Suppose that you are the chief economist for a benevolent dictatorship. You are given the following assignment.

You are to allocate all of the resources in the economy. We will give you whatever information you ask for. Based on that information, you must tell each person how much to work each day, and at what job. You must decide how much of every intermediate and final good to produce. You must decide which combination of inputs to use to produce every good. You must decide how much of each final good to give to each person to consume. When you make all of these millions of decisions, they have to satisfy this rule for economic efficiency: each person in the economy is as well off as he or she could possibly be without making someone else worse off. That is, when you are finished with your allocations, there is no re-allocation that could improve the happiness of one person while leaving everyone else's happiness unchanged or improved.

(The efficiency criterion is know as Pareto optimality, after Italian economist Vilfredo Pareto, who articulated the concept in 1906. It is a condition for efficiency, but it has nothing to say about equity or fairness.)

As the chief economist for a benevolent dictatorship, you probably would find your task overwhelming. Trying to allocate resources among millions of different uses to try to produce an efficient result seems to be an immensely complex task.

What we will be learning in this part of the course is that when property rights are clearly defined and markets are competitive, the resource allocation that takes place on the basis of decentralized individual decisions achieves Pareto optimality. Even if as chief economist for a benevolent dictatorship you were given complete information about technology, skills, and individual preferences, you could not devise a better allocation than what will be arrived at by the market. Economists view markets as a remarkable decentralized process for processing information and allocating resources.

We also learn from the study of markets, or microeconomics, that there are situations in which the market allocation mechanism will lead to an outcome that is not efficient. Understanding these potential market failure situations helps us to identify opportunities where government intervention might improve on the decentralized market outcome.

One task for decentralized markets is to enable consumers to choose the goods and services that will give them the most satisfaction. Instead of "satisfaction" or "pleasure," we use the term utility. We say that consumers try to maximize utility.

When you go into an ice cream shop, what are you likely to order? One scoop of chocolate in a sugar cone? Two scoops of pistachio? Frozen yogurt in a cup? A large sundae?

As an economist, I cannot predict which choice you will make. But I'll bet you never walk up to the counter and say, "Give me ten gallons of every flavor you've got in the freezer." Why not?

You might say that you do not order all of that ice cream because you could not afford it. That may be true, and that is a reasonable answer. However, you might have enough money or credit to pay for gallons of ice cream. Even so, you would not buy that much. Eating ice cream obeys the law of diminishing returns. You do not spend more than a few dollars at a time on ice cream, because the additional ice cream is not worth as much to you as the first scoop or two.

Here is a numerical example that we can use to drive home this point, which is really nothing but common sense. Suppose that each scoop of ice cream costs one dollar, and that the total utility you get from the ice cream you consume at a single sitting obeys this pattern:

If you look at the table and say that the optimal number of scoops of ice cream is 4, then you've got the wrong answer. It is a reasonable mistake, but it is important to understand why it is wrong.

It is true that $7.80 is the most satisfaction that you can get from ice cream, because after that you become satiated and your satisfaction goes down after eating more ice cream. But optimization means comparing benefits and costs, and when you take cost into account, 4 scoops of ice cream is too many.

What a consumer tries to do is maximize consumer's surplus, which is the difference between benefits and costs. With 4 scoops of ice cream, the consumer's surplus is $7.80 - $4.00, or $3.80. With 3 scoops of ice cream, the consumer's surplus is $7.10 - $3.00, or $4.10. With 2 scoops of ice cream, the consumer's surplus is $5.70 - $2.00, or $3.70.

The consumer should order 3 scoops of ice cream, because that is what maximizes consumer's surplus. Another way to see this is to compare marginal benefits with marginal costs. Marginal means "the next unit's." To maximize consumer's surplus, we keep consuming more units as long as the marginal benefit exceeds the marginal cost. Starting with no scoops of ice cream, the first scoop brings $4 of marginal benefits at $1 of marginal cost. The second scoop brings $1.70 of marginal benefit (the difference between $5.70 for two scoops and $4.00 for one scoop) at $1 of marginal cost. The third scoop brings $1.40 of marginal benefit at $1 of marginal cost. The fourth scoop brings only $0.70 of marginal benefit at $1.00 of marginal cost. The marginal cost of the fourth scoop exceeds the marginal benefit, which is why the consumer should stop with 3 scoops.

(If the jargon of calculus appeals to you, then think of marginal as the first derivative of a function. By the same token, the law of diminishing returns is a statement about the second derivative, namely that it is negative.)

Who in the world thinks this way about ordering ice cream? Does anybody assign a dollar value to the satisfaction they get from each scoop of ice cream, and then pick the number of scoops to order based on such a valuation schedule? Of course not.

Economists believe that consumers make these sorts of decisions instinctively. In fact, consumers probably solve their optimization problems better intuitively than they could by trying to use explicit numerical modeling. Milton Friedman, a Nobel Prize winner and outstanding economics teacher, uses the metaphor of a billiard player. A great billiard player does not line up her shots by doing calculations based on the laws of physics. However, to a scientist observing her behavior, it will appear that she is acting as if she were making such calculations. To economists, consumers are like expert billiard players, successfully solving complex problems using experience and instinct.

We say that consumers get the most possible utility out of what their endowment allows them to consume. You might say that you enjoy listening to music. An economist would say that you get utility out of listening to music. It sounds as though "utility" is just jargon, and in a way, that is all it is. However, having an unusual expression allows us to articulate its properties without having to deal with the baggage of what people mean by terms like "enjoyment" or"pleasure" or "satisfaction."

Economists like to use the term utility function. Using this concept, we might say that my utility is a function of the amount of cookies that I eat, the amount of hours each week I spend folk dancing, the reliability of my car, the comfort of my clothes, the quality of the work of my tax accountant, and on and on. Every good or service that I buy goes into my utility function. In addition, the sheer amount of leisure time that I have goes into my utility function.

Some characteristics of utility functions

We assume that my utility depends on the goods and services that I consume, not on the goods and services that you consume. In reality, people like to see their friends get stuff, and they may even like to see their enemies lose stuff. However, it is easiest to work with a utility function that depends only on what I consume, not on what other people consume. We say that we assume that utility is not interdependent between consumers.

We assume that more of something is always better than less. I always would like more comfortable clothes, a more reliable car, and so on. If something is a "bad," like smelly garbage or getting mugged, then what goes in my utility function is something like "avoiding smelly garbage" or "security from mugging." That is, we take the opposite of a bad and use that as the element in the utility function.

Although more is always better than less, we invoke the principle of diminishing marginal returns. We say that with every good or service, the consumer reaches a point of diminishing marginal utility, meaning that the next unit of consumption brings less utility than the last unit of consumption. For example, when I have had nothing to eat in the morning, the first bowl of cereal gives me a lot of utility. The second bowl of cereal still gives me some utility. By the time we get to the fifth bowl, the utility is still positive, but it is small. In other words, I get diminishing marginal utility from eating cereal in the morning.

For each good or service in the economy, every consumer will act as if he increased his purchase of the good or service until the dollar value of the utility from the next unit no longer exceeds the price. We say that the consumer equates marginal utility to price.

When the marginal utility is equal to price for all goods and services, then a consumer cannot improve her well-being by altering her consumption behavior. Suppose that over the course of a year a particular consumer buys 20 comic books and goes to 30 movies. If she buys just enough comic books so that the marginal utility of a comic book is equal to the price, and she goes to just enough movies so that the marginal utility of a movie is equal to the price, then she will be worse off if she goes to fewer movies and buys another comic book.

Suppose that a comic book costs $4 and a movie costs $8. Then to go to another movie, a consumer has to give up two comic books. This is the relative price of movies. Given that relative price, a consumer will go to movies until the marginal utility of the next movie is no more than the marginal utility from two more comic books.

Suppose that comic book prices drop to $3 and movies go up to $9. Now, to go to a movie, you have to give up three comic books. This is an increase in the relative price of movies. In response to this higher relative price, consumers probably will go to fewer movies and buy more comic books. This is known as the law of demand: the quantity of a good that consumers demand is inversely related to the relative price of that good.

Suppose that comic book prices drop from $4 to $3 and movie prices drop from $8 to $6. Then the relative price of movies remains the same. Does that mean that consumers will choose the same number of comic books and movies as before? Probably not. Relative to other goods in the economy, the price of comic books has fallen, and the law of demand would predict that consumers will buy more comic books. The same is true for movies, also.

Elasticity of Demand

With lower prices relative to other goods in the economy, but the same relative price to one another, will the increase in demand for movies be more, less, or the same as the increase in demand for comic books? This is an empirical question--we cannot predict the outcome of such an experiment based on theory alone.

It could be that a 25 percent drop in the price of movies leads to a 50 percent increase in demand for movies, while a 25 percent drop in the price of comic books leads to only a 10 percent increase in demand for comic books. If this is the case, we would say that the demand for movies is more elastic than the demand for comic books.

The percentage increase in quantity demanded that comes from a one percent drop in price of a good is known as the elasticity of demand for that good. If a one percent price drop leads to a one percent increase in units demanded, then we say that the elasticity is one. If a one percent price drop leads to a two percent increase in units demanded, we say that the elasticity is two. When the elasticity of demand is greater than one, we say that demand is elastic. When the elasticity of demand is less than one, we say that demand is inelastic.

When demand is elastic, a drop in the price of a good leads to an increase in spending on that good. If the price drops by one percent and quantity remained the same, then spending would drop by one percent. However, if quantity increases by more than one percent, then total spending (price times quantity) actually goes up.

If the price of gasoline sold everywhere goes down by 20 percent, your family is not likely to make many changes in your use of cars in the short run. Thus, the demand for gasoline is likely to be inelastic in the short run.

On the other hand, suppose that the price of one brand of gasoline falls by 20 percent, and other brands' prices stay the same. Then many people will switch to the low-priced brand. For that company, demand for gasoline will be very elastic.

Leisure

One of the most important decisions that a consumer must make is how much time to spend working. Although some people enjoy their jobs, it is safe to say that most people prefer leisure. Economists treat leisure as a good, and work as a "bad" (something people try to avoid).

The price of an hour of leisure is the money income that you give up by not working that hour. Therefore, the price of leisure is your hourly wage.

Economic theory says that you optimize with respect to your choice of leisure just as you optimize other consumption decisions. To optimize, you take enjoy leisure until the marginal utility of the next hour of leisure is no longer greater than your hourly wage.

There are a number of peculiarities in the labor-leisure trade-off. For one thing, taxes play a role. The money income from work is taxed through the income tax and the Social Security tax. Your leisure time, including time spent doing odd jobs around the house, is not taxed. In addition, when you spend money income on goods and services, you pay sales taxes. On the other hand, the pure consumption of leisure (just sitting around) does not give rise to sales taxes. The effect of taxes is to reduce your take-home pay, or net wage. Thus, taxes lower the relative price of leisure. The higher the tax rate on the next hour of labor, the more leisure you will consume.

Another peculiarity is that for many people, the work week is an "all-or-nothing" 40-hour package. You may not be able to choose to work 27 hours and 13 minutes a week, even if that is what you calculate to be the point where your marginal utility of leisure equals your wage rate. By the same token, people who work for a salary often cannot increase their money income by working extra hours on top of what is expected.

If these peculiarities were not present, then I would expect to see fewer people doing household projects, like papering their walls or planting shrubs. Instead, someone would work additional hours and use the income to pay professionals to do wallpapering or shrub planting. If my comparative advantage were planting shrubs, then I should plant shrubs for a living. The fact that I do not plant shrubs for a living suggests that I am better at something else. I tell friends that if I ever plant shrubs, that is a sign that markets are not working as well as they should.

Leisure as a Unit of Measurement

One way to measure the cost of something you buy is to count how many hours you have to work in order to pay for it. For example, if a movie costs $8 and you earn $6 an hour, then you have to work one hour and twenty minutes to pay for a movie. That is, a movie costs you one hour and twenty minutes of leisure. In this way, leisure becomes a unit of measurement.

For someone who earns $16 an hour, the leisure cost of a movie is less. You only have to give up half an hour of leisure to pay for the movie.

One way to describe economic growth is that it has dramatically reduced the leisure cost of many goods for the average person. The sticker prices on cars are higher than they were 50 years ago, but much of that change represents general inflation. Using leisure as the unit of measurement is a way to abstract from inflation. John Shepler points out that

a 1908 Ford Model T cost most people about 2 years wages. A 1997 Taurus has an equivalent cost of 8 months...

But what about gasoline? Surely the oil crisis of the mid 70's and the continuing tensions in the Middle East have made cheap gas a luxury of the past. Not really. Those prices at the pump truly are less than a few years ago. Now get this. You worked 5.4 minutes to buy a gallon of gas in 1997. You worked 6.6 minutes to buy that same gallon in 1970, before the Arab oil embargo and about the time I remember handing quarters to the station attendants.

Think milk is expensive? A half-gallon took 39 minutes to earn in 1919, 16 minutes for our folks in 1950, 10 minutes in 1975 and it's down to 7 minutes for us today. Ground beef has followed a similar pattern, dropping from 30 minutes a pound in 1919 to 6 minutes in 1997. In fact a market basket of typical food items has slid from 9.5 hours work in 1919 to 3.5 hours in 1950 and is now only 1.6 hours.

Cox and Alm, in Myths of Rich and Poor, point out that the average leisure cost of a pair of Levis was 9 hours and 42 minutes in 1900, compared to just 3 hours and 24 minutes a few years ago. The average leisure cost of a three-pound chicken has fallen from 2 hours and 40 minutes to 14 minutes. The cost of a Hershey chocolate bar has fallen from 20 minutes to 2.1 minutes. In 1910, a 3-minute coast-to-coast phone call cost 90 hours and 40 minutes of leisure! Today, many people treat such phone calls as free.

Although better technology has lowered the average leisure cost of many products, there are some goods that are more expensive than they were years ago. For example, a movie ticket cost 19 minutes recently, and it cost only 17 minutes in 1960.

The consumer's motivation to borrow or save is to shift consumption over time. If the consumer wants to consume more now and less later, the consumer borrows. If the consumer wants to consume less now and more later, the consumer saves.

The relative price of consumption now vs. a year from now is the interest rate. If the interest rate is 4 percent per year, then by deferring $100 of purchases today you can have $104 in purchases a year from now.

To make a decision as to how much to spend this year relative to income, a family has to optimize with respect to the relative price, namely the interest rate. You spend until the marginal utility of $1 of spending today is no greater than (1 plus the interest rate) times the marginal utility of spending $1 a year from now.

If the interest rate is high, that means that the cost of moving consumption from the future to the present is high. For most consumers, that means that they will choose to borrow less or save more. A high interest rate means that by putting off a little bit of enjoyment now you can have a lot more later. Just as the relative price of apples and oranges enters into your decision about which fruit to buy, the interest rate affects your decision about how much you want to shift consumption between the present and the future.

In reality, there are many forms of saving. You can have a savings account, a money market fund, a certificate of deposit, or shares of stock, among other vehicles. There also are many forms of borrowing. You can have a mortgage loan on your home, a car loan, or credit card debt, among other instruments.

Consumer Durables

One form of saving is through buying durable consumer goods. For example, suppose that we spend $30,000 on a new car, and we plan to keep the car for ten years. How should we account for that in terms of this year's consumption?

The answer is to treat durable consumer goods (goods that last several years) as capital goods. This year's consumption is equal to the amount of the car that we "use up" in the first year. One way to think of this is to look at the price for which we could sell the car in a year. If that price is $23,000, then the first year's consumption is $7,000. The remaining $23,000 should be counted as saving for future years' consumption.

To see this, imagine two families, each with $30,000 in income. Family A leases a car for $8,000 a year, spends $30,000 on other goods and services, and saves $22,000. Family B also spends $30,000 on other goods and services, but spends the remaining $30,000 on a car.

A year later, suppose that each family must use all its income for other goods and services. Family A has to lease a car for another year, so it has to use some of its cash savings. Family B keeps using the car that it bought the first year. Both families are using savings, with A's savings in the form of cash and B's savings in the form of the car.

Consumer durables create an accounting issue. If you were to add up all of your spending in a year, you probably would include a $30,000 car purchase. However, an economist would treat as consumption only the value of the car that you "use" this year, say, $7,000. On a cash flow basis, you have spent $30,000. On an economic basis, you have consumed $7,000 and saved $23,000.

Human Capital

In addition to financial saving, there is another way that you can forego some consumption in the near term in order to increase your consumption in the long term. That is by investing in human capital. Human capital is the term that we use for education and skill that make you more productive.

For example, consider the decision faced by a college basketball player who might be drafted by the pros at the end of his junior year. Suppose that if he stays in college, his skills will improve so that his salary will be $5 million a year for his first two years as a pro. On the other hand, if he goes pro right now, his salary will be $3 million dollars a year for the next three years. What should he do?

Suppose that the interest rate is 10 percent. The present value of $5 million one year from now is $5/1.1 = $4.55 million. Similarly, we can calculate the present value of the player's salary for the next three years. The results are in the following table, with salaries shown in millions of dollars, comparing the choice to go pro immediately or to defer going pro.

According to these calculations, it pays for this player to wait until turning pro, because the present value of his future earnings will be slightly higher. Of course, taking into account other factors, such as the risk of injury in college, he might choose to go pro right away.

Another factor that might lead the player to turn pro is the fact that if he turns pro he can start right away to consume at a high level. In theory, he could stay in college and borrow a couple of million dollars, to be repaid after he turns pro. However, in reality this is impossible, for a number of reasons. In fact, it is generally the case that it is difficult or impossible for people to borrow against their human capital. Human capital tends to be illiquid, and that tends to bias people against investing in human capital.

Few of us go to college in order to become better basketball players. However, for many people, education is an investment. Economists generally find that the rate of return for additional years of schooling is high. However, there is controversy over whether the additional investment involved in going to, say, Harvard, pays off compared with the lower tuition of, say, the University of Maryland. When you control for the level of ability at the point of high school graduation, as measured by grades and SAT scores, it is not clear that the incomes of people who go to expensive private colleges are dramatically higher than those of people who attend state universities.

Another example of human capital investment is medical school. To pay for medical school, most students take out large loans. Those loans are paid back out of the returns that you earn as a doctor.

Specific Human Capital

Economists also believe that the concept of human capital applies to on-the-job training. We call this specific human capital, because much of what you learn on a job may apply only at that specific company. One joke is that specific human capital means knowing the location of the bathroom, and general human capital means being able to find it by reading the sign on the door.

When I acquire specific human capital at a company, I learn procedures, terminology, and best practices at that company. If I go to a different company, not everything that I learned at the first company will be transferable. Only my general human capital goes with me everywhere.

If I have a valuable general human capital, such as database programming skills, my employer is forced to pay me a high salary. Otherwise, I will go elsewhere. On the other hand, my knowledge of a particular company's data terminology is not useful elsewhere. That is specific human capital, and my company does not necessarily have to pay me a premium for it.

Although a company need not pay a premium salary to employees with specific human capital, the company will pay for the cost of acquiring that human capital. A company pay to put me through a training program on its data terminology, because the benefit of that training will accrue to the company rather than to me. On the other hand, if the company were to pay for me to get general database expertise, I could then use that expertise to get a higher salary elsewhere.

When a company pays for general training, it may require you to commit to staying with the company a certain number of years. If you do not stay, then you may have to reimburse the company for the cost of the training.

Overall, the decision to invest in specific human capital is made primarily by the firm. The firm also retains most of the benefits. On the other hand, the decision to invest in general human capital is made primarily by the individual. The individual retains most of the benefits.

In economic theory, people play two main roles in the market. As we have just seen, they are consumers. The other main role is producers. For producers, the economic problem is to maximize profits. The key decisions are which outputs to produce, how much of each output to produce, and which inputs to use to produce the outputs. We will take these decisions one at at time.

How Much Output?

Let us return to Josh's lawn mowing business, and focus on the decision of how many lawns to mow each day. To make things simple, suppose he already has leased a lawnmower and a pickup truck. Also, to avoid confusing the output decision with Josh's labor-leisure choice, let us assume that all of the labor is done by two hired workers.

Now, Josh has to decide how many hours for which to hire the workers, which in turn will determine how many lawns his company mows. For example, if each worker works 5 hours, then the total hours worked will be 10 and the total number of lawns mowed will be, say, 9. The key factors in Josh's decision will be worker productivity, the wage rate, and the price he can charge for mowing lawns.

Suppose that Josh receives $18 for each lawn that his workers mow. Finally, suppose that his workers' lawnmowing productivity is as follows.

How many hours should Josh have his employees work? We look at profit, which is revenue minus cost, to try to find a maximum. The maximum profit is at 14 hours of work, mowing 13 lawns, with revenue of $234, cost of $154, and profit of $80.

Another way to find the point of maximum profit is for Josh to hire additional hours until the next hour will add less in revenue than in cost. When we start at 12 hours of work, the next two hours produce two more lawns mowed, which gives Josh $36 in additional revenue compared with $22 in marginal cost. However, when the employees work a total of 14 hours (7 hours apiece), the next two-hour increment produces only one more lawn mowed, which means only $18 in revenue. This is less than the cost of two additional hours, which is $22. So, he should stop after 14 hours.

Another way of putting this is that a firm should increase its output as long as the marginal cost of producing additional output is less than the price of output. In short, we stop increasing output when price equals marginal cost.

Which Outputs?

Suppose that two partners are just starting a business in the field of email management solutions for corporations. They are in the process of discussing the strategy for their new venture. One partner is a computer wizard, named Cool. The other partner is a marketing and sales expert, named Slick.

A difficult decision that the partnership faces is whether it should try to make money by developing a product or by selling consulting services. Cool thinks that the company should focus on product development. "We'll get a lot more leverage out of my computer skills if we can sell a product," Cool says.

"I don't agree," Slick replies. "Products are really hard to sell. It means I'll be wasting a lot of time giving presentations to companies that are not ready to make up their minds. I say we should start out doing consulting. It's much easier to get a decision on a consulting contract."

Cool and Slick continue to argue. Cool does not like consulting, because it uses up a lot of his time and has limited revenue potential. Slick likes consulting because the cost of sale is lower. How can this issue be resolved?

The firm's goal is to maximize profits. To do so, Cool and Slick are going to have to make some estimates about the the technology and about prices.

The technology issue concerns what they can produce with their inputs, which consist of technical effort and sales effort. The price issue concerns what the prices are for a product and for consulting services.

Slick and Cool each have 2000 hours a year that they can spend working. Slick says, "For every 400 hours I put into selling consulting services, I can generate 6 consulting contracts. Each contract is worth $8000. So I can generate 30 contracts in a year, for a total of $240,000 a year in revenue."

"That's great," Cool replies. "But each contract takes 10 hours of my time, and I don't have 3000 hours. So the most we can do in consulting is 2000 hours, or $160,000 worth. What if you put all of your time into product sales?"

"Well," Slick says, "that means you put all of your time into product development, so we have a really cool product. In that case, I could sell maybe 1000 licenses for $150 each, or a total of $150,000. We're better off with consulting."

"Not so fast," says Cool. "What if we compromise? I don't develop quite as fancy a product, but I make myself available to spend some time doing consulting."

After a while, they arrive at the following estimates of what would happen under alternative allocations of time.

From the standpoint of maximizing revenue, the best approach is for Cool to spend 800 hours on product development and 1200 hours on consulting. Slick will spend 1200 on product sales, and 800 hours on consulting sales.

We say that by shifting hours from product development to consulting, Cool and Slick can transform their output from product licenses to consulting contracts. Going from the first row in the table to the second row, product licenses decrease by 230 and consulting contracts increase by 6. The transformation ratio, of 6/230, is greater than the price ratio, of $150/$8000, so on the margin the transformation is profitable. Similarly, from the second row to the third row, the transformation ratio is 6/290, which is still greater than the price ratio. However, moving from the third row to the fourth row, the transformation ratio is 6/340, which is less than the price ratio. On the margin, it does not pay to transform 340 site licenses into 6 consulting contracts.

In general, we say that the producer sets the marginal rate of transformation between two outputs to be equal to the relative price of those two outputs.

Choice of Inputs

We already encountered the issue of the choice of inputs when we discussed substitution. The problem is to choose the optimal levels of input to produce a given level of output.

For example, suppose that Cool and Slick hire employees to do consulting. An expert programmer charges $80 an hour, and a novice programmer charges $25 an hour. The more expert hours we use, the fewer novice hours we need. The problem is to choose the optimal mix to complete two consulting contracts. The combinations that can do this are:

The cost-minimizing combination is 80 hours of experts with 300 hours of novices. Once again, we can see find the answer by looking at marginal changes.

• When we increase expert hours from 40 to 50, we reduce novice hours from 600 to 400. On average, we save 20 novice hours for each additional expert hour. This is higher than the ratio of the expert wage to the novice wage, so that it pays to add experts.

• When we increase expert hours from 50 to 80, we reduce novice hours from 400 to 300. On average, we save 3.3 novice hours per expert hour, and this is slightly higher than the ratio of the expert wage to the novice wage.

• When we increase expert hours from 80 to 100, we reduce novice hours from 300 to 240. On average, we save 3.0 novice hours per expert hour, and this is slightly lower than the ratio of the expert wage to the novice wage. Thus, at the margin it does not pay to increase expert hours from 80 to 100.

The way we describe this optimization is to say that the producer sets the marginal rate of substitution between inputs equal to the ratio of the prices of the inputs.

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: