ECON191 (Spring 2011)
27 & 29.4.2011 (Tutorial 9)
Chapter 10 Market Power: Monopoly and Monosony
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Monopoly: market with only one seller
Demand function, TR, AR, and MR
 MR(q)  AR(q) for all q except q = 0.
 In order to sell 1 extra unit, the monopoly must lower the price
for that extra unit as well as for the previous units.
P
a
 There is an exact relationship between MR and AR.
 Slope of MR is twice as steep as the slope of DD (AR).
p=a – bq
MR =a –2bq
MR
AR=DD
Q
 Suppose we have a linear inverse DD function: p  a  bq
dTR(q)
 MR(q) 
dq
 TR(q)  p(q)q  aq  bq 2
 MR  a  2bq
 Slope of MR is –2b while slope of DD is –b.
Profit Maximization of a monopoly
P
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MC
P*
MR
Q*
DD
 A monopolist’s objective is to maximize profit.
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The monopolist is facing a maximizing problem.
Given: Demand function: P(Q)
Total cost function: C(Q)
Q
A monopoly will never price a commodity on the inelastic portion of the demand curve
The more inelastic the demand, the larger the divergence between MC and P. (The higher
the ability the monopolist to charge a price above MC)
The steeper the demand curve, the higher the monopoly power
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Example: (P.347)
Suppose the cost of production is C(Q) = 50 + Q2 and the demand is given by P(Q) = 40 – Q.
Find the monopoly price, quantity and the level of profit.
The monopolist’s profit is maximized when MR = MC
Demand curve is given by P(Q) = 40 – Q, thus MR = 40 – 2Q
dC (Q)
 2Q
Total cost is C (Q)  50  Q 2 ,thus MC =
dQ
Equating MR and MC, 40 – 2Q = 2Q
Q* = 10, P* = 30
Profit = 300 – 150 = 150
Monopoly power
MR and the price elasticity of demand
 Price elasticity of demand (facing the firm):
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
(What is the interpretation?)

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 A monopoly’s profit is maximized when MR = MC,

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when Ed    P(Q)  MC (Q)
 The price charged by the monopolist inversely related to E d .
 The above expression shows that when Ed   , MR = P. That means the more inelastic
the demand (the smaller the absolute value of E d ), the larger the divergence between MC
and P. (The higher the ability the monopolist to charge a price above MC)
 The steeper the demand curve, the higher the monopoly power
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A firm’s market power depends on the elasticity of market demand, the level of
competition, number of firms in the market, etc.
Elasticity of market demand positively affects the elasticity of demand facing the firm
The more competitive the market is, the larger the absolute value of E d
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Measuring monopoly power: Lerner’s index
 Measure of monopoly power calculated as excess of price over MC
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
(0 < L < 1)
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High monopoly power does not necessarily imply high profit, it depends on AC relative to
price
Example: Supermarkets and convenience stores (P.358)
 Supermarkets: several firms selling similar products
 No single supermarket can raise its price very much without losing customers to other
stores
 The elasticity of demand for individual supermarket: –10
 P = MC/(1 – 0.1) = 1.11MC
 Lerner index: (P – MC)/P = –1/Ed = 0.1
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Convenience stores: charge a higher price than supermarkets (less elastic demand)
The elasticity of demand for individual supermarket: –5
P = MC/(1 – 0.2) = 1.25MC
Learner index: (P – MC)/P = –1/Ed = 0.2
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Convenience stores have more monopoly power.
Convenience stores do not have higher profits than supermarkets however, as volume is
far smaller and average fixed costs are larger
Welfare implications and socially optimal price and quantity
P
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We measure the welfare of the society by consumer surplus
and producer surplus.
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Consumer surplus: total willingness to pay – actual payment
Produce surplus: total revenue – total variable cost
Total surplus: (CS + PS)
MC
CS
p*
DWL
PS
MR
DD
q*
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Following the profit maximizing rules:
Qmonopolist’s profit is maximized, however it is
not socially optimal. (Since at q*, p>MC). A kind of dead weight loss is generated.
From the society point of view, the price is too high and the quantity is too little.
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Other issues: rent seeking, price regulation
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The multi-plant firm
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For some firms, production takes place in more than one plant each with different costs.
Firm must determine how to distribute production between both plants
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Production should be split so that the MC in the plants is the same. Output is chosen
where MR = MC.
 Profits is maximized when MR = MC at each plant
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Total output:
Total profit:
Firm should increase output from each plant
until the additional profit from last unit
produced at Plant 1and Plant 2 equals 0
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Similarly, for Plant 2,
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The firm should produce so that
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Example: Chapter 10 Problem 9
A drug company has a monopoly on a new patented medicine. The product can be made in
either of two plants. The costs of production for the two plants are MC1 = 20 + 2Q1, and MC2 =
10 + 5Q2. The firm’s estimate of the demand for the product is P = 20 - 3(Q1 + Q2). How much
should the firm plan to produce in each plant? At what price should it plan to sell the product?
From the diagram, we see that only MC2 is relevant because MC1lies above the demand
curve.
Price
30
MC2 = 10 + 5Q2
DD: P = 20 – 3Q2.
MR = 20 – 6Q2.
MC1 = 20 +2Q1
20
To determine the profit-maximizing level of
output, equate MR and MC2:
20 – 6Q2 = 10 + 5Q2, or Q = Q2 = 0.91
P = 20 – 3(0.91) = 17.3
17.3
10
MR
0.91
3.3
D
6.7
Q
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Natural monopoly and regulation
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Natural monopoly: A firm that can produce the entire output of an industry at a cost
lower than what it would be if there were several firms.
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It usually arises when there are large economies of scale
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Splitting the market into two firms results in higher AC for each firm than when only
one firm was producing
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Unregulated, the monopolist would produce Qm
and charge Pm.
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If the price were regulate to be Pc, the firm would
lose money and go out of business.
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Setting the price at Pr giving profits as large as
possible without going out of business
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It is very difficult to estimate the firm's cost and
demand functions because they change with
evolving market conditions. (Alternatives?)
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Rate of return regulation: the firms to set a maximum price based on the expected rate or
return that the firm will earn.
Regulatory agencies often use
to determine price
Problems: (1) Firm’s capital stock is difficult to value, (2) “Fair” rate of return based on
actual cost of capital, that cost is based on regulatory behavior and investor’s perception
of allowed rates in the future (3) Time lags in regulatory response to changes in cost and
other market conditions
Price Cap set based on firms variable costs, past prices, and possibly inflation and
productivity growth
A firm is typically allowed to raise its price each year without approval from regulatory
agency by amount equal to inflation minus expected productivity growth
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Monopsony
 Monopsony: a market in which there is a single buyer.
 Monopsony power is the ability of the buyer to affect the price of the good and pay less
than the price that would exist in a competitive market.
 Marginal value: the additional benefit derived from purchasing one more unit of a good
 Demand curve is the MV curve
 Average expenditure: the additional cost of buying one more unit of a good
 Supply curve is the AE curve as it shows how much must be paid per unit
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Marginal expenditure: the additional cost of buying one more unit of a good
 Upward sloping supply implies the ME curve must lie above AE
 If a buyer wants to buy one more unit, he has to pay a higher price for that unit as well as
for the previous units.
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
Total expenditure =
Marginal expenditure =
(What is the interpretation?)
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Typically a monopsony chooses to buy until the benefit from last unit equals that unit’s
cost
 Marginal value = Marginal expenditure (MV = ME)
Monopsony power
 Price elasticity of supply (facing the firm):
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A monopsony’s benefit is maximized when MV = ME

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
Measure of monopsony power calculated as excess of MV over price

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(0 < L < 1)
The smaller the elasticity of supply facing the buyer, the higher the monopsony power to
mark down the price (pay a price lower than MV)
The degree of monopsony power depends on the elasticity of market supply, number of
buyers, interaction among buyers, etc
Example: Chapter 10, Problem 14
The employment of teaching assistants (TAs) by major universities can be characterized as a
monopsony. Suppose the demand for TAs is W = 30,000 - 125n, where W is the wage (as an
annual salary), and n is the number of TAs hired. The supply of TAs is given by W = 1000 +
75n.
(a) If the university takes advantage of its monopsonist position, how many TAs will it hire?
What wage will it pay?
Supply curve = Average expenditure curve: W = 1000 + 75n
2
2
Total Expenditure = AE(n)75n = 1000n + 75n
Marginal Expenditure = dTE/dn = 1000 + 150n
A monopsonist, the university would equate marginal value (demand) with
marginal expenditure to determine the number of TAs to hire: 30000 – 125n =
1000 + 150n
n = 105.5
Substituting n = 105.5 into the supply curve to determine the wage:
1000 + (75)(105.5) = $8909 annually
(b) If, instead, the university faced an infinite supply of TAs at the annual wage level of
$10,000, how many TAs would it hire?
With an infinite number of TAs at $10000, the supply curve is horizontal at
$10000. Total expenditure is 10000n, and marginal expenditure is 10000. Equating
marginal value and marginal expenditure: 30000 – 125n = 10,000
n = 160
Comparing Monopoly and Monopsony
Monopoly
Monopsony
MR < P (MR below the demand, AR)
ME > P ( ME above the supply, AE)
P > MC
P < MV
QM < QC (competitive quantity)
QM < QC (competitive quantity)
PM > PC (competitive price)
PM < PC (competitive price)
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