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Evaluating Different Market Structures December 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.

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Monopolistic Markets December 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
  • Lots of buyers

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.