ECON 330 Lecture 10 Thursday, October 18

Today’s menu How to estimate the DWL of market power Solving the in-class exercise from Tuesday What you should know be able to do at this point A few words on where we are and what is coming next

In class exercise at the end of the lecture: Please show more effort Next week: Thursday OCT 25 NO Class Bayram break Tuesday OCT 23 lecture: Problem solving In class exercise at the end of the lecture: Please show more effort A few words on class participation

Solve the in-class exercise from last lecture 5 minutes for Solve the in-class exercise from last lecture

In class exercise DEMAND Q P 10 2 9 4 8 6 7 5 12 14 3 16 10 2 9 4 8 6 7 5 12 14 3 16 The dominant firm has AC = MC = 1, and unlimited production capacity. Each of the small firms has AC = MC = 4, and a combined production capacity of K = 2. You are the owner of the dominant firm. What price will you set to max profits?

Solution P profit Q QR 10 9 2 8 14 4 7 24 6 30 5 32 12 3,99 35,9 3 28 16 Do the math: The residual demand is QR = 20 – 2P – 2 for P ≥ 4 QR = 20 – 2P for P < 4. If P < 4 the best price is P = 3.99. The profits are 35,9 (almost 36). If P ≥ 4, to find the best price: QR = 20 – 2P – 2 = 18 – 2P. The inverse residual demand P = 9 –0.5QR. MRR = 9 – QR  Use the condition MRR = MC 9 – QR = 1  Q* = 8, P* = 5, profits are 32. SO the profit maximizing price is 3.99.

Option 1 set P < 4. Eliminate the small firms Option 1 set P < 4. Eliminate the small firms. The best price is P = 3.99. The profits are 35,9 (almost 36).

Do the math for P ≥ 4 The residual demand is QR = 20 – 2P – 2 = 18 – 2P Solve the monopoly’s profit max problem Step 1 Write the inverse demand for the residual demand P = 9 –0.5QR. Profit = revenue – cost = P(QR)·QR –1·QR Step 2 Profit = (9 –0.5QR)·QR –1·QR Step 3 Differentiate the revenue to get MRR = 9 – QR MC = 1 Step 4 Use the condition MRR = MC 9 – QR = 1  Q* = 8, substitute back into the residual demand to find P* = 5, profits are (P–AC)xQ = 32.

Option 1: Set P < 4. Eliminate the small firms. The best price is P = 3.99. The profits are 35,9 (≈36). Option 2 : Set P > 4 and give some market share to the fringe firms, in that case the best price is P* = 5, you produce Q* = 8, small firms produce 2, profits are (P–AC)xQ = 32. SO the profit maximizing price is 3.99.

Q = 120,01 or P = 3,99

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

Big question: Is the deadweight loss of market power for real economies is big? 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.”

George Joseph Stigler (1911 –1991) won the Nobel in Economic s in 1982 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.

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

Back to work: Estimating the DWL

Example: 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 that may be monopolies or oligopolies, we face 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 AC = MC = $5 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 $250,000?

There are two famous papers 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. Al 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… The ABC area is given by  DWL = (1/2)(PM−PC)(QC−QM) 

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

Now

So, the DWL is

is the profit rate! If 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.

Harberger’s result 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 industry-level 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 (1/2) r PQ. Use r ≡ (P−MC)/P, and rewrite the formula as (1/2) x(PQ). P and P cancel, we have DWL = (1/2)(P−MC)Q. As before, assume MC = AC. So, (P−AC)Q is the monopoly profits, and the DWL is 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.

Assuming that 12 percent is a "normal" rate of return on capital, 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.  

Example 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. Compute the DWL (the welfare loss) as a percentage of the GDP?

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 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.

Now it is your turn What happens to our DWL estimates if MC = AC is not a good assumption?

In class exercise 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.

Solution to the in-class exercise 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.