Econ 330 Lecture 9 Monday, October 21

The inefficiency of monopoly Today’s lecture The inefficiency of monopoly

A completely different set-up But first… A completely different set-up

Please turn off laptops tablets phones etc!

There is one unit of a good (or service) to be traded For example, a hair cut Value to the buyer is v v is measured in monetary units, say in $ or ₺ (or € or ₨ or ₧) Cost to the seller is c c is also measured in $, ₺, €, ₨,or ₧ If v > c, then trade creates a welfare of v – c > 0. If trade occurs at price p such that p > c and p < v, then the consumer’s surplus is v – p, and the producer’s surplus is p – c.

Example v = 10, c = 5; trade occurs at price p = 8. CS = 10 – 8 = 2 PS = 8 – 5 = 3 Total (social) welfare CS + PS = 2 + 3 = 5. It will inefficient if trade doesn’t occur for whatever reason. Then we say that there is a deadweight loss.

Tax The government says whenever there is trade, the buyer must pay a tax of t = 6. The buyer’s value if 10, she will not pay more than 4. This is less than the seller’s cost c = 5. Because of the tax, there will be no trade. So, no CS no PS And certainly no tax revenue!  DWL = 5!

Market power The seller is a monopoly, the buyer’s v is not known to the seller. The seller thinks that v can be either 12 or 8, with equal probability of ½. The seller sets the price at 12! (convince yourself that this is the prof max price) Expected profits are (12 – 5)x½ = 3.5 (If P = 8 profits are 8 – 5 = 3. So P = 8 is not the prof max price) Expected CS = 0. DWL = (8 – 5)x½ = 1.5 Why? Since v > c efficiency requires that trade always occurs. So total (social) welfare could have been (8 – 5)x½ + (12 – 5)x½ = 5.

A few definitions Social welfare is defined as the sum of Consumer Surplus and Producer Surplus.

Efficiency defined A market outcome is (said to be) efficient if the sum of consumer surplus (CS) and producer surplus (PS) is maximized. The competitive equilibrium is efficient. The monopoly equilibrium is not efficient.

The efficiency of the competitive equilibrium $/output unit The efficient output level Qe satisfies p(Q) = MC(Q). Total gains-to-trade is maximized. Demand CS MC(Q) (supply) p(Qe) PS Qe Q

On a demand and supply graph the CS is shown as the area under the demand curve and above the price line, up to the equilibrium quantity. The PS is shown as the area above the supply curve (or the marginal cost curve) and under the price line up to the equilibrium quantity.

The Inefficiency of Monopoly $/output unit Q* is the monopoly output. Q* is less than the efficient quantity Qe. Demand CS p(Q*) MC(Q) (supply) PS Q* Q MR(Q)

The Inefficiency of Monopoly $/output unit The monopoly produces less than the efficient quantity, Demand p(Q*) MC(Q) (supply) DWL p(Qe) Q* Qe Q MR(Q)

The in-class exercise The Dead Weight Loss of Monopoly

There are three groups of potential readers. A well known publishing company has bought the rights to the latest Orhan Pamuk novel at a neat sum of 250,000 TL. There are three groups of potential readers. A group of 10,000 Pamuk-crazy individuals will pay up to 20 TL for the book. A second group of 30,000 people will buy the book if its price is not higher than 15 TL. In addition, there are 50,000 readers who will pay only up to 9 TL. It costs 5 TL to print and distribute a book. What price will maximize profits? Compute the deadweight loss when profits are maximized.

Suggested answers

There are 3 candidates for profit maximizing price: 20 15 9 There are 3 candidates for profit maximizing price: 20 15 9! Why is P = 18 not a good price?

We will use brute force! Compute profit at all three prices If P = 20 (only group 1 buy) profit (20 – 5)x 10,000 = 150,000 If P = 15 (group 1 and 2 buy) profit (15 – 5)x40,000 = 400,000 If P = 9 (all three groups buy) profit (9 – 5)x 90,000 = 360,000 The profit maximizing price is P =15, only the first two groups buy.

Welfare and inefficiency (DWL) CONSUMER SURPLUS Group 1 10,000x(20 – 15) = 50,000, Group 2 0 Total CS is 50,000

Welfare and inefficiency (DWL) Producer Surplus (excluding the 250,000TL fee for the author) (15 – 5)x40,000 = 400,000 Social welfare = CS + PS 50,000 + 400,000 = 450,000 BUT Social welfare could have been as large as 650,000!

So, if this is true … We are falling short of this upper bound (our full potential) by 200,000! This 200,000 is the inefficiency, DWL, of monopoly!

DWL = 50,000x(9 – 5) = 200,000 This is the (additional) surplus that could have been realized if we could sell the book also to the third group at some price between 5 and 9.

Again, use brute force! Consider a sufficiently low (but profitable) price, so that all three groups can buy the book. Say P = 8, Re-compute the CS and PS at P = 8.

Consumer Surplus Group 1 CS 10,000x(20 – 8) = 120,000 Group 2 CS 30,000x(15 – 8) = 210,000 Group 3 CS 50,000x(9 – 8) = 50,000 The total CS is 380,000

Producer Surplus (excluding the 250,000 TL fee) (8– 5)x90,000 = 270,000 Social welfare = 650,000 This is 200,000 more than the social welfare achieved with the monopoly price.

Let’s see this on the graph

DWL DWL = (9 – 5)x50,000 = 200,000 Profit max price Marginal cost Monopoly quantity

Computing the DWL: The real world NOW… Computing the DWL: The real world

Big question: Is the deadweight loss due to market power substantial in advanced industrialized economies? Because if it is not, then as George Stigler said back in 1966, “economists might serve a more useful purpose if they fought fires or termites instead of monopoly.”

Who is George Stigler? George Joseph Stigler (1911–1991) won the Nobel in Economic s in 1982. He was a key leader of the Chicago School of Economics, along with his close friend Milton Friedman.

Prof Stigler was a humorous person He was once asked why there were no Nobel Prizes awarded in the other social sciences, sociology, psychology, history, etc. “Don’t worry”, he said, “they have already have a Nobel Prize in literature.”

"No scientific discovery is named after its original discoverer." Stigler's law This is Stephen Stigler, George’s son, professor of statistics at Uni of Chicago "No scientific discovery is named after its original discoverer." Stigler named the sociologist Robert K. Merton as the discoverer of "Stigler's law", consciously making "Stigler's law" exemplify itself.

Back to work: Estimating the DWL

Monopoly equilibrium and the DWL 6 = DWL 2 = 4 = 8 =

We can compute the DWL in this example because we know the cost and demand functions. But when we want to replicate this computation for real industries where firms have market power, (that may be monopolies or oligopolies) we run into some serious data problems. We don’t know the cost functions of the firms nor the demand functions of the consumers. How can we estimate the DWL using the limited available date?

Remember the book publisher as a monopoly firm Demand structure: three groups of consumers Group 1 10,000, willingness to pay $20 Group 2 30,000, willingness to pay $15 Group 3 50,000, willingness to pay $9 Costs MC = $5 (do we have AC = MC?) Monopoly price is P = $15; 40,00 books are sold; the DWL is $200,000.

How can you compute the DWL if you only know that the price is $15; and 40,00 books are sold; and profits are $150,000 (net of the author’s fee of 250,000)? We will go through the procedure, and then I will ask you to answer this question.

There are two well-known works in this line of research The first one is: Arnold Harberger, 1954, "Monopoly and Resource Allocation," American Economic Review, Dec. 1954: 77- 87 ] Arnold “Al” Harberger : The Harberger's Triangle, widely used in welfare economics, is named after him. Harberger has been influential in his leadership of the Chicago Boys, a group of economists who were instrumental in implementing free-market reforms to the Chilean economy in the early '70s, under Gen. Pinochet.

Harberger started like this… DWL equals the area ABC. DWL = (1/2)(PM−PC)(QC−QM) 

Let PM−PC ≡ ΔP and QC−QM ≡ ΔQ DWL Take Divide by P and Q; then multiply with P and Q.

Now do this

So, the DWL is

is the profit rate! We assume constant unit costs (MC = AC) We can write (P − MC)/P as = (P − AC)/P = (PQ − AC∙Q)/PQ = (Total revenue − Total Cost)/Total Revenue. ΔP/P ≈ profit/revenue

So, what about EP? Harberger assumed that the price elasticity is -1.

Remember the book publisher as a monopoly firm Demand structure: three groups of consumers Group 1 10,000, willingness to pay $20 Group 2 30,000, willingness to pay $15 Group 3 50,000, willingness to pay $9 Costs AC = MC = $5 Monopoly price is P = $15; 40,00 books are sold; the DWL is $200,000.

Now you know how to compute the DWL with the limited information that the price is $15; 40,00 books are sold; and profits are $150,000! (note that the profit number is net of the author’s fee of 250,000) Please compute the DWL!

Harberger’s result for the US economy… Based on data for US manufacturing industries 1924-28, Harberger estimated the DWL due to monopoly to be equal to 1/10 of 1 percent of GNP. The welfare loss due to pricing above marginal cost is small. There is no need to spend substantial resources on antitrust enforcement.

The second paper is by Cowling and Mueller from 1978 The second paper is by Cowling and Mueller from 1978. [Keith Cowling and Dennis Mueller. "The Social Costs of Monopoly Power," Economic Journal, December 1978: 727-48. ]

Cowling and Mueller 1978 The estimates of DWL are sensitive to assumptions made about elasticity of demand (EP). Their major improvement/innovation is how they handle the key assumption of Harberger; namely, that for all industries, EP = 1. They also have better data: They use a sample of 734 U.S. firms for 1963-66.

To estimate the price elasticity (EP), Cowling and Mueller use the fact that the firm’s profit maximizing price (PM) satisfies the condition (PM−MC)/PM = 1/EP Define r ≡ (PM−MC)/PM Write the condition as r = 1/EP

Now back to the algebra : Start with DWL = (1/2) r2 EP PQ. Use r = 1/EP. The formula simplifies to DWL = (1/2) r PQ. Use r ≡ (P−MC)/P, and rewrite the formula as (1/2) x[PxQ]. P and P cancel, we have DWL = (1/2)(P−MC)Q. Assume MC = AC. So, (P−AC)Q is the monopoly profits, so… the DWL equals half the monopoly profits.

SUMMARY of Cowling and Mueller : The DWL for an industry is equal to ½ of the economic profits () of firms in the industry.

Cowling and Mueller produced two different estimates of DWL in the U.S. economy: The lower estimate, which does not include advertising expenditures as a component of the dead weight loss, was 4 percent of GNP (about $403 billion in 2001). The larger estimate, which reckoned advertising expenditures as "wasted resources," was 13 percent of GNP (about $1.394 trillion in 2001).

Assuming that the advertising expenditures is "wasted resources," is more controversial : Advertising is seen as an expenditure on acquiring and maintaining monopoly position.

One last example

Please try to do this… US Manufacturing firms had profit of 245 billion dollars in 1998. Total Sales were 4,591 billion. The US GDP in 1998 was 8790 billion dollars. Suppose ALL of the measure profits is monopoly profit. Please compute the DWL as a percentage of the GDP.

Answers HARBERGER method : The profit rate on sales is r = 0.053. r = (P−MC)/P. Total sales (TR) = 4,591 billion.

The Harberger methods gives the DWL triangle as (1/2)∙r2∙εP∙TR, where εP is the price elasticity of demand. The triangle loss is = .5 (0.053)(0.053) (4591) = 6.5 billion dollars. The US GDP in 1998 was 8790 billion dollars, so the loss is .07% of GDP. (less than 1/10 or 1% of the GDP. This is a very small number!!

Cowling and Mueller method US Manufacturing firms had profit of 245 billion dollars in 1998. So DWL is 245/2 = 123 billion. 123/8800 = 1.5% of GDP. The US GDP in 1998 was 8790 billion dollars.

Yet one more exercise on estimating the DWL What happens to our DWL estimates if MC = AC is not a good assumption?

Study question A monopoly firm is facing the market demand Q=10 – P. The total cost is c(q) = 8 + 2q, where q denotes the monopolist’s output level. A. Find the profit maximizing q for the monopolist. Compute profits, total revenue and the DWL. B. Use only the total revenue and profit you computed in part A and compute the DWL with Harberger’s method. C. Redo part B using Cowling and Mueller’s method. D. Compare A to (B and C). A is the exact measure of the DWL; B and C are approximations. Comment.

Solutions Demand is Q = 10 – P, the cost function is c(q) = 8+2q Solutions Demand is Q = 10 – P, the cost function is c(q) = 8+2q. Inverse demand: P = 10 – Q. Profit = revenue – cost = PxQ – (8 + 2Q) = (10 – Q)Q – 8–2Q A. Differentiate and set equal to 0: 10 –2Q–2 = 0  Q* = 4, use the inverse demand to compute the price P* = 6. Profit = 24–8– 8 = 8, DWL = (P–MC)(QC–QM) = 0.5(4x4) = 8. B. Harberger r = Profit/sales = 0.3 DWL 0.5x(0.32)x(24) = 1.33 C. Cowling Mueller DWL Half of profits = 4 D. Both methods underestimate the ‘true’ DWL which is 8. The reason is that both methods replace MC by AC. In this case this is not a good assumption.