## Evaluating Different Market StructuresDecember 13, 2012

Posted by tomflesher in Micro, Teaching.
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Market structures, like perfect competition, monopoly, and Cournot competition have different implications for the consumer and the firm. Measuring the differences can be very informative, but first we have to understand how to do it.

Measuring the firm’s welfare is fairly simple. Most of the time we’re thinking about firms, what we’re thinking about will be their profit. A business’s profit function is always of the form

Profit = Total Revenue – Total Costs

Total revenue is the total money a firm takes in. In a simple one-good market, this is just the number of goods sold (the quantity) times the amount charged for each good (the price). Marginal revenue represents how much extra money will be taken in for producing another unit. Total costs need to take into account two pieces: the fixed cost, which represents things the firm cannot avoid paying in the short term (like rent and bills that are already due) and the variable cost, which is the cost of producing each unit. If a firm has a constant variable cost then the cost of producing the third item is the same as the cost of producing the 1000th; in other words, constant variable costs imply a constant marginal cost as well. If marginal cost is falling, then there’s efficiency in producing more goods; if it’s rising, then each unit is more expensive than the last. The marginal cost is the derivative of the variable cost, but it can also be figured out by looking at the change in cost from one unit to the next.

Measuring the consumer’s welfare is a bit more difficult. We need to take all of the goods sold and meausre how much more people were willing to pay than they actually did. To do that we’ll need a consumer demand function, which represents the marginal buyer’s willingness to pay (that is, what the price would have to be to get one more person to buy the good). Let’s say the market demand is governed by the function

QD = 250 – 2P

That is, at a price of \$0, 250 people will line up to buy the good. At a price of \$125, no one wants the good (QD = 0). In between, quantity demanded is positive. We’ll also need to know what price is actually charged. Let’s try it with a few different prices, but we’ll always use the following format1:

Consumer Surplus = (1/2)*(pmax – pactual)*QD

where pmax is the price where 0 units would be sold and QD is the quantity demanded at the actual price. In our example, that’s 125.

Let’s say that we set a price of \$125. Then, no goods are demanded, and anything times 0 is 0.

What about \$120? At that price, the quantity demanded is (250 – 240) or 10; the price difference is (125 – 120) or 5; half of 5*10 is 25, so that’s the consumer surplus. That means that the people who bought those 10 units were willing to pay \$25 more, in total, than they actually had to pay.2

Finally, at a price of \$50, 100 units are demanded; the total consumer surplus is (1/2)(75)(100) or 1875.

Whenever the number of firms goes up, the price decreases, and quantity increases. When quantity increases or when price decreases, all else equal, consumer surplus will go up; consequently, more firms in competition are better for the consumer.

Note:
1 Does this remind you of the formula for the area of a triangle? Yes. Yes it does.
2 If you add up each person’s willingness to pay and subtract 120 from each, you’ll underestimate this slightly. That’s because it ignores the slope between points, meaning that there’s a bit of in-between willingness to pay necessary to make the curve a bit smoother. Breaking this up into 100 buyers instead of 10 would lead to a closer approximation, and 1000 instead of 100 even closer. This is known mathematically as taking limits.

## Duopoly and Cournot EquilibriumDecember 12, 2012

Posted by tomflesher in Micro, Teaching.
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A few days ago, we discussed perfectly competitive markets; yesterday, we talked about monopolistic markets. Now, let’s expand into a case in between – a duopolistic, or two-seller, market. This is usually called a Cournot problem, after the economist who invented it.

We’ll maintain the assumption of identical goods, so that consumers won’t be loyal to one company or the other. We’ll also assume that each company has the same costs, so we’re looking at identical firms as well. Finally, assume that there are a lot of buyers, so the firms face a market demand of, let’s say, QD(P) = 500 – 2P, so P = 250 – QD(P)/2. Since the firms are producing the same goods, then QS(P) = q1(P) + q2(P).

Neither firm knows what the other is doing, but each firm knows the other is identical to it, and each firm knows the other knows this. Even though neither firm knows what’s going on behind the scenes, they’ll assume that a firm facing the same costs and revenues is rational and will optimize its own profit, sothey can make good, educated guesses about what the other firm will do. Each firm will determine the other firm’s likely course of action and compute its own best response. (That’s the one that maximizes its profit.)

Now, let’s take a look at what the firms’ profit functions will look like.

Recall that Total Profit = Total Revenue – Total Cost, and that Marginal Profit = Marginal Revenue – Marginal Cost. Companies will choose quantity to optimize their profit, so they’ll continue producing until their expected Marginal Profit is 0, and then produce no more. Firm 1’s total revenue is Pxq1 – revenue is always price times quantity. Keeping in mind that price is a function of quantity, we can rewrite this as (250 – QD(P)/2)xq1. Since QD(P) = q1 + q2, this is the same as writing (250 – (1/2)(q1 + q2))q1. Then, we need to come up with a total cost function. Let’s say it’s 25 + q12, where 25 is a fixed cost (representing, say, rent for the factory) and q12 is the variable cost of producing each good. Then, Firm 1’s profit function is:

Profit1 = (250 – (1/2)(q1 + q2))q1 – 25 – q12

or

Profit1 = (250 – q1 /2 – q2/2)q1 – 25 – q12

or

Profit1 = 250q1 – q12/2 – q1q2/2 – 25 – q12

The marginal profit is the change in the total profit function if Firm 1 produces one more unit; in this case it’s easier to just use the calculus concept of taking a derivative, which yields

Marginal Profit1 = 250 – q1 – q2/2 – 2q1 = 250 – 3q1 – q2/2

Since the firms are identical, though, firm 1 knows that firm 2 is doing the same optimization! So, q1 = q2, and we can substitute it in.

Marginal Profit1 = 250 – 3q1 – q1/2 = 250 – 5q1/2

This is 0 where 250 = 5q1/2, or where q1 = 100. Firm 2 will also produce 100 units. Total supplied quantity is then 200, and total price will be 200. We can figure out each firm’s profit simply by plugging in these numbers:

Total Revenue = Pxq12 = 200×100 = 20,000

Total cost = 25 + q12 = 25 + 100×100 = 25 + 10,000 = 10,025

Total Profit = 9,075

This was a bit heavier on the mathematics than some of the other problems we’ve talked about, but all that math is just getting to one big idea: it’s rational to produce when you expect your marginal benefit to be at least as much as your marginal cost.

## Monopolistic MarketsDecember 11, 2012

Posted by tomflesher in Micro, Teaching.
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Continuing our whistle-stop tour through market types, today’s topic is monopolies. Yesterday’s discussion was of perfectly competitive markets, where three conditions held:

• Identical goods
• Lots of sellers

Today, we’ll talk about what happens when that second condition doesn’t hold – that is, when sellers have market power. When sellers don’t have market power, they have to price according to what the market will bear. If they price too high, someone will undercut them, but if they price too low, they’ll lose money. The only thing they can do is price at their break-even point, where price is equal to marginal cost. (This is sometimes called the zero profit condition.)

When only one seller exists, he is called a monopolist, and the market is called a monopoly. A monopoly can arise for one of two reasons: either it can be because the owner has exclusive access to some important resource, called a natural monopoly, or the owner has an ordinary monopoly because of laws, barriers to entry, or some other reason.

A natural monopoly is one that arises not because of anticompetitive action by the monopolist but because of exclusive access to some resource. For example, owning a waterfall means you have unbridled access to it for hydroelectric purposes; being the first to lay cable or pipelines makes it inefficient for anyone else to access those resources; essentially, anything where there’s a high fixed cost and a zero marginal cost are good candidates for natural monopoly status.

Regardless of whether a monopoly is natural or ordinary, a monopolist isn’t subject to the same zero-profit condition as he would be in a perfectly competitive market, since there’s no one to undercut him if he prices higher than his own marginal cost. He’s free to do the absolute best he can – in other words, to maximize his profit. The monopolist doesn’t have to take the price, as a perfectly competitive market would force him to; he’ll choose the price himself by choosing the quantity he produces.

The monopolist’s profit-maximization condition is that his marginal revenue = marginal cost. This derives from the monopolist’s profit function, Profit = Total Revenue – Total Cost. The monopolist will produce as long as each unit provides positive profit – in other words, as long as marginal profit ≥ 0. In non-economic terms, he’ll continue producing as long as it’s worth it for him – as long as each extra unit he produces gives him at least a little bit of profit. Once his marginal profit is 0, there’s no point in producing any further, since every unit he produces will then cost him a little bit of profit. Because Profit = Total Revenue – Total Cost, another equation holds: Marginal Profit =Marginal Revenue – Marginal Cost. Saying that marginal profit is nonnegative means exactly that marginal revenue is at least as much as marginal cost.

Finally, note that marginal revenue is the price of the last (marginal) unit, but keep in mind that the monopolist has control over the quantity that’s produced. Thus, he has control over the price, and will choose quantity to get his optimal profit.

## Perfectly Competitive MarketsDecember 10, 2012

Posted by tomflesher in Micro, Teaching.
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When solving economic problems, the type of firm you’re dealing with can lead you to use different techniques to figure out the firm’s rational choice of action. This week, I’ll set up a thumbnail sketch of how to solve different firms’ types of problems, since a common exam question in intermediate microeconomics is to set up a firm’s production function and ask a series of different questions. The important thing to remember about all types of markets is that every economic agent is optimizing something.

In a perfectly competitive market, three conditions hold:

• All goods are identical. If the seller is selling apples, then all apples are the same – there are no MacIntosh apples, no Red Delicious apples, just apples.
• There are lots of sellers, so sellers can’t price-fix because there will always be another seller who will undercut.
• There are lots of buyers, so a buyer boycotting won’t make a difference.

The last two conditions sum up together to mean that no one has any market power. That means, essentially, that no action an individual buyer or seller takes can affect the price of the goods. If ANY of these conditions isn’t true, then we’re not dealing with a perfectly competitive market – it might be a monopoly or a monopsony, or it might be possible to price-discriminate, but you’ll have to do a bit more to find an equilibrium.

Speaking of that, an equilibrium in microeconomics happens when we find a price where buyers are willing to buy exactly as much as sellers are willing to sell. Mathematically, an equilibrium price is a price such that QS(P) = QD(P), where QS is the quantity supplied, QD is the quantity demanded, and the (P) means that the quantities depend on the price P. Since the quantity is the same, economists sometimes call an equilibrium quantity Q* and the equilibrium price P*.

Consumers are optimizing their utility, or happiness. This might be represented using something called a utility function, or it might be aggregated and presented as a market demand function where the quantity demanded by everyone in the world is decided as a function of the price of the good. A common demand function would look like this:

QD(P) = 100 – 2*P

That means if the price is \$0, there are 100 people willing to buy one good each; at a price of \$1, there are (100 – 2*1) = 98 people willing to buy one good each; and so on, until no one is willing to buy if the price is \$50. Demand curves slope downward because as price goes up, demand goes down. Essentially, a demand function allows us to ignore the consumer optimization step. Demand represents the marginal buyer’s willingness to pay; price equalling willingness to pay is something to remember.

Firms optimize profit, which is defined as Total revenue, minus total costs. If we have a firm’s costs, we can figure out how much they’d need to charge to break even on each sale. Let’s say that it costs a firm \$39 to produce a each good. They won’t produce at all until they’ll at least break even – or, until their marginal benefit is at least equal to their marginal cost, at which point they’ll be indifferent. Then, as the price rises above \$39, charging more will lead to more profit. Even if the firm’s marginal cost changes as they produce more unity, the price of the marginal unit will need to be at least as much as the marginal cost for that unit. Otherwise, selling it wouldn’t make sense.

The first condition to remember when solving microeconomics problems is that in a perfectly competitive market, a firm will set Price equal to Marginal Cost. If you have price and a marginal cost function, you can find the equilibrium quantity. If you have supply and demand functions, set QS(P) = QD(P) and solve for the price, or simply graph the functions and figure out where they meet.