The optimizing behavior of producers and consumers leads to a resource allocation that is efficient, in the sense that no one could be made better off without making someone else worse off. Here is a summary of the complete set of problems solved by decentralized markets.

1. How do we know that goods and services could not be better allocated between consumers? That is, how do we know that a consumer could not find another consumer and make a trade that would make them both better off?

   For this efficiency condition to be met, the marginal rate of substitution between any two goods must be the same for all consumers. Otherwise, there are welfare-enhancing trades to be made. For example, suppose that at the margin you think that one apple is worth three scoops of ice cream, and I think that one apple is worth one scoop of ice cream. In that case, if I were to trade you one apple for two scoops of ice cream, both of us would be better off.

   Decentralized markets can achieve the efficient allocation because consumers set their marginal rates of substitution equal to relative prices. All consumers face the same set of prices. Each consumer sets marginal utility equal to price. Therefore, for any two goods, the ratios of the marginal utilities will be the same for all consumers. That is, the marginal rate of substitution will be the same for all consumers.

2. How do we know that firms are producing the optimal mix of output? That is, how do we know that a firm could not make the economy better off by producing less of one output and more of another output?

   For this efficiency condition to be met, the marginal rate of transformation in production must be equal to the marginal rate of substitution in consumption. Suppose that the marginal rate of substitution in consumption is that one apple is worth two scoops of ice cream. In that case, if it were possible to shift production around to increase ice cream production by three while reducing apple production by only one, then that would be more efficient.

   Decentralized markets can achieve equality between the marginal rate of transformation and the marginal rate of substitution because firms set the marginal rate of transformation between two goods equal to the relative price. All firms face the same set of prices. Each firm sets the marginal rate of product transformation equal to the the relative price of the two outputs. Since the ratio of the relative prices is also the ratio of the marginal utilities, the rate of product transformation is the same as the ratio of the marginal utilities. This says that there is no gain in utility to be had from producing more of one output and less than another.

3. How do we know that the choice of inputs is efficient? That is, how do we know that the economy could not produce more output by changing the mix of inputs used in different products?

   This efficiency condition states that the economy must use the lowest-cost production methods. If a firm can substitute $4 of one input for $5 of another input and produce the same total output, then that is a more efficient production technique.

   Decentralized markets can achieve efficiency in production by having firms equate the marginal rate of substition between inputs to the relative prices of those inputs. All firms face the same prices for inputs, including wage rates. Firms set the marginal rate of substitution between inputs equal to their relative prices. That means that it is impossible to switch around inputs in order to produce the same output at lower cost.

4. How do we know that firms use the right level of inputs, not too much and not too little?

   This efficiency condition states that one firm does not use inputs that could be used more efficiently by another firm. If shifting some inputs from my company to your company would yield more valuable output, then the current allocation is not efficient.

   Decentralized markets achieve an efficient allocation of inputs across firms by the process of profit maximization, in which firms add input right up to the point where price equals marginal cost. All firms face the same prices for inputs and outputs. Each firm supplies output until the point where the marginal cost of producting the next unit is equal to its price. To produce less output would mean passing up an opportunity to have higher profits and to increase overall well-being. To produce more output would mean incurring a loss at the margin, and also would mean that the marginal cost to society is greater than the additional output's value.

Supply and Demand

Prices play a central role in the efficiency story. Producers and consumers rely on prices as signals of the cost of making substitution decisions at the margin. How are prices determined?

Economic theory says that the price of something will tend toward a point where the quantity demanded is equal to the quantity supplied. This price is known as the market-clearing price, because it "clears away" any excess supply or excess demand.

Market clearing is based on the famous law of supply and demand. As the price of a good goes up, consumers demand less of it and more supply enters the market. If the price is too high, the supply will be greater than demand, and producers will be stuck with the excess. Conversely, as the price of a good goes down, consumers demand more of it and less supply enters the market. If the price is too low, demand will exceed supply, and some consumers will be unable to obtain as much as they would like at that price--we say that supply is rationed.

Here is an example to illustrate the law of supply and demand. For a particular Saturday night, we look at the willingness of restaurants in Wheaton to supply a nice dinner for two and the willingness of couples to dine out in Wheaton, depending on the price of the dinner.

There are five restaurants, each with a seating capacity of 30 couples. One restaurant is willing to supply a nice dinner for $15 a couple, but the others require higher prices. If the price were $15, everyone would show up at the one restaurant, so that it would have a very long line. Only 30 lucky couples would get to eat.

There are 250 couples willing to go out for dinner, if the price were as low as $12 a couple. Twenty couples would be willing to pay as much as $80, but everyone else requires lower prices. Here is the whole picture.

Who Sets the Market-clearing Price?

For an example of a market where a single individual sets the price, consider the market on the New York Stock Exchange for shares of Freddie Mac stock. The individual who sets the price of Freddie Mac stock is called a specialist. All of the orders to buy and sell Freddie Mac stock are delivered to the specialist, who decides which price will best balance supply and demand.

At any moment when the exchange is open, the specialist will have a list of orders to buy and sell at a particular price. There might be an order that says, "Sell 1000 shares if the price reaches 60-1/2." The seller will not accept a lower price, but will accept a price of 60-1/2 or higher. This type of order is called a limit order. There might be another order that says, "Sell 800 shares if the price reaches 60-3/4." There might be another other that says, "Buy 800 shares if the price falls to 59-1/2."

All together, the outstanding orders to buy or sell at specific price limits make up what is called the limit order book for the specialist. In addition to limit orders, there are "market orders." A market order is an order to buy or sell a specific quantity of stock at the market price--whatever that happens to be.

The specialist moves the price of Freddie Mac stock up and down, depending on the pressure that she gets from market orders. For example, if the specialist gets a large market order to buy Freddie Mac stock, she has to figure out how high to set the price in order to trigger enough limit-order sales to fulfill the market order. That price becomes the new market price for Freddie Mac stock.

In most goods markets, sellers set the price. However, that does not mean that sellers control the price. For example, in the market for gasoline, individual service stations set the price. If most stations charge $1.50 a gallon for regular unleaded gasoline, then a station that charges $1.75 a gallon will not get much business, and a station that charges $1.25 a gallon will get plenty of business but probably lose money. The individual gas station does not have control over the impersonal market forces that determine the equilibrium price for gasoline.

If every station charges $1.75 and consumers cut back on gasoline purchases as a result, then every station will find itself with a little bit of excess capacity. One station will try to cut the price to $1.70 in order to sell more gasoline. This reduces demand at the other stations, so then another station will try to reduce its excess capacity, by cutting its price to, say, $1.65 per gallon. This will cause other stations to have more excess capacity, so that they will reduce their prices. The process will continue until the price reaches $1.50 (assuming that is where supply and demand are in balance).

In the labor market, workers are the source of supply and producers are the source of demand. In this case, it is the buyers (producers) who typically set the price, which is called the wage rate. If the wage rate a company sets is too high, it will overpay its workers and lose money. If it sets a wage that is too low, it will lose workers to competing firms. Eventually, the wage rate will be driven to the level that balances supply and demand.

Equilibrium and Disturbances

When the price is just right, so that there is no excess supply or demand, we say that the market is in equilibrium. However, events are always happening that cause changes to the equilibrium. We call these events disturbances. For example, suppose that a fire burns down one of the low-price restaurants in Wheaton. This is a negative supply disturbance. If the other low-priced restaurant keeps its price at $35 a meal, it will find that 60 customers is more than it can handle. So they will raise their prices, which will reduce the total demand for restaurant meals. The new equilibrium price might be $45, the same as the price set by a higher-price restaurant. At this price, 50 couples will dine out, with 25 going to each restaurant that charges that price.

In general, there are four types of supply and demand disturbances, and their impact is summarized below. We use the example of the market for restaurant meals in Wheaton.

Short Run and Long Run

In the past, oil producing countries occasionally have engineered supply disruptions. In the short run, this tends to cause a spike in prices of oil products, such as gasoline. In the long run, the prices of oil products tend to settle down.

This is a common pattern with disturbances. In the short run, prices move by a lot. In the long run, new supply comes in and demand diminishes.

For example, in the oil market, in the short run people do not change their driving habits much in response to an increase in gasoline prices. In the long run, they may drive less and switch to more fuel-efficient cars. In the short run, competing suppliers cannot increase production much in response to an increase in price. In the long run, oil exploration rises when prices are higher, which helps to bring on more supply.

The elasticity of demand is the percentage decrease in demand in response to a one percent increase in price. The elasticity of supply is the percentage increase in supply in response to a one percent increase in price. The elasticities of supply and demand usually are higher in the long run than in the short run. There are more substitution possibilities in the long run than in the short run. When elasticities are high, market disturbances tend to affect prices relatively little and quantities transacted relatively a lot.

The elasticity of supply in an industry will be very large if there is no important resource that is fixed. For example, in the lawn mowing business, it is easy for new firms to get started, and it is easy to add new capital and labor to the industry. It is also easy for people to get out of the business if demand drops off. Overall, we would expect the elasticity of supply to be very high, so that we could have a large increase in the demand for lawn mowing service without having a large impact on price.

When the computer language Java first was released in 1996, many companies wanted to try using Java in Web applications. The elasticity of supply was low--no matter how much you were willing to pay for a Java programmer, there were few professionals with experience in the new language. The elasticity of demand also was low, in that companies that wanted to develop in Java were reluctant to substitute alternative languages.

In the short run, with these low elasticities, the wages for Java programmers shot up, to $200 an hour and more. In the long run, more people learned Java and some companies postponed Java projects to save on expense. Eventually, the wage rate for Java programmers settled down to something more reasonable.

H = 10W where H is hours of labor and W is the wage rate, in dollars.

A this point, the demand for Java programmers was low. It was given by

H = 2,000 - 40W

Supply and demand were equal when W = $40 and H = 400.

Next, suppose that once Java was released officially, the demand for Java programmers shot up. The new demand for Java programmers in the short run was given by

H = 10,000 - 40W

Suppose that in the short run the supply of Java programmers was given by

H = 10W

Setting supply equal to demand, we have

10,000 - 40W = 10W

Solving for W gives a value of $200 for equilibrium wage rate. This means that H is 2000, so that the equilibrium quantity is 2000 hours of Java programming.

Next, however, suppose that the long-run elasticity of supply were higher, so that we have

H = 160W

In the long run, programmers who are earning $40 an hour using other languages will obtain training in Java. In the short run, not enough programmers have this training. In the short-run supply schedule, each $1 increase in wages only increased hours supplied by 10. In the long-run supply schedule, each $1 increase in wages increases hours supplied by 160. This means a much higher elasticity of supply.

Now, when we solve for W we get $50 for the equilibrium wage rate. The hours of Java programming are now 8000. We can summarize the results as follows: