Chapter 10 Market Power:

Monopoly & Monopsony

CHAPTER 10 OUTLINE

10.1 Monopoly

10.2 Monopoly Power

10.3 Sources of Monopoly Power

10.4 The Social Costs of Monopoly Power

10.5 Monopsony

10.6 Monopsony Power

• A Monopoly is the only supplier of a good for which there is no close substitute.

• A monopoly’s output is the market output, and the demand curve a monopoly faces is the market demand curve.

• Entry is not possible.

• Unlike a competitive firm, a monopolist can set its price.

• A monopolist has to decide the output (q) to produce and the price per unit to charge (P) to maximize profit.

MONOPOLY10.1

Average Revenue and Marginal Revenue

● marginal revenue Change in revenue resulting from a one-unit increase in output.

To see the relationship among total, average, and marginal revenue, consider a firm facing the following demand curve:

P = 6 – Q

TABLE 10.1 TOTAL, MARGINAL, AND AVERAGE REVENUE

PRICE (P) QUANTITY (Q)TOTAL REVENUE

(R)MARGINAL REVENUE

(MR)AVERAGE REVENUE

(AR)

$6 0 $0 — —

5 1 5 $5 $5

4 2 8 3 4

3 3 9 1 3

2 4 8 1 2

1 5 5 3 1

• Average Revenue & Marginal Revenue

1. Demand faced by the monopolist is the market demand (i.e. downward sloping) P = 6 − Q.

2. The monopolist’s average revenue curve is also the market demand curve .

3. The marginal revenue curve:MR = 6 −2Q

D=AR

Market demand: P=a-bQMarginal Revenue: MR=a-2bQ

For all linear demand functions with the form:P(q)= a-bq

TR(q)=P*q MR=TR/q

=(Pq+qP)/q= P+q(P/q)

Since P(q)= a-bq P/q = -b (the slope) MR= P-bq = a-bq-bq = a-2bq

MR=a-2bq

For all linear demand functions with the form:P(q)= a-bq

MR(q)=a-2bq1. MR curve is a straight line that starts at the same

point on the vertical (price) axis as the demand curve.

2. The MR has twice the slope of the demand curve.3. The MR curve hits the horizontal (quantity) axis at

half the quantity as the demand curve.

Marginal Revenue Curve and Demand Curve

Practice Questions

The market demand is Q=100-5P. Find the MR function.

1. Find the inverse demand function. Solve for P in Q=100-5P. Find P=20-(q/5) that is P=20-0.2q Slope: -0.2 and intercept 20

2. Then MR is MR(q) = 20-2*0.2 qSo, MR(q)= 20-0.4q

• The Monopolist’s Output Decision

• At Q*, MR = MC. • If the firm produces Q1—it

sacrifices some profit because the extra revenue exceeds the cost of producing them.

• Increase Q* to Q2 would reduce profit because the additional cost would exceed the additional revenue.

Profit Is Maximized When MR=MC

Example of Profit Maximization

(a) shows total revenue R, total cost C, and profit.(b) shows AR, MR, AC, and MC.

MR is the slope of the total revenue curve, and MC is the slope of the total cost curve.

The profit-maximizing output is Q* = 10, the point where MR=MC (i.e., slopes of the total revenue and total cost curves are equal).

The profit per unit is $15, the difference between average revenue and average cost. Because 10 units are produced, total profit is $150.

Question: Consider a Monopolist with TC(q)= 50+ q2 and MC(q)= 2q. Let the market demand be P=40-q. Find the profit max price & quantity. Determine the economic profit.

P=40-q so we know MR=40-2q

Profit Max Rule: MR=MC

40-2q=2q , solve for q. q*=10.

Sub q*=10 into the demand functionP=40-q =40-10, so P*=30

Economic profit= TR-TC= P* q*-TC=30*10-50-102 =150

A Rule of Thumb for PricingWe want to translate MR=MC into a rule of thumb that can be easily applied in practice.

The extra revenue from supplying one more unit has two components:1) Producing one extra unit and selling it at price P brings in revenue (1)*(P) = P.2) Because the firm faces a downward-sloping demand curve, selling this extra

unit results in a small drop in price ΔP/ΔQ, which reduces the revenue from all units sold (i.e., a change in revenue Q[ΔP/ΔQ]).

Thus,

(Q/P)(ΔP/ΔQ) is the inverse of the elasticity of demand, 1/Ed, measured at the profit-maximizing output

Because the firm’s objective is to maximize profit, we can set MR=MC

Rearranging this equation:

Or, we can express price directly as a markup over marginal cost:

With downward-sloping demand, when output increases (say of 1 unit), then the price falls. The change in total revenue depends on the elasticity of the demand.

Recall If demand is elastic, TR increases when price falls.If demand is inelastic, TR decreases when price falls.

When q increases, p falls, then1. If demand is elastic, MR is positive 2. If demand is inelastic, MR is negative3. If demand is unitary elastic, MR is zero

Profit-maximizing P* will NEVER be in the inelastic part of the demand. The monopolist will set a price in the elastic part of the demand

Consider: Shifts in Demand

A monopolist has no supply curve —i.e., there is no one-to-one relationship between price and quantity produced. In (a), the demand curve D1 moves to D2.

The new marginal revenue curve MR2 intersects MC at the same point as the old marginal revenue curve MR1.

The profit-maximizing output remains the same, although price falls from P1 to P2.

In (b), MR2 intersects MC at a higher output level Q2.

Because demand is now more elastic, price remains the same.

• The Effect of a Tax

Suppose a specific tax of t dollars per unit is levied, so that the monopolist must pay t dollars to the government for every unit it sells.

With a tax t per unit, the firm’s effective marginal cost is increased by the amount t to MC + t. In this example, the increase in price ΔP is larger than the tax t.

Suppose a firm has two plants. What should its total output be, and how much of that output should each plant produce? Let Q1 and C1, Q2 and C2 be the output and cost of production for Plant 1 and 2.

QT = Q1 + Q2 be total output. Then profit

The Multiplant Firm

Thus, the profit maximization rule for the multiplant firm is:

The total output should be divided between the two plants so that (1) marginal cost is the same in each plant, and (2) the MR should be equal to marginal costs.

A firm with two plants maximizes profits by choosing output levels Q1 and Q2 so that marginal revenue MR (which depends on total output) equals marginal costs for each plant, MC1 and MC2.

Production with Two Plants

Example

P = 120 - 3Q demandMC1 = 10 + 20Q1 plant 1MC2 = 60 + 5Q2 plant 2a. What are the monopolist's optimal total quantity and price?

Step 1: Derive MCT as the horizontal sum of MC1 and MC2

Inverting marginal cost (to get Q as a function of MC), we have:

Q1 = -1/2 + (1/20)MC1 Q2 = -12 + (1/5)MC2

Now, sum Q1 and Q2 to get QT = Q1 + Q2 =(-1/2 + (1/20)MC1)+(-12 + (1/5)MC2 ). Hence QT =-12.5+ (1/20)MC1 + (1/5)MC2

Let MCT equal the common marginal cost level in the two plants. Then: MCT= MC1= MC2 and QT =-12.5 + (1/20)MC1 + (1/5)MC2 becomes QT =-12.5 + (1/20)MCT + (1/5)MCT

That is QT = Q1 + Q2 = -12.5 + .25MCT

And, writing this as MCT as a function of QT:MCT = 50 + 4QT

Using the monopolist's profit maximization condition:

MR = MCT 120 - 6QT = 50 + 4QT

QT* = 7

P* = 120 - 3(7) = 99

b. What is the optimal division of output across the monopolist's plants?

MCT (QT* )= 50 + 4(7) = 78

Therefore,

Q1* = -1/2 + (1/20)(78) = 3.4

Q2* = -12 + (1/5)(78) = 3.6

MONOPOLY POWER

• Measuring Monopoly Power

10.2

Remember: For the competitive firm, P=MC; for the firm with monopoly power, P>MC.

● Lerner Index of Monopoly Power Measure of monopoly power calculated as excess of price over marginal cost as a fraction of price.

This index of monopoly power can also be expressed in terms of the elasticity of demand.

The Rule of Thumb for Pricing

The markup (P − MC)/P is equal to -1/Ed. If the firm’s demand is elastic, as in (a), the markup is small and the firm has little monopoly power.The opposite is true if demand is relatively inelastic, as in (b).

Elasticity of Demand and Price Markup

SOURCES OF MONOPOLY POWER10.3

Three factors determine a firm’s market power.

1. The elasticity of market demand.

2. The number of firms in the market.

3. The interaction among firms.

• Firms might compete aggressively, undercutting one another’s prices to capture more market share. This could drive prices down to nearly competitive levels.

• Firms might even collude (in violation of the antitrust laws), agreeing to limit output and raise prices. Collusion can generate substantial monopoly power.

The Interaction Among Firms

THE SOCIAL COSTS OF MONOPOLY POWER10.4

Deadweight Loss from Monopoly Power

Competitive price and quantity:Pc and Qc,

A monopolist’s price and quantity: Pm and Qm.

Consumers lose A + B Producer gains A − C.

The deadweight loss is B + C.

Price Regulation

If left alone, a monopolist produces Qm and charges Pm.

When the government imposes a price ceiling of P1 the firm’s AR and MR are constant and equal to P1 for output levels up to Q1.

For Q>Q1, the original AR and MR curves apply.

The new marginal revenue curve is, therefore, the dark purple line, which intersects the MC at Q1.

When P=Pc, at the point where MC intersects AR curve, output increases to its maximum Qc.

This is the output that would be produced by a competitive industry.

Lowering price further, to P3 reduces output to Q3 and causes a shortage, Q’3 − Q3.

• Natural Monopoly● Firm that can produce the entire output of the market at a cost lower

than what it would be if there were several firms.

A firm is a natural monopoly because it has economies of scale (declining average and marginal costs) over its entire output range. If price were regulated to be Pc the firm would lose money and go out of business. Setting the price at Pr yields the largest possible output consistent with the firm’s remaining in business; excess profit is zero.

Regulating the Price of a Natural Monopoly

• Regulation in Practice

● rate-of-return regulation Maximum price allowed by a regulatory agency is based on the (expected) rate of return that a firm will earn.

The difficulty of agreeing on a set of numbers to be used in rate-of-return calculations often leads to delays in the regulatory response to changes in cost and other market conditions.The net result is regulatory lag—the delays of a year or more usually entailed in changing regulated prices.

MONOPSONY10.5

● oligopsony Market with only a few buyers.

● monopsony power Buyer’s ability to affect the price of a good.

● marginal value Additional benefit derived from purchasing one more unit of a good.

● Total expenditure Total cost of buying Qs units of a good. TE=P*Qs

● marginal expenditure Additional cost of buying one more unit of a good. ME=TE/Qs

● average expenditure Price paid per unit of a good. AE=TE/Qs

In (a), the competitive buyer takes market price P* as given. Therefore, marginal expenditure and average expenditure are constant and equal; quantity purchased is found by equating price to marginal value (demand).

In (b), the competitive seller also takes price as given. Marginal revenue and average revenue are constant and equal; quantity sold is found by equating price to marginal cost.

Competitive Buyer Compared to Competitive Seller

The market supply curve is monopsonist’s average expenditure curve AE. Marginal expenditure (ME) lies above AE.The monopsonist purchases Q*m, where marginal expenditure and marginal value (demand) intersect. The price paid per unit P*m is then found from the average expenditure (supply) curve.

In a competitive market, price and quantity, Pc and Qc, are both higher.

Pc and Qc are found at the point where average expenditure (supply) and marginal value (demand) intersect.

Monopsonist Buyer

Profit Max Rule: ME=MV(MV is also the demand curve)

• Monopsony and Monopoly Compared

a) The monopolist produces where MR=MC. AR exceeds MR, so that P>MC. b) The monopsonist purchases up to the point where ME=MV. ME exceeds

AE, so that MV exceeds P.

D=AR

MONOPSONY POWER10.6

Monopsony power depends on the elasticity of supply. When supply is elastic, as in (a), marginal expenditure and average expenditure do not differ by much, so price is close to what it would be in a competitive market. The opposite is true when supply is inelastic, as in (b).

Monopsony Power: Elastic versus Inelastic Supply

Relationship between Supply and ME

If Supply curve P = c+dQ, then ME =c+2dQ

ExampleSay that the (inverse) supply is P=4Q+3Calculate the ME

Answer: Double the slope in the expression of the (inverse) supply and get ME

That is double “4” in P=4Q+3 and get ME =8Q+3

For all linear supply functions with the form:

P(q)= c+dq Total Expenditure :TE(q)=P*q

ME=TE/q

=(Pq+qP)/q

= P+q(P/q)

Since P(q)= c+dq P/q = d (the slope) ME= P+dq =(c+dq)+dq = c+2dq

ME= c+2dq

We have shown that:

ME=TE/qs =(Pq+qP)/q = P+q(P/q)

ME= P+ P*(1/P) *q(P/q) =P+P*(q/P)*(P/q)

(q is the quantity supplied)

(q/P)*(P/q) is the inverse of the elasticity of supply Es

ME= P+P*(1/Es)

Recall that the profit max rule: MV=ME

At the optimal Q, MV= P+P*(1/Es)

(MV-P)/P=1/Es Since Es>0 (law of supply), so MV>P

Practice:

The employment of nurses by the only local hospital can be

characterized as a monopsony.

Demand for nurses: w=30,000-125q

Supply for nurses: w=1000+75q

a. Find the optimal w* and employment of nurses for the hospital.

b. If instead, the hospital faced an infinite supply of nurses at the wage level of $10,000, how many nurses would it hire?

a.

Supply for nurses: w=1000+75q

So we can derive that ME=1000+150q

Profit max rule is ME=MVWe know that MV (marginal value curve) is the demand curve

So 1000+150q=30,000-125q

q*=106

Sub it into the supply curve, w* =1000+75*106=8950

b. In this new condition, the supply curve changes. It is now a horizontal line at $10,000. This means that the hospital is no longer a monopsonist. It is a competitive buyer now.

New supply curve is W=10,000

It means that when it hires one more nurse, the marginal expenditure is always 10,000

ME=supply curve=10,000

Profit Max Rule: MV=ME30,000-125q=10,000

q*=160

• Sources of Monopsony Power

• Elasticity of Market Supply• Number of Buyers• Interaction Among Buyers

• The Social Costs of Monopsony Power

Competitive price and quantity: Pc and Qc,

Monopsonist’s price and quantity: Pm and Qm.

Change in buyer (consumer) surplus: A − B. Producer surplus falls by A + C

Deadweight loss : B and C.

• Bilateral Monopoly

● bilateral monopoly Market with only one seller and one buyer.

• Monopsony power and monopoly power will tend to counteract each other.

• The optimal P and Q depend on the relative bargaining position of the two parties.