Econ 330 Lecture 6 Wednesday, October 2

The equilibrium in the competitive market!

The short-run vs. the long-run equilibrium We define the short-run as the period when the number of firms is fixed, whereas, in the long run, we also consider the possibility of entry and exit.

The short-run Consider an industry with a given number of firms and a corresponding market supply curve. The intersection of supply and demand determines the equilibrium price.

The short-run Depending on the demand and the number of firms in the market, this may result in a short-run equilibrium in which price is above average cost, so that firms are making above-normal profits, or price is below average cost, so that firms are losing money

The competitive equilibrium in the long-run In the long run, we consider the possibility of entry and exit. When there are above-normal profits in an industry, new firms will want to enter. With entry, output (supply) will increase. This will cause the price to fall, which will lower profits. New firms continue to enter until (all/most) above-normal profits are eliminated. When above normal profits gone, entry will stop. All firms now make zero economic profits. No new firm wants to enter, no incumbent firm wants to exit. We can say that the long run equilibrium has been reached!

Long-Run Competitive Equilibrium When firms in an industry make less than normal profits this creates incentives for firms to exit, With fewer firms less output will be produced (supplied) This will cause the price to increase Firms continue to exit until losses are eliminated and normal (zero economic) profits are restored. When that happens exit stops. Again, we can say that the long run equilibrium has been reached!

The process of free entry and exit eliminates excess profits or losses. So that the zero economic profit condition defines the long-run equilibrium of a competitive industry.

The long run equilibrium: Entry and exit The zero economic profit condition implies that the long run equilibrium P* = minimum of AC! This price is the lowest price that the firms find “acceptable” . This is Adam Smith’s “natural price” of the “price of pure competition”.

So, how does the math work out?

Computing the long run equilibrium in 5 steps! Use the firm’s cost function to compute the output level at which the AC is at its minimum. Call this output level qLR. Free entry/exit forces the long run equilibrium price to be equal to min AC. Compute AC at q = qLR. This is the long-run equilibrium price. Use the given market demand and the long run equilibrium price to compute the long run equilibrium quantity. Call this QLR. Compute the number of firms by QLR/qLR. If this number is not an integer, round it down to the nearest integer.

Let’s try this method with the numerical example from Monday’s lecture All firms have TC(q) = F + q + 0.05q2, with MC = 1 + 0.1q The market demand is QD = 10300 – 50P Find q at which AC reaches its minimum. To do that, first, compute the AC function, then use the condition AC = MC

This is why we are using AC = MC condition

TC(q) = F + q + 0. 05q2, MC = 1 + 0. 1q AC = TC/q = (F + q + 0 TC(q) = F + q + 0.05q2, MC = 1 + 0.1q AC = TC/q = (F + q + 0.05q2)/q = F/q + 1 + 0.05q for F = 40, AC looks like this

Now, use AC = MC to find q at which AC reaches its minimum Now, use AC = MC to find q at which AC reaches its minimum. Some algebra for AC = MC F/q + 1 + 0.05q = 1 + 0.1q F/q + 0.05q = 0.1q F/q = 0.05q F = 0.05q2 q2 = F/0.05 Finally, we have

AC(q) = F/q + 1 + 0.05q For example, if we let F = 80, then tells us that AC is reaches its minimum value at q = 40. The minimum AC is 5. This means that the long run equilibrium price must be 5. The market demand is QD = 10300 – 50P. With P = 5, the equilibrium quantity is 10050. We have 10050/40 = 251.25, so, there will be 251 firms in the market.

P = 5 q = 40

Now something more complicated!

What happens if firms have different cost structures What happens if firms have different cost structures? How does the long run equilibrium look like?

If firms have different cost structures then in a long run competitive equilibrium (with many price-taking firms who are small relative to the overall market), the least efficient firm (aka the marginal firm) will be the one for which p = AC holds. Those firms that have cost advantages will be earning a positive profit, a profit we refer to as a rent. Firms earn rents in competitive markets when their cost function is better than their rivals'.

Some firms that are better than others See if you can answer the following…

All firms in the industry… have the same total cost function TC(q) = M + 10q + wq2, where M is the salary paid to the manager, and w is the market wage rate for workers. All firms face an output price of P = 30, and a wage rate of w = 2. Merlin is like all other managers in this industry except in one respect: Because of his great sense of humor, people are willing to work for him for half the market wage rate.

a. How much output will Merlin’s firm produce a. How much output will Merlin’s firm produce? How much output will a regular firm produce? b. Compared to other firms how much profit will Merlin’s firm make? c. Compute the value of M so that the output price (P = 30) is the long run equilibrium price. Also compute price, quantity, and profits in that equilibrium. What piece of information is missing for part c?

Let’s do it! TC(q) = M + 10q + wq2… The marginal cost function is MC(q) = 10 + 2wq. A regular firm pays w = 2, so it has MC = 10 + 2x2xq. P = MC for that firm is 30 = 10 + 4xq  q* = 5. Merlin’s firm pays w = 1, so its MC is 10 + 2xq. P = MC for Merlin’s firm is 30 = 10 + 2q  qM = 10.

Profit = revenue – cost Profit of a regular firm πR = 5x30 – M – 10x5 –2x52 = 50 – M. Profit of Merlin’s firm πM = 10x30 – M – 10x10 –1x102 = 100 – M

So, Merlin’s firm makes more profit than other firms It also has a larger market share!

Finally part c: What value of M will make this price the long-run equilibrium price? How many firms will there be in the market? In particular, will Merlin’s firm make 0 profit in the long-run equilibrium? Let the market demand be QD(P) = 80 – P

The answer is… M = 50. When M = 50 and P = 30, regular firms produce q= 5 and make 0 profit. Merlin’s firm will produce q = 10 and make a profit of 50. At P = 30 quantity demanded is QD(P) = 80 – P = 50. How many firms will there be in the market? There will be 8 regular firms and Merlin’s firm.

FROM THEORY TO FACTS

What does the model of perfect competition have to say about entry, exit, firm size distribution, and profits?

Theory If all firms have the same U-shaped cost functions, then all firms must be of the same size in the long run equilibrium! There is only one output level that minimizes the average cost.

Facts: Firm size distribution The size distribution of firms displays a number of regularities and is not concentrated on a single size. It is remarkably stable across many market definitions, industries, and levels of aggregation. This was first noted by Herbert Simon and Charles Bonini in 1958.

Herbert Simon (1916 - 2001) studied economics at the University of Chicago was awarded the Nobel Prize for economics in 1978… to considerable surprise, since by then he had not taught economics for two decades. was most famous for what is known to economists as the theory of bounded rationality, made contributions to psychology, management, computer science (AI), and philosophy of science.

From Simon and Bonini, (1958), “The size distribution of business firms”

This asymmetrical (skewed) size distribution with many small firms and a few large firms is called The log-normal distribution, and looks like this…

The log-normal distribution

As opposed to the normal distribution which looks like this…

LA DISTRIBUTION NORMALE

Firm size distributions of all manufacturing firms, selected countries, (number of workers)

These countries are very different in size, but the distributions look remarkably similar. Similar results are obtained with sectoral distributions.

Theory The perfect competition model predicts that, at any given time, there will either be entry into an industry (active firms are earning supra-normal profits); or exit from that industry (active firms are earning less than the normal profit rates).

Facts The empirical evidence suggests that, in any given period and industry, entry and exit take place at the same time, with the gross entry and exit rates being much higher (typically one order of magnitude higher) than the net entry rate.

For example, in Norway and in the period 1980-85, the average gross entry rate for an industry was 8.2%, the average exit rate was 8.7%. The difference, 8.2 – 8.7 = 0.5%, the net entry rate, is less than one-tenth of either the gross entry or the gross exit rate.

Patterns of Firm Entry and Exit in U. S Patterns of Firm Entry and Exit in U.S. Manufacturing Industries, 1988 Timothy Dunne. Mark J. Roberts and. Larry Samuelson Hypothetical industry with 100 firms, and total annual sales of $100 million

There will be 30–40 new firms, with combined sales of $12–20 mill. In 5 years time (by 2001) There will be 30–40 new firms, with combined sales of $12–20 mill. about 50% diversified, 50% new firms. 30–40 existing firms will have left, sales of $12–20 mill. 40% of exiting firms diversified.

Entry and exit rates vary across industries Entry and exit rates vary across industries. High rates of entry: apparel, lumber, furniture, printing, fabricated metal. High rates of exit: apparel, lumber, furniture, printing, leather. Little entry: food processing, tobacco, paper, chemicals, primary metals. Little exit: tobacco, paper, chemicals, primary metals, petroleum, coal.

Entrants and exiters are smaller than established firms Entrants and exiters are smaller than established firms. Typical entrant about 1/3 of typical incumbent. Exiting firms are also 1/3 size of the average incumbent.

Most entrants don’t survive ten years, but survivors grow very quickly Most entrants don’t survive ten years, but survivors grow very quickly. Roughly 60% of new entrants in 1996–2001 will exit by 2006. Survivors will double their size between 2001 and 2006.

Entry and exit … Smaller firms grow faster than large firms, younger firms grow faster than the older firms. But it is mainly young and small firms that exit.

Facts about profits in the long-run Empirical evidence suggests that profit rates are persistent in the long run! Dennis Mueller examined profit rates for a sample of 600 U.S. firms from 1950 to 1972. He put firms in groups of 100 according to average profits in 1950-1952 He computed average profit rates in the whole 23-year period for each of the groups. Differences in profitability across the groups persist even after 23 years.

Productivity differences are large In the U.S. manufacturing sector, on average a plant in the 90th percentile has a productivity level that is twice that of a plant in the 10th percentile. With the same inputs, a plant in the 90th percentile produces twice as much as a plant in the 10th percentile. Moreover, productivity levels are highly correlated across time.

End of the lecture