Post on 11-Feb-2016
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Chapter 17
The Age of Entrepreneurship:Monopoly
DefinitionsRevenue = price * quantity
TR=pqProfit = Revenue – Costs
π = TR – C Marginal revenue= ΔTR/Δq
Change in total revenue from selling an extra unit of output
2
A Monopoly’s Total, Average, and Marginal Revenue
A Monopoly’s Revenue Marginal Revenue
∆TR/∆Q = MR How does MR compare to P in a monopoly market?
To sell an extra unit the monopolist has to lower price.
He sells the extra unit at the new price (thus total revenue rises), but lowers price on all previous units sold (which reduces total revenue)
MR<P
A Monopoly’s RevenueAn increase in sales has two effects on total
revenue The output effect—revenue earned on the extra unit The price effect—revenue lost on previous units.
$5 $5 $5
$4 $4 $4 $4
P Q TR MR
$5 3 15$1$4 4 16
Note that MR<P
MR=P + (Δp/Δq)(q)
Total Revenue
Quantity
Price
$1110
9876543210
–1–2–3–4
1 2 3 4 5 6 7 8
Total Revenue increases and then decreases.
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Total Revenue
Q
Total Revenue
Q
Marginal Revenue
• Marginal Revenue is the slope of the total revenue curve
• Marginal revenue is positive (negative) when total revenue is increasing (decreasing)
• Marginal revenue is zero when total revenue reaches a maximum
Marginal Revenue Marginal revenue curve
Below demand curve Slope = 2* Slope of demand curve MR=P + (Δp/Δq) (q) MR=p-|Δp/Δq|(q)=p(1-1/|ξ|)
ξ = elasticity of demand
8
Marginal revenue and demand 9
The marginal revenue curve is steeper than the demand curve. With a straight-line demand curve, the slope of the marginal revenue curve is twice the slope of the demand curve
Quantity 0
Price
D
p = A - bq
MR = A - 2bq
a
• Inverse demand function p= f(q)=A-bq Price – from any given quantity
• Demand function: q = f(p)= (A-p)/b quantity demanded at each price
Demand and Elasticity 10
Quantity 0
Price
pMAX
A
p1μ
|ξ|>1
|ξ|=1
|ξ|<1
Quantity demanded: q = A - bp
Pricing and Quantity Decisions The Elasticity Rule
The firm will never choose a point on inelastic portion of demand curve When |ξ|<1, then marginal revenue is negative Selling an extra unit of output will reduce profit
It increases costs and decreases revenue
11
Optimal Price and Quantity Results Profit-maximizing quantity, q*
Increase production if MR>MC Until MR=MC
Profit-maximizing price, p* On demand curve, at q*
12
Optimal price and quantity 13
The profit-maximizing price and quantity equate marginal cost with marginal revenue
Quantity 0
Price
D
MR
MC
α
q*
ρp*
Optimal Price and Quantity Results # 2: Profit-maximizing price
On the demand curve At optimal quantity MR=p(1-1/|ξ|)
p=MR(1-1/|ξ|); MR=MC p=MC(1-1/|ξ|)
14
Optimal Price and Quantity Results Deadweight loss
Dollar measure - Loss to society For
Marginal social benefit > marginal social cost No production
Profit-maximizing firm
15
Optimal Price and Quantity Results Societal consumer surplus
Difference – consumers Willing to pay Selling price (pays)
Producer surplus Difference – producer
Receives (selling price) Cost of production
16
The socially optimal price 17
The price-quantity combination that maximizes the sum of consumer surplus and producer surplus equates marginal cost with price (willingness to pay).
Quantity 0
Price
MR
MC
b
f
D
d
p
q
Two-Part Tariffs
Monopolist charges A lump sum fee A unit price
The two part tariff allows the monopoly to Capture consumer surplus Earn extra-normal profit Sell the optimal output level
18
Two-Part Tariffs
Assume there are identical consumers in the market Consumers buy more of the good as its price declines Each gets the same consumer surplus
Two-Part Tariffs20
Quantity 0
Price
MR
ed
MCb
a
c
Fee
Unit Price
The producer charges each consumer, in addition to the per-unit price, a fixed fee equal to her share of the consumer surplus: Fee=CS/N
Two-Part Tariffs and Profit21
Quantity 0
Price
MR
ed
MCb
a
c
Unit Price
The producer earns a higher profit
Profit
Two-Part Tariffs and A Higher Profit22
Quantity 0
Price
MR
e
MCUnit Price
The producer earns a higher profit if he lowers the price to MC and charges a higher fee
Profit
Two-Part Tariffs and Efficiency23
Quantity 0
Price
MR
e
MCUnit Price
The producer is efficient:• He sells the socially optimal
amount• Sets a price equals MC
Profit
E
A two-part tariff enables the monopolist to earn positive profits
Quantity 0
Price MC
AC
q
c
p
Two-Part Tariffs when the monopoly realizes a loss
Problems with uniform Pricing
When consumers are not identical Some buyers with a willingness to pay above marginal cost do
not buy because the price is high Lowering price to capture this market segment may reduce
monopoly profit.
When the monopoly charges a single price……
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Transactions represented by the blue line are not undertaken
Quantity 0
Price
MR
MC
b
f
D
d
p
q
B
Two part Tariff may not be optimal when consumers are not identical
The Elizabeths are willing to pay the fixed fee, but the Geoffreys are not
Quantity 0
Price
DGeoffreysDElizabeths
p*
q1 q2
A
Non uniform pricing / Price Discrimination
Separate consumers Groups/ markets Slightly different products
Tastes No reselling
Different prices
Price Discrimination Price discrimination
Charge different prices to different consumers Segmented markets
Physical separation/other characteristics Arbitrage - impossible
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Price Discrimination: the Market for Movie Tickets
Demand
Marginal cost
MRDemand
Q 2
MR
Q 1
(b) Senior citizen demand(b) Demand by people below age 60PP1
P2
The relative prices charged will depend on the price elasticity of demand in each market:
21
21
11
11PP
Price Discrimination
#4: Price Discrimination in Segmented Markets Produce q* (profit maximizing quantity)
Marginal revenue (any market) = marginal cost Marginal revenue (one market) = Marginal revenue (other) market MRg=MRe=MCt
Practice Questions: #1
Given: Inverse demand: P=100 - Q MC constant at $50 and no fixed costs
Find Socially optimal output level Monopoly output and price If the monopoly can charge a fee in addition to the above price,
what is the fee? The profit? What is the optimal price and fee? The profit?
Practice Questions: #2
Given: Two groups of buyers: P1=130-2Q1 and P2=60-Q2 MC constant at $50 and no fixed costs
Find Price and quantity to each group Is the monopoly output socially efficient?