car or
hiring one more worker?

Profit Maximization
• The Output Decision
– π(q) = R(q) – TC(q)
– The firm chooses the level of output that generates the largest
profit.
– The firm choose the level of output for which the difference
between revenue and costs is the largest.

Profit Maximization: Graphical Approach
Output per week
Costs,
Revenue
Profit
s
Costs (TC)
Revenues (R)
Profits
q*
Output per week
q1
q2

Profit Maximization: Golden Rule
• At q* what condition must hold?
• Marginal Revenue = Marginal Cost
• Why?
– If at the current level of output, MR > MC, the firm should . . .
– If at the current level of output, MR < MC, the firm should . . .
– Therefore, if MR = MC, the firms maximizes profits.

Profit Maximization: Graphical Approach
Output per week
Costs,
Revenue
Profit
s
Costs (TC)
Revenues (R)
Profits
q*
Output per week
q1
q2
slope = MR
slope = MC

Profit Maximization: Calculus
• π(q) = R(q) – TC(q)
– To maximize a function set the first derivative equal to zero
– dπ(q)/dq = dR(q)/dq – dTC(q)/dq = 0
– MR(q) – MC(q) = 0
– MR(q) = MC(q)

Profit Maximization: Calculus
• π(q) = 20q – (50 + 10q + 0.1q2
)
dπ(q)/dq = ?
20 – (10 + 0.2q) = 0
q* = 50
20 – (10 + 0.2q)

Marginal Revenue
• Marginal revenue is the additional revenue from selling one more
unit.
• What happens to marginal revenue as the firm sells more or less
output?
• Price taker is a firm whose decisions have no effect on the
prevailing market price of a good.
• For a price taking firm MR = P.

Marginal Revenue
• What about for a firm that faces a downward sloping demand
curve?
• To sell one more unit the firm would have to cut the price for all
units sold, not just the last one.
• Revenue from the last unit = new price – revenue lost from selling
the other units at a lower price
• MR < P

A Numerical Example: q = 10 - P
What happens to TR and MR as output increases?

Marginal Revenue
Price
Quantity
Demand
$7
3 4
$6
Loss in revenue from cutting price by $1 = $3
Gain in revenue from selling one more unit = $6
Marginal revenue = $3

Marginal Revenue and Elasticity
• The price elasticity of demand in a market:
• The price elasticity of demand for a firm:

• What is the relationship between elasticity and marginal revenue?
– When demand is elastic, eq,P
< -1, MR > 0
– When demand is unit elastic, eq,P
= 1, MR = 0
– When demand is inelastic, eq, P
> -1, MR < 0
• In general, can show that: MR = (1 + 1/eq,P
)
– If eq,P
= -2 (elastic), MR = (1 + 1/-2) = 1/2 > 0
– If eq,P
= -0.5 (inelastic), MR = (1 + 1/-0.5) = -1 < 0

• The firm can use elasticity information to see what happens to
revenue if it sells one more unit?
• Suppose eq,P
= -2 and the current price is $10.
– MR = $10 x (1 + 1/-2) = $5
• The firm will sell one more unit as long as MC < $5

Marginal Revenue Curve
Price
Quantity
Demand (average revenue)
Marginal revenue
P1
q1
A marginal revenue curve shows the relation
between the quantity a firm sells and the revenue
yielded by the last unit sold.
The marginal revenue curve will lie below the
demand curve or the average revenue curve.

Marginal Revenue Curve for Linear
Demand Curves
• Derive the marginal revenue curve for q = 10 – P.
– Solve for P so P = 10 – q
– MR = 10 – 2q
• For a linear demand curve, the marginal revenue curve has the
same intercept but twice the slope.
– If P = a – bQ, MR = a – 2bQ

Marginal Revenue Curve
Price
Quantity
Demand: q=10-P or P = 10-q
10
5 10
MR = 10 – 2q

Supply Decision for a Price Taking Firm
• When does it make sense to assume that firms are price takers?
• Suppose the market demand for corn is:
– Q = 16,000,000,000 – 2,000,000,000P
– P = 8 – Q/2,000,000,000
– Assume there are 1 million corn farmers who each produce
10,000 bushels per year
– P = $3 and Q = 1 billion bushels
– What if one farmer decides to stop growing corn?
– Q = 9,999,990,000 and P = $3.000005
– If one farmer doubles output, P = $2.999995

• If there are many suppliers in the market, each producing a small
percentage of total output, their decisions will have no impact on
the market price.
• Short Run Profit Maximization
– A price taking firm will maximize profits by producing a level of
output where ....?
– P* = MC
– The profit maximizing condition is still MR = MC.

Price
Quantity
SMC
SAC
P*=MR
q*

Profits for a Price Taking Firm
• Profit = π = Total Revenue – Total Cost = P*q* - STC(q*)
• Profit = π = q*(P* - STC/q*) = q*[P* - SAC(q*)]
– If P* > SAC(q*), then profit > 0
– If P* = SAC(q*), then profit = 0
– If P* < SAC(q*), then profit < 0

Economic Profit: P* > SAC
Price
Quantity
SMC
SAC
P*=MR
q*

Economic Loss: P* < SAC
Price
Quantity
SMC
SAC
P*=MR
q*

The Price Taking Firm’s Supply Curve
Price
Quantity
SMC
SAC
P*=MR
q*
P**
q**
P***
q***

The Shut Down Decision
• If profits are negative, the firm must compare losses from
producing some output to how much it would lose if it shut
down: q = 0.
• If it shuts down it only loses its fixed costs.
• Therefore, a firm will stay open as long as it can cover its VC.
– P x q ≥ SVC or P ≥ SVC/q = AVC
• To stay open price must be greater than or equal to short run
average variable cost.

The Price Taking Firm’s Supply Curve
Price
Quantity
SMC
SAC
P*=MR
q*
P**
q**
P***
q***
PSD
qSD

Summary
• Any firm maximizes profits by producing where MR=MC.
• If a firm faces a downward sloping demand curve, MR < P and the
marginal revenue curve will lie below the demand curve.
• With many firms in the market one firm’s actions will not affect
the market price. Therefore, P = MR.
• A price taking firm will maximize profits where P = MC, and the
firm’s supply curve is its short-run marginal cost curve.
• If price is less than average variable cost, the firm will shut down
and only incur its fixed costs.

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