1 G604, Profit-Concentration Lectures Spring 2006, 10 January 2006 Eric Rasmusen, [email protected]@Indiana.edu.

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G604, Profit-Concentration Lectures

Spring 2006, 10 January 2006Eric Rasmusen, [email protected]

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Why Do Some Firms Have Higher Profit?

(ask students to answer)

(why is this interesting?)

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Does Concentration Create Monopoly Profit?

How would you address this question?

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PROFITS AND CONCENTRATION

It is not obvious how to measure concentration. Tirole (p. 221-222) has a good discussion of this.

3-firm concentration ratio: if 3 firms have 90 percent of the market, the ratio is 90 percent.

steel market shares: (70, 10, 10) car : (30, 30,30)

(1a) Encaoua and Jacquemin (1980)

1. Symmetry between firms. If Apex and Brydox switch places in market share, the index should be unaffected.

2. If market share moves from any firm to a bigger firm, the index must report higher concentration.

3. If the number of identical firms in the industry grows, concentration measured for just that part of the industry must decrease.

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Herfindahl Index H = s_1^2 +s_2^2 + …. + s_n^2

Shares H C4

100 10,000 100

1x100 100 4

50,50 5,000 100

90,10 8,200 100

50, 50x1 2,550 50

25x4 2,500 100

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Measuring ProfitReturn on equity

Return on sales

Return on stock

Return on capital

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PROFITS AND CONCENTRATION

Bain (1951, 1956) found that industry concentration and profitability were correlated, and he thought this was evidence that concentration promotes collusion.

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PERFECT COMPETITION

The problem with Bain's reasoning is that a competitive market should also have a correlation between concentration and profits. Demsetz (1973) pointed this out

A simple reason why firms have different sizes is that fixed costs vary across industries.

If fixed costs are sunk, they won't show up in current economic profits, which will be huge if the fixed cost is big. They will have shown up in big losses in the first year of operation, however, so overall profits will be zero. If fixed costs are recurring, then current economic profits will be zero. If the accounting system spreads a fixed cost across, say, two years, but the revenues it generates are all received in one year, then the company will have positive accounting profits.

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INTEGER PROBLEMS

Economic profits might be positive and higher with greater concentration.

There might be an integer problem. If an industry has fixed costs, then for some number N, N firms can operate profitably, but demand would not be big enough for (N+1) to cover their fixed costs.

If N=1, the industry is a natural monopoly, highly concentrated, and even if that firm is a price-taker it can earn large positive profits.

If N=100, then each price-taking firm can earn a small profit, but neither firm nor industry profit is as large.

Wal-Mart in small towns is an example.

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POSITIVE ECONOMIC PROFITS

Some firms might have lower costs.

Suppose an unlimited number of firms could operate in an industry with a capacity of 1 and a marginal cost of c , and that demand is perfectly inelastic at amount Q .

Number N of firms, however, have capacities of K each and marginal costs of c_0 <c .

We will assume that N K <Q , so the low-cost firms cannot supply the entire market.

The competitive price will be P=c , and in the unique Nash equilibrium, the low-cost firms will all produce at capacity and earn positive profits.

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GAME THEORY DIGRESSION.

This is the Bertrand game with different marginal costs and limited capacity.

(A) Why doesn't the Edgeworth paradox apply? The high-cost firms prevent any low-cost firm from raising its price above P=c , even though the low-cost firms are all at capacity.

(B) The equilibrium described is weak, since consumers are indifferent between low and high-cost firms when they all charge P=c . Aren't there other equilibria where the low-cost firms don't all sell to capacity because not enough consumers choose them?

No, because any low-cost firm that did not sell to capacity would reduce its price to P=c-\epsilon . This deviation knocks out all those conjectured other equilibria.

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PRICE THEORY DIGRESSION.

Are the low-cost firms actually earning economic profits? The price exceeds their marginal cost, to be sure, but shouldn't we call that extra revenue a rent to their special technology and limited capacity?

Like a rent to land or to a person's natural talents, the firm's `profits` in this situation are not eliminated by competition, rise or fall depending on the marginal player in the market, and are based on ownership of a non-produced resource, fixed in quantity.

On the other hand, we think of profit as a return to a firm qua firm, as opposed to inputs being purchased from outside. If the firm's low-cost technology is inalienable-- that is, it can't be bought or sold aside from buying the entire firm-- then it has no opportunity cost to the firm, which must use it or lose it.

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THE BAIN REGRESSION

Profitability = alpha + beta*concentration

What problems are there?

MARTIN: BROZELL PROBLEMS:

1. Disequilibrium? No.

2. Bias in industry selection. No.

3. Firm selection bias. Industries with small firms would not be included. That's OK.

We’ll look at some other problems.

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PROBLEM 1: Serial Correlation

This is not mentioned in Martin. Some industries have high profits at the same time because of omitted variables that are correlated. So the data sample is really smaller than it seems. Some observations are:

Motor vehicles

Washing machines

Steel works and rolling mills

Cast iron pipe

Wire

Doors and shutters, metal

Are these independent disturbances? No. The price of iron is in all of them.

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PROBLEM 2: UNIT OF ANALYSIS

Bain used industries such as Cigarettes, Soap, Paper Goods. He used government definitions, throwing out some clearly wrong ones (Cane sugar vs. Beet sugar) since demand, not supply, is what is relevant here.

He averaged together the profitabilities of different firms.

Firms could be used instead. Which is better?

Can you do both?

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PROBLEM 3: RISK

(not in Martin)

An omitted variable problem: More risky industries will need higher returns.

Leverage is also part of this. A firm can get capital, by DEBT and by EQUITY. Equity is what the owners put in, and debt is what they borrow.

Some people form a corporation by putting in 1,000 dollars with which to buy capital. They use it to buy sewing machines. The corporation has 1,000 shares, with an initial value of 1 dollar each. Each shareholder gets as many shares as he put dollars into the company. Each share has one vote for the choice of who will be on the board of directors that runs the company.

The company has no debt, so we say it is UNLEVERAGED.

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JUST EQUITY

If the company has net revenue ("net" meaning after variable costs) of $200 in the first year, the return on equity is +20%.

The return on assets is the same, since the company has no debt.

If the company's net revenue had been $50, the return on equity would have been 5%.

The book value of the equity is 1000 dollars, and so is the market value, at the start of the firm.

Suppose the price of sewing machines falls in half. The company's assets now have a market value of only 500 dollars, so the stock price will fall to 50 cents per share, and the market value falls to 500 dollars.

The book value of equity is still 1000 dollars, however.

If the shareholders want to, they can revise the book value. They do this by "writing down" the assets by $500. But they do not have to do that, and companies only write down assets occasionally.

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DEBT

Suppose the price of sewing machines goes back up, so the assets are worth $1000 again. The directors decide to borrow $2000 from a bank, at an interest rate of 15%. The company is now "highly leveraged".

The company has revenues of $600 the next year, because it has tripled in size and the return on assets is still 20%. The company must pay $300 in interest to the bank, though, which leaves $300 in cash flow for the shareholders.

Thus, the return on equity is 30%--bigger.

Suppose the net revenue had been $150 (a 5% return on assets). The company must pay $300 in interest to the bank, which leaves -$150 for the shareholders (the company would have to sell some sewing machines to come up with the money). The return on equity would be - 15%.

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LEVERAGE

Leverage increases the riskiness of the company's stock even though it does not increase the riskiness of the company's assets.

An unleveraged company would have had a return on equity of either 20% or 5%. The leveraged company has a return of either 30% or -15%.

Thus, any company can affect the riskiness of its stock by deciding how much debt to hold.

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RESIDUAL CLAIMANTS

The "residual claimants" of a company are the

people who get whatever profits are left over once all the debts are paid.

In this example, they are the shareholders. The bank has first claim on the cash flow, and the shareholders are legally allowed to keep only money in excess of the interest payments. The residual claimants have the riskiest claims. The bank still runs some risk---it could be that the company loses $1100 in one year, for example, so it cannot pay the $300 in interest even if it sells off assets-- but the bank's risk is less than the shareholders'.

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ASYMMETRIES

1. The downside risk of the shareholders is limited to losing the $1000 that they invested in the company.

2. The downside risk of the bank is limited to losing the $2000 loan it made.

3. The upside gain of the shareholder is unlimited. If the company earns $10,000, then after paying the bank $300 in interest, the shareholders keep all the excess.

4. The upside gain of the bank is limited to the $300 interest it was promised.

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PROBLEM 4: ACCOUNTING

Profit rates vary across industries because of accounting rules and the types of expenses.

The problem arises because costs and revenues arrive at different times. Suppose two firms each have 100 in capital.

Firm 1 pays 50 for labor and raw materials and gets 80 in revenue each year. Profit is 30, and the return on capital is 30%. Over two years, total profit is 60.

Firm 2 pays 50 for labor and 60 for raw materials inventory in the first year, and gets revenue of 110. Profit is 0 and the return on capital is 0%.

Firm 2 pays 50 for labor and 0 for raw materials in the second year, and gets revenue of 110. Profit is 60 and the return on capital is 60%. Over two years, total profit is 60.

Growing industries will look less profitable.

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Survival Bias

Some firms died. Those remaining have to be extra profitable. (Demsetz flavor)

This is like the problem of entry into an industry requiring a fixed cost.

If an industry or firm has a differentiated product, it will price at greater than marginal cost. (Differentiated Bertrand model). If entry is free, fixed costs, recurring or one-time, will eat up the profit. If they are one-time fixed costs, they won’t show up in the accounting profits later.

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PROBLEM 5: THE DEMSETZ CRITIQUE

(Simultaneity)

Suppose some firms have low costs. They will grow, and the market becomes concentrated.

(Simultaneity: Concentration depends on profitability. )

To test this, do a regression at the firm level:

Profitability = alpha + beta*concentration + gamma*market_share + industry_dummy

If you run this, it turns out that beta is insignificant.

Does it matter that market share is not independnet between obeservations? No-RHS variable.

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THREE CONCEPTS YOU SHOULD KNOW FOR EMPIRICAL WORK IN

I.O

Conjectural Variation

The Lerner Index

Tobin's q