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Analysis of firm behavior and the management of resources begins with the firm’s production function, which describes how resources are turned into output. There are three broad categories of resources, which are also sometimes called inputs or factors of production. The first category is labor, by which we mean the physical human effort that goes into production.

The second category is capital, which can be subdivided into two components, physical capital and human capital. Physical capital refers to things like factories, machines, and equipment that are part of the production process. Human capital refers to know-how and managerial skills that go into production -- more the thinking side of human production, compared to the sheer labor effort.

Finally, the third category is thought of as land, particularly when referring to agricultural production. Capital needs a special note. First, in the context of production, economists do not mean money when they refer to capital.

In common parlance, people may refer to money as capital, specifically financial capital, when they talk about starting a business, for example. However, money itself does not produce anything therefore is not part of the production function; instead it buys the resources that produce things. Second, both physical the human capital share some characteristics: both are produced themselves (human capital being produced by education), and neither is “used up” in production.

Sometimes economist refer to the production function as the “technology” used to produce something. Production functions take on different characteristics in the short run and in the long run. The short run refers to the period of time in which some resources -- especially capital -- are fixed.

For example, we often may only be able to alter our employment of labor in the short run. In the long run, all inputs are variable and nothing is fixed. The marginal product of an input is a measure on how output changes as more of that input is added, holding everything else constant.

The law of diminishing marginal product says that although output may go up as an input is added, ceteris paribus, the rate at which output goes up will decline. In other words, marginal product will be positive, but declining, as the input increases. This makes sense: picture a firm with a given factory size (capital) adding workers.

As it does so, output should go up -- but not at a constant rate, because eventually the limited size of the factory becomes a “bottleneck” inhibiting increased production. In the long run, production functions can be characterized by returns to scale. Increasing returns to scale means that scaling up all inputs by x percent leads to an increase in output of more than x percent.

Similarly, decreasing returns to scale means that increasing all inputs by x percent leads to an increase in output of less than x percent. Many real-world production functions are characterized by constant returns to scale: increasing inputs by a certain percent leads to the same percentage rise in output. It is important to keep in mind the distinctions between marginal product and returns to scale.

The cost functions of a firm are derived directly from its production function. In the short run, firms have fixed costs associated with their fixed inputs. Likewise, variable costs are associated with variable inputs.

The sum of fixed and variable costs are total costs. The marginal cost of production is the extra cost associated with producing another unit of output. Marginal cost is directly related to marginal product for the short run.

For example, if labor is the only variable input in the short run, then the law of diminishing product implies that the marginal cost of production will have to rise eventually. Average costs are also used frequently. In the short run, firms have average fixed costs and average variable costs, which sum to average total cost.

Typically the average variable and average total cost curves are “U-shaped” meaning that they initially decline but eventually rise as output increases, at lest in the short run. In the long run, all costs are variable. The average total cost curve for the long run is the “lower envelope” of all the different possible short run averages total costs curves, each typically associated with a differing amount of capital.

If the average cost of production declines initially as output increases, the firm enjoys economies of scale in the long run -- a phenomenon associated with increasing returns to scale in production. Economies of scale are exhausted at minimum efficient scale. Constant returns to scale imply constant average total costs in the long run, and decreasing returns to scale imply rising average total costs in the ling run, or diseconomies of scale.

Managers need to employ marginal analysis to maximize profits for the firm. In terms of output, this means comparing marginal revenue to marginal cost. Marginal revenue is the additional revenue generated by producing and selling another unit of output.

Marginal cost, as noted above, refers to the additional cost of producing that output. If marginal revenue is greater than marginal cost, producing another unit of output is profitable and production should be increased. If marginal revenue is less than marginal cost, producing another unit of output is not profitable and in fact output should be decreased.

If initially marginal revenue is greater than marginal cost and the firm increases production, marginal revenue will fall (except in perfect competition, where it remains constant for the price-taking firm), because the firm will have to lower its price to sell more units. At the same time, increasing output means facing higher marginal costs, especially in the short run due to the law of diminishing marginal product. Thus as output increases, marginal revenue falls and marginal cost rises until the two are equal.

At this point the firm will have maximized it profits, leading to a very important principle in managerial economics: a necessary condition for profit maximization is marginal revenue must equal marginal cost. Similarly, marginal analysis can be employed in thinking about the optimal employment of resources. Once again, the manager weighs the benefits of employing one more unit of a resource with the costs.

Hiring one more unit of a resource resulting in more output, by the amount of the marginal product of that resource. If that output is then sold in the marketplace, the firm earns the value of the marginal product for that resource as income. The effective manager must compare the value of the marginal product with the marginal resource cost.

Suppose for example that a firm was considering hiring one more worker for a day, and the worker could produce an extra 20 widgets. If widgets sell for $5 each, then the value of the marginal product of that worker would be $100 (20 x 5 = 100). If the marginal resource cost of the worker is, say $80 per day in wages, then the firm will find it profitable to hire the worker, since $100 of revenue coming in more than the $80 of wages expended.

On the other hand, if the worker costs $120 per day, it is not worth it to the firm to hire the worker. Suppose the firm pays the worker $80 and there fore hires him. The firm then considers hiring another worker.

But perhaps the marginal product of labor is declining, and that worker’s marginal product is less than 20 widgets. The firm must go through the same computations, looking at this set of rules: if the value of the marginal product is greater than the marginal resource cost, hire more workers. If the value of the marginal product is less than the marginal resource cost, hire fewer workers.

As with output, the optimum is achieved only when the marginal values are the same. A necessary condition for profit-maximizing resource employment is the value of the marginal product must equal marginal resource cost. To most people capital means a bank account, a hundred shares of IBM stock, assembly lines, or steel plants in the Chicago area.

These are all forms of capital in the sense that they are assets that yield income and other useful outputs over long periods of time. But these tangible forms of capital are not the only ones. Schooling, a computer training course, expenditures of medical care, and lectures on the virtues of punctuality and honesty also are capital.

That is because they raise earnings, improve health, or add to a person’s good habits over much of his lifetime. Therefore, economists regard expenditures on education, training, medical care, and so on as investments in human capital. They are called human capital because people cannot be separated from their knowledge, skills, health, or values in the way they can be separated from their financial and physical assets.

Education and training are the most important investments in human capital. Many studies have shown that high school and college education in the United States greatly raise a person’s income, even after netting out direct and indirect costs of schooling, and even after adjusting for the fact that people with more education tend to have higher Iqs and better-educated and richer parents. Similar evidence is now available for many years from over a hundred countries with different cultures and economic systems.

The earnings of more educated people are almost always well above average, although the gains are generally larger in less developed countries. Consider the differences in average earnings between college and high school graduates in the United States during the past fifty years. Until the early sixties college graduates earned about 45 percent more than high school graduates.

In the sixties this premium from college education shot up to almost 60 percent, but it fell back in the seventies to under 50 percent. The fall during the seventies led some economists and the media to worry about “overeducated Americans.” Indeed, in 1976 Harvard economist Richard Freeman wrote a book titled The Overeducated American.

This sharp fall in the return to investments in human capital put the concept of human capital itself into some disrepute. Among other things it caused doubt about whether education and training really do raise productivity or simply provide signals (“credentials”) about talents and abilities. But the monetary gains from a college education rose sharply again during the eighties, to the highest level in the past fifty years.

Economists Kevin M Murphy and Finis Welch have shown that the premium on getting a college education in the eighties was over 65 percent. Lawyers, accountants, engineers, and many other professionals experienced especially rapid advances in earnings. The earnings advantage of high school graduates over high school dropouts has also greatly increased.

Talk about overeducated Americans has vanished, and it has been replaced by concern once more about whether the United States provides adequate quality and quantity of education and other training. This concern is justified. Real wage rates of young high school dropouts have fallen by ore than 25 percent since the early seventies, a truly remarkable decline.

Whether because of school problems, family instability, or other factors, young people without a college or a full high school education are not being adequately prepared for work in modern economies. Thinking about higher education as an investment in human capital helps us understand why the fraction of high school graduates who go to college increases and decreases from time to time. When the benefits of a college degree fell in the seventies, for example, the fraction of white high school graduates who started college fell, from 51 percent in 1970 to 46 percent in 1975. many educators expected enrollments to continue declining in the eighties, partly because the number of eighteen-year-olds was declining, but also because college tuition was rising rapidly.

They were wrong about whites. The fraction of white high school graduates who enter college rose steadily in the eighties, reaching 60 percent in 1988, and caused an absolute increase in the number of whites enrolling despite the smaller number of college-age people. This makes sense.

The benefits of a college education, as noted, increased in the eighties. And tuition and fees, although they rose about 39 percent from 1980 to 1986 in real, inflation-adjusted terms, are not the only cost of going to college. Indeed, for most college students they are not even the major cost.

On average, three-fourths of the private cost—the cost borne by the student and by the student’s family—of a college education is the income that college students give up by not working. A good measure of this “opportunity cost” is the income that a newly minted high school graduate could earn by working full-time. And during the eighties this forgone income, unlike tuition, did not ri8se in real terms.

Therefore, even a 39percent increase in real tuition costs translated into an increase of just 10percent in the total cost to students of a college education. The economics of human capital also account for the fall in the fraction of black high school graduates who went on to college in the early eighties. As Harvard economist Thomas J.

Kane has pointed out, costs rose more for black college students than for whites. That is because a higher percentage of blacks are from low-income families and, therefore, had been heavily subsidized by the federal government. Cuts in federal grants to them in the early eighties substantially raised their cost of a college education.

According to the 1982 “Report of the Commission on Graduate Education” at the University of Chicago, demographic-based college enrollment forecasts had been wide of the mark during the twenty years prior to that time. This is not surprising to a “human capitalist.” Such forecasts ignored the changing incentives—on the cost side and on the benefit side—to enroll in college.

The economics of human capital have brought about a particularly dramatic change in the incentives for women to invest in college education in recent decades. Prior to the sixties American women were more likely than men to graduate from high school but less likely to continue on to college. Women who did go to college shunned or were excluded from math, sciences, economics, and law, and gravitated toward teaching, home economics, foreign languages, and literature.

Because relatively few married women continued to work for pay, they rationally chose an education that helped in “household production”—and no doubt also in the marriage market—by improving their social skills and cultural interests. All this has changed radically. The enormous increase in the labor participation of married women is the most important labor force change during the past twenty-five years.

Many women now take little time off from their jobs even to have children. As a result the value to women of market skills has increased enormously, and they are bypassing traditional “women’s” fields to enter accounting, law, medicine, engineering, and other subjects that pay well. Indeed, women now comprise one-third or so of enrollments in law, business, and medical schools, and many home economics departments have either shut down or are emphasizing the “new home economics.”

Improvements in the economic position of black women have been especially rapid, and they now earn just about as much as white women. Of course, formal education is not the only way to invest in human capital. Workers also learn and are trained outside of schools, especially on jobs.

Even college graduates are not fully prepared for the labor market when they leave school, and are fitted into their jobs through formal and informal training programs. The amount of on-the-job training ranges from an hour or so at simple jobs like dishwashing to several years at complicated tasks like engineering in an auto plant. The limited data available indicates that on-the-job training is an important source of the very large increase in earnings that workers get as they gain greater experience at work.

Recent bold estimates by Columbia University economist Jacob Mincer suggest that the total investment in on-the-job training may be well over $100 billion a year, or almost 2 percent of GNP. No discussion of human capital can omit the influence of families on the knowledge, skills, values, and habits of their children. Parents affect educational attainment, marital stability, propensities to smoke and to get to work on time, as well as many other dimensions of their children’s lives.

The enormous influence of the family would seem to imply a very close relation between the earnings, education, and occupations of parents and children. Therefore, it is rather surprising that the positive relation between the earnings of parents and children is not strong, although the relation between the years of schooling of parents and children is stronger. For example, if fathers earn 20 percent above the mean of their generation, sons at similar ages tend to earn about 8 percent above the mean of theirs.

Similar relations hold in Western European countries, Japan, Taiwan, and many other places. The old adage of “from shirtsleeves to shirtsleeves in three generations” is no myth; the earnings of grandsons and grandparents are hardly related. Apparently, the opportunities provided by a modern economy, along with extensive public support of education, enable the majority of those who come from lower-income backgrounds to do reasonably well in the labor market.

The same opportunities that foster upward mobility for the poor create an equal amount of downward mobility for those higher up on the income ladder. The continuing growth in per capita incomes of many countries during the nineteenth and twentieth centuries is partly due to the expansion of scientific and technical knowledge that raises the productivity of labor and other inputs in production. And the increasing reliance of industry on sophisticated knowledge greatly enhances the value of education, technical schooling, on-the-job training, and other human capital.

New technological advances clearly are of little value to countries that have very few skilled workers who know how to use them economic growth closely depends on the synergies between new knowledge and human capital, which is why large increases in education and training have accompanied major advances in technological knowledge in all countries that have achieved significant economic growth. The outstanding economic records of Japan, Taiwan, and other Asian economies in recent decades dramatically illustrate the importance of human capital to growth. Lacking natural resources—they import almost all their energy, for example—and facing discrimination against their exports by the West, these so-called Asian tigers grew rapidly by relying on a well-trained, educated, hardworking, and conscientious labor force that makes excellent use of modern technologies.

The problem when resources are “free” is that wrong mix of goods and services will be produced. This is a common result when decision-makers do not take into account some by-product of their actions that burdens or benefits others. A polluter, for example, considers air or water free.

For him, dumping pollutants into their air or water is a cheap way to dispose of wastes. Yet, his actions do involve costs because he affects the alternatives that others face. The polluter may make others forego clean water.

One could say that the polluter imposes some costs of production on others, although this use of the word “cost” differs from the normal meaning of cost. Those who bear this cost are not involved in the choice, and in its pure meaning cost is an alternative foregone in a choice. It is easy to show that when a decision-maker ignores some costs of his decision, his decision may be economically inefficient.

The demand curve represents the marginal benefit to consumers (and to firms because they are price takers). The supply curve represents the marginal cost to sellers, and because producing the product requires resources that could be used elsewhere, it also represents a cost to buyers. But the production of the product also generates and unwanted by-product that sellers ignore.

The marginal cost from the point of view of society as a whole includes this by-product and is thus higher than it seems to the firm. If negative externalities cause too much of a product to be produced, positive externalities should cause too little to be produced. When a person improves his house, his neighbors benefit.

Because the decision-maker will not generally consider these spillover advantages to others, less than the efficient amount of the activity will take place. When scarce resources are perceived as “free”, there will be potential value that a market will not capture. Is it possible for a society to capture this value, and if so, how?

A common “solution” to this problem has been to assume it away. This solution is especially common in plans for utopias, and writers in the Marxian tradition frequently illustrate it. In some of these arguments, pollution exists because capitalistic man is greedy, but when the new socialist man comes into existence, the problem will cease.

Solution by assumption has at times crept into mainstream economic thinking as well. A more practical solution is to increase private ownership in the system of property rights. This is an ironic solution in a way, because many environmentalists and ecologists have argued that the existence of externalities proves that a market system is seriously flawed and should be scrapped for an alternative, generally with greater state ownership and control.

Economic analysis, however, shows that externalities exist when property rights are incomplete. Reducing the role of private property would make the externality problem worse. When no one owns the air or water, there is no incentive to avoid an overuse of the resource.

In a classic example of the problem of the commons, buffalo were hunted almost to extinction in the 19th century. If an individual hunter limited his kills, he was unlikely to benefit from his restraint. A buffalo that he did not kill would probably be killed by someone else.

Yet, from the point of view of buffalo hunters as a group, the optimal strategy would have been to limit killing so that the industry could maintain itself indefinitely. In contrast with the buffalo, the number of cattle in the American West increased during the 19th century. The key difference between the different fates of buffalo and cattle was not that buffalo hunters were greedy and cattle raisers were not.

It was that cattle were privately owned and buffalo were “free”. Private-property rights force people to take into account all costs and benefits of their actions. A cattleman’s decision to kill or not kill his cattle did not affect other cattlemen in the ay that a buffalo hunter’s decision to kill or not kill buffalo affected other buffalo hunters.

When a resource is owned by all, when it is “free,” there is a strong tendency for individuals to misuse that resource. The existence of private property rights allows the law to deal with externality problems. A person who is harmed by someone’s actions can ask the courts to decide about compensation.

The court’s decision will depend on whether or not he has a right to some good or service. Courts have established property rights for clean air, clean water, scenic views, sunshine, and quiet. If a person is not due compensation, then he does not have the property rights but the other party may have them.

In this case he can pay the party harming him to stop the offending activity. Victims of pollution seldom band together and sue the polluter, nor do they band together and pay him not to pollute. The difficulty with legal action is that there are serious problems (and thus large costs) in contracting and organizing large groups for legal action.

One of these problems is the free-rider problem. Ronald Coase pointed out that pollution problems would not exist if there were no difficulties and expenses in making contracts between polluter and victim. The implication of Coase’s work is that externalities should not be a small-group problem because legal remedies will exist if only a very few people are involved.

It will only be a large-group problem. Coase shows that private-property rights are not always a feasible way to solve the externality problem of “free” resources. Another solution is for the government to act as if it were the owner of these resources.

The government does this when it regulates the number of ducks that hunters can kill. It says in effect that the government does this when it regulates the number of ducks that hungers can kill. It says in effect that the government owns the ducks, and people cannot kill them without the permission of the government.

Government can charge for the use of its resources. It could, for example, charge polluters for the use of clean water and air. This charge would make polluters take into account the side effects of their activities (or in the jargon of economists, they would internalize the externalities), and would move marginal cost curve in the graph upward.

There is some user fee (pollution tax) that would make the decision-makers’ marginal cost curves coincide with the marginal-cost-to-society curve, and thus correct the efficiency problem. Government policy dealing with pollution and negative externalities has largely been one of regulation. Most economists believe that this is a less-desirable (efficient) method of dealing with the problem than a policy of a pollution tax.

Finally, there may not be a good solution to the problem of “free” resources for two reasons. First, the cost of a solution may be greater than the benefits of the solution. Most economists believe that there is some “optimal level: of pollution.

Many productive processes produce waste products. These waste products, when considered damaging to people, are pollution. To remove them or to transform them into a form that no one considers damaging requires resources, and the use of those resources means that fewer other products can be produced.

Thus the reduction of pollution involves the weighting of costs and benefits as does virtually all other activity that economists discuss. The optimal level of pollution becomes that level at which the marginal benefit of any more reduction just equals the marginal cost of any more reduction If removing pollution that causes $1.00 worth of harm costs $10.00, it is economically inefficient to remove it. It is extremely unlikely that the optimal (economic efficient) level will ever be zero.

Second, there may be externality problems within the government just as there can be externality problems in the market. When there are externality problems in the market, we can call on the government as an outside agent to solve them. But if there problems exist in the government, there is no one to turn to.

For example, suppose that the citizens of a country are split into fifty special interest groups, and each group gets special benefits from the government. To pay for those benefits, the government must tax the citizens. The citizens end up paying a dollar in taxes to get eighty cents of special benefits.

(Bureaucracy eats up the other 20%). Though all would be better off getting rid of all special benefits, no one group will want to give up its special benefits, and the costs of organizing the fifty different groups to come up with an agreement may be very large. There may be no solution to this problem of the commons.

The reasons why free trade is desirable can be developed by extending the discussion of the Crusoe economy that is commonly used to illustrate production-possibilities frontiers. Suppose that Robinson Crusoe, living on an almost deserted desert isle, can either catch four fish a day or find eight coconuts. One day, he discovers that Friday also lives on the island.

If Friday can either catch six fish a day or find seven coconuts, can Crusoe and Friday profit by specialization and trade? The answer is clearly “yes”. Crusoe is the better coconut gatherer, and Friday the better fisherman.

However, suppose that Friday can either catch ten fish or find then coconuts. Friday is now better than Crusoe in both activities. Can there be mutual benefit from trade in this case?

Or should Friday do all the work and Crusoe none? Or should Friday refuse to trade since he is better in both? It was a major achievement of David Ricardo early in the 19th century to show that in this second Crusoe-Friday story both parties could benefit from trade.

His results contributed to the long reign of relatively free trade in 19th century England, and thus to the prosperity that England enjoyed in this period. To see that mutually beneficial trade is possible even though Friday is better in all activities, one must look to opportunity costs. Individually, both Friday and Crusoe trade with nature in the production process.

Crusoe can get another fish only by giving up time in which he could find two coconuts, and in getting another coconut he sacrifices one-half of a fish. Thus, a fish costs Crusoe two coconuts and a coconut costs one-half of a fish. Friday can get another fish by giving up the time during which he can find another coconut, or one-tenth of the day.

During this time, he could find one coconut. For Friday, trading with nature means that one fish costs one coconut and vice versa. Looking at these opportunity costs tells us that Crusoe finds coconuts cheaper and Friday finds fish cheaper.

The table below summarizes these results. We still have not discovered whether Friday and Crusoe could do better trading with each other rather than with nature. A way to answer this question is to try a few prices.

Suppose that one fish was worth one-half a coconut, or one coconut was worth two fish. With this trading ratio both would find fish cheap and coconuts expensive. Therefore, both would want to sell coconuts and buy fish.

Hence at this price no trading would take place. Suppose that the trading ratio were one fish for 1.8 coconuts (and thus one coconut cost 5/9 fish). With this ratio, Crusoe would find fish cheap—rather than spend two coconuts to catch one, he could spend 1.8 coconuts and buy one.

Hence, Crusoe would be willing to sell coconuts. Friday would find coconuts cheap—rather than give up one fish by gathering his own coconuts, he could sell 5/9th of a fish and get one. Hence, Friday would be willing to sell fish.

Trade will take place because both individuals find that it improves their well-being. In the above example, trade occurs because of comparative advantage. Friday is better in everything than Crusoe, but he is “more better” in catching fish and “less better” in finding coconuts.

Crusoe is worse than Friday in everything, but he is “less worse” in finding coconuts. Though they both benefit from trade, Friday will maintain a higher standard of living. The example of Crusoe and Friday also illustrates that exchange is not a zero-sum game, but a positive sum game.

In a zero-sum game, whatever anyone wins comes at someone else’s expense. In poker, for example, if one person wins $100, some other person(s) must have lost $100. If the amount of winnings is added up and the amount of losings is subtracted away, the result will be zero.

The term “Zero-sum game” reflects this total. In contrast, both parties in a voluntary exchange can benefit. Because total winnings exceed any losses, the name “positive-sum” game is appropriate.

A negative-sum game, in which winnings will be less than losses, is also possible. War is one example and a bad marriage is another. A possible reason that few people prior to Adam Smith seem to have recognized this mutually beneficial aspect of exchange may be that in his day much exchange involved bargaining.

In bargaining, the seller tries to get as high a price as he can and the buyer as low a price as possible. If the seller can get $2.50 for a product rather than $2.00, he benefits from the higher price at the expense of the buyer. People do discuss who got the “better of the bargain.”

This feature of exchange, which is of vital importance to those involved in a market, can obscure the fact that no exchange will take place unless both parties believe that they benefit from it. Bargaining determines how big the producer’s surplus will be relative to the size of the consumer’s surplus, but unless both buyer and seller each have some surplus, no trade will take place. Crusoe and Friday could be replaced by two nations.

The principle of comparative advantage continues to hold, and it implies that the world as a whole will not be operating on its production-possibilities curve—that it will be production inefficient—if each nation is self-sufficient. The inefficiency can be illustrated by putting the numbers of the second Crusoe-Friday into production possibilities tables. Suppose that in self sufficiency Crusoe chooses three fish and two coconuts, and Friday chooses five fish and five coconuts.

The total island production is then eight fish and seven coconuts. But with total specialization, with Crusoe producing only coconuts and Friday producing only fish, island production would be ten fish and eight coconuts, which means that under self-sufficiency island resources were used inefficiently. Or, suppose that originally Crusoe was self-sufficient at one fish and six coconuts, and Friday was self-sufficient at five fish and five coconuts.

Island production is six fish and eleven coconuts. In this case, only partial specialization might be desirable. If Friday produces three coconuts and Crusoe produces eight, island production could be eleven coconuts and seven fish, which is a gain of one fish compared to production with no specialization.

The law of diminishing returns says that adding more of one input while holding other inputs constant results eventually in smaller and smaller increases in added output.. If capital is held constant at two, the marginal output of labor (which economists usually call marginal product of labor) is shown in the table below. The first unit of labor increases production by 13, and as more labor is added, the increases in production gradually fall. The law of diminishing returns does not take effect immediately in all production functions.

The second to add six, and the third to add seven. If a production function had this pattern, it would have increasing returns between the first and third worker. What the law of diminishing returns says is that as one continues to add workers, eventually one will reach a point where increasing returns stop and decreasing returns set in.

The law of diminishing returns is not caused because the first worker has more ability than the second worker, and the second is more able than the third. By assumption, all workers are the same. It is not ability that changes, but rather the environment into which workers (or any other variable input) are placed.

As additional workers are added to a firm with a fixed amount of equipment, the equipment must be stretched over more and more workers. Eventually, the environment becomes less and less favorable to the additional worker. People’s productivity depends not only on their skills and abilities, but also on the work environment they are in.

The law of diminishing returns was a central piece of economic theory in the 19th century and accounted for economists’ gloomy expectations of the future. They saw the amount of land as fixed, and the number of people who could work the land as variable. If the number of people expended, eventually adding one more person would result in very little additional food production.

And if population had a tendency to expand rapidly, as economists thought it did, one would predict that (in equilibrium) there would always be some people almost starving. Though history has shown the gloomy expectations wrong, the idea had an influence on the work of Charles Darwin and traces of it still float around today among environmentalists. If one increases all inputs in equal proportions, one travels out from the origin on a ray.

There is no law to predict what will happen to output in this case. If a 10% increase in all inputs yields more than a 10% increase in output, the production function has increasing returns to scale. If it yields less than a 10% increase in output, the production function has decreasing returns to scale.

And if it yields exactly a 10% increase in output, to has constant returns to scale. Returns to scale are important for determining how many firms will populate an industry. When increasing returns to scale exist, one large firm will produce more cheaply than two small firms.

Small firms will thus have a tendency to merge to increase profits, and those that do not merge will eventually fail. On the other hand, if an industry has decreasing returns to scale, a merger of two small firms to create a large firm will cut output, raise average costs, and lower profits. In such industries, many small firms should exist rather than a few large firms.

Socialism—defined as a centrally planned economy in which the government controls all means of production—was the tragic failure of the twentieth century. Born of a commitment to remedy the economic and moral defects of capitalism, it has far surpassed capitalism in both economic malfunction and moral cruelty. Yet the idea and the ideal of socialism linger on.

Whether socialism in some form will eventually return as a major organizing force in human affairs is unknown, but no one can accurately appraise its prospects who has not taken into account the dramatic story of its rise and fall. It is often thought that the idea of socialism derives from the work of Karl Marx. In fact, Marx wrote only a few pages about socialism, as either a moral or a practical blueprint for society the true architect of a socialist order was Lenin, who first faced the practical difficulties of organizing an economic system without the driving incentives of profit seeking or the self-generating constraints of competition.

Lenin began from the long-standing delusion that economic organization would become less complex once the profit drive and the market mechanism had been dispensed with—“as self-evident,” he wrote, as “the extraordinarily simple operations of watching, recording, and issuing receipts, within the reach of anybody who can read and write and knows the first four rules of arithmetic.” In fact, economic life pursued under these first four rules rapidly became so disorganized that within four years of the 1917 revolution, Soviet production had fallen to 14 percent of its prerevolutionary level. By 1921 Lenin was forced to institute the New Economic Policy (NEP), a partial return to the market incentives of capitalism.

This brief mixture of socialism and capitalism cam to an end in 1927 after Stalin instituted the process of forced collectivization that was to mobilize Russian resources for its leap into industrial power. The system that evolved under Stalin and his successors took the form of a pyramid of command. At its apex was Gosplan, the highest state planning agency, which established such general directives for the economy as the target rate of growth, the allocation of effort between military and civilian outputs, between heavy and light industry, or among various regions.

Gosplan transmitted the general directives to successive ministries of industrial and regional planning, whose technical advisers broke down the overall national plan into directives assigned to particular factories, industrial power centers, collective farms, or whatever. These thousands of individual subplans were finally scrutinized by the factory managers and engineers who would eventually have to implement them. Thereafter, the blueprint for production reascended the pyramid, together with the suggestions, emendations, and pleas of those who had seen it.

Ultimately, a completed plan would be reached by negotiation, voted on by the Supreme Soviet, and passed into law. Thus, the final plan resembled an immense order book, specifying the nuts and bolts, steel girders, grain outputs, tractors, cotton, cardboard, and coal that, in their entirety, constituted the national output. In theory such an order book should enable planners to reconstitute a working economy each year—provided, of course, that the nuts fitted the bolts, the girders were of the right dimensions, the grain output was properly stored, the tractors operable, and the cotton, cardboard, and coal of the kinds needed for their manifold uses.

But there was a vast and widening gap between theory and practice. The gap did not appear immediately. In retrospect, we can see that the task facing Lenin and Stalin in the early years was not so much economic as quasimilitary--mobilizing a peasantry into a work force to build roads and rail lines, dams and electric grids, steel complexes and tractor factories.

This was a formidable assignment, but far less formidable than what would confront socialism fifty years later, when the task was not so much to create enormous undertakings, but relatively self-contained ones, and to fit all the outputs into a dovetailing whole. Through the sixties the Soviet economy continued to report strong overall growth—roughly twice that of the United States—but observers began to spot signs of impending trouble. One was the difficulty of specifying outputs in terms that would maximize the well-being of everyone in the economy, not merely the bonuses earned by individual factory managers for “over fulfilling” their assigned objectives.

The problem was that the plan specified outputs in physical terms. One consequence was the managers maximized yardages or tonnages of output, not its quality. A famous cartoon in the satirical magazine Krokodil showed a factory manager proudly displaying his record output, a single gigantic nail suspended from a crane.

At the economic flow became increasingly clogged and clotted, production took the form of “stormings” at the end of each quarter or year, when every resource was pressed into use to meet preassigned targets. The same rigid system soon produced expeditors, or tolkachi, to arrange shipments to harassed managers who needed unplanned—and therefore unobtainable—inputs to achieve their production goals. Worse, in the absence of the right to buy their own supplies or to hire or fire their own workers, factories set up fabricating shops, then commissaries, and finally their own worker housing to maintain control over their own small bailiwicks.

It is not surprising that this increasingly Byzantine system began to create serious dysfunctions beneath the overall statistics of growth. During the sixties the Soviet Union became he first industrial country in history to suffer a prolonged peacetime fall in average life expectancy, a symptom of its disastrous misallocation of resources. Military research facilities could get whatever they needed, but hospitals were low on the priority list.

By the seventies the figures clearly indicated a slowing of overall production. By the eighties the Soviet Union officially acknowledged a near end to growth that was, in reality, an unofficial decline. In 1987 the first official law embodying Mikhail Gorbachev announced his intention to revamp the economy from top to bottom by introducing the market, reestablishing private ownership, and opening the system to free economic interchange with the West.

Seventy years of socialist rise had come to an end. Understanding of the difficulties of central planning was slow to emerge. In the midthirties, while the Russian industrialization drive was at full tilt, few voices were raised about its problems.

Among those few were Ludwig von Mises, and articulate and exceedingly argumentative free-market economist, and Friedrick Hayek, of much more contemplative temperament, later to be awarded a Nobel Prize for his work in monetary theory. Together, Mises and Hayek launched an attack on the feasibility of socialism that seemed at the time unconvincing in its argument as to the functional problems of a planned economy. Mises in particular contended that a socialist system was “impossible” because there was no way for the planners to acquire the information—“produce his, not that”—needed for a coherent economy.

This information, Hayek emphasized, emerged spontaneously in a market system from the rise and fall of prices. A planning system was bound to fail precisely because it lacked such a signaling mechanism. The Mises-Hayek argument met its most formidable counterargument in two brilliant articles by Oskar Lange, a young economist who would become the first polish ambassador to the United States after World War II.

Lange set out to show that the planners would, in fact, have precisely the same information as that which guided a market economy. The information would be revealed as inventories of goods rose and fell, signaling either that supply was greater than demand or demand greater than supply. Thus, as planners watched inventory levels, they were also learning which of their administered (i.e.

, state-dictated) prices were too high and which too low. It only remained, therefore, to adjust prices so that supply and demand balanced, exactly as in the marketplace. Lange’s answer was so simple and clear that many believed the Mises-Hayek argument had been demolished.

In fact, we now know that their argument was all too prescient. Ironically, though, Mises and Hayek were right for a reason that they did not foresee as clearly as Lange himself. “The real danger of socialism,” Lange wrote, in italics, “is that of a bureaucratization of economic life.”

But he took away the force of the remark by adding, without italics, “Unfortunately, we do not see how the same or even greater danger can be averted under monopolistic capitalism.” The effects of the “bureaucratization of economic life” are dramatically related in The Turning Point, a scathing attack on the realities of socialist economic planning by two Soviet economist, Nikolai Smelev and Vladimir Popov, that gives examples of the planning process in actual operation. In 1982, to stimulate the production of gloves from moleskins, the Soviet government raised the price it was willing to pay for moleskins from twenty to fifty kopecks per pelt.

State purchases increased, and now all the distribution centers are filled with these pelts. Industry is unable to use them all, and they often rot in warehouses before they can be processed. The Ministry of Light Industry has already requested Goskomtsen the State Committee on prices twice to lower prices, but “the question has not been decided” yet.

This is not surprising. Its members are too busy to decide. They have no time: besides setting prices on these pelts, they have to keep track of another 24 million prices.

And how can they possibly know how much to lower the price today, so they won’t have to raise it tomorrow? This story speaks volumes about the problem of a centrally planned system. The crucial missing element is not so much “information,” as Mises and Hayek argued, as it is the motivation to act on information.

After all, the inventories of moleskins did tell the planners that their production was at first too low and then too high. What was missing was the willingness—better yet, the necessity—to respond to the signals of changing inventories. A capitalist firm responds to changing prices because failure to do so will cause it to lose money.

A socialist ministry ignores changing inventories because bureaucrats learn that doing something is more likely to get them in trouble than doing noting, unless doing nothing results in absolute disaster. Absolute economic disaster has now been reached in the Soviet Union and its Eastern former satellites, and we are watching efforts to construct some form of economic structure that will no longer display the deadly symptoms of inertia and indifference that have come to be the hallmarks of socialism. It is too early to predict whether these efforts will succeed.

The main obstacle to real perestroika is the impossibility of creating a working market system without a firm basis of private ownership, and it is clear that the creation of such a basis encounters the opposition of the former state bureaucracy and the hostility of ordinary people who have long been trained to be suspicious of the pursuit of wealth. In the face of such uncertainties, all predictions are foolhardy save one: no quick or easy transition from socialism to some form of nonsocialism is possible. Transformations of such magnitude are historic convulsions, not mere changes in policy.

Their completion must be measured in decades or generations, not years. “Reaganomics” was the most serious attempt to change the course of U. Economic policy of any administration since the new Deal.

“Only by reducing the growth of government,” said Ronald Reagan, “can we increase the growth of the economy.” Reagan’s 1981 Program for Economic Recovery had four major policy objectives: (1) reduce the growth of government spending, (2) reduce the marginal tax rates on income from both labor and capital, (3) reduce regulation, and (4) reduce inflation by controlling the growth of the money supply. These major policy changes, in turn, were expected to increase saving and investment, increase economic growth, balance the budget, restore healthy financial markets, and reduce inflation and interest rates.

Any evaluation of the Reagan economic program should thus address two general questions: How much of the proposed policy changes were approved? And how much of the expected economic effects were realized: Reagonomics continues to be a controversial issue. For those who do not view Reagonomics through an idealogical lens, however, one’s evaluation of this major change in economic policy will depend on the balance of the realized economic effects.

President Reagan delivered on each of his four major policy objectives, although not to the extent that he and his supporters had hoped. The annual increase in real (inflation-adjusted) federal spending declined from 4.0 percent during the Carter administration to 2.5 percent during the Reagan administration, despite a record peacetime increase in real defense spending. This part of Reagan’s fiscal record, however, reflected only a moderation, not a reversal, of prior fiscal trends.

Reagan made no significant changes to the major transfer payment programs (such as Social Security and Medicare), and he proposed no substantial reductions in other domestic programs after his first budget. Moreover, the growth of defense spending during his first term was higher than Reagan had proposed during the 1980 campaign, and since economic growth was somewhat slower than expected, Reagan did not achieve a significant reduction in federal spending as a percent of national output. Federal spending was 22.9 percent of gross domestic product (GDP) in fiscal 1981, increased somewhat during the middle years of his administration, and declined to 22.1 percent of GDP in fiscal 1989.

This part of the Reagan record was probably the greatest disappointment to his supporters. The changes to the federal tax code were much more substantial. The top marginal tax rate on individual income was reduced from 70 percent to 28 percent.

The corporate income tax rate was reduced from 48 percent to 34 percent. The individual tax brackets were indexed for inflation. And most of the poor were exempted from the individual income tax.

These measures were somewhat offset by several tax increases. An increase in Social Security tax rates legislated in 1977 but scheduled for the eighties was accelerated slightly. Some excise tax rates were increased, and some deductions were reduced or eliminated.

More important, there was a major reversal in the tax treatment of business income. A complex package of investment incentives was approved in 1981 only to be gradually reduced in each subsequent year through 1985. And in 1986 the base for the taxation of business income was substantially broadened, reducing the tax bias among types of investment but increasing the average effective tax rate on new investment.

It is not clear whether this measure was a net improvement in the tax code. Overall, the combination of lower tax rates and a broader tax base for both individuals and business reduced the federal revenue share of GDP from 20.2 percent in fiscal 1981 to 19.2 percent in fiscal 1989. The reduction in economic regulation that started in the Carter administration continued, but at a slower rate.

Reagan eased or eliminated price controls on oil and natural gas, cable TV, long-distance telephone service, interstate bus service, and ocean shipping. Banks were allowed to invest in a somewhat broader set of assets, and the scope of the antitrust laws was reduced. The major exception to this pattern was a substantial increase in import barriers.

The Reagan administration did not propose changes in the legislation affecting health, safety, and the environment, but it reduced the number of new regulations under the existing laws. Deregulation was clearly the lowest priority among the major elements of the Reagan economic program. Monetary policy was somewhat erratic but, on net, quite successful.

Reagan endorsed the reduction in money growth initiated by the Federal Reserve in late 1979, a policy that led to both the severe 1982 recession and a large reduction in inflation and interest rates. The administration reversed its position on one dimension of monetary policy: during the first term, the administration did not intervene in the markets for foreign exchange but, beginning in 1985, occasionally intervened with the objective to reduce and then stabilize the foreign-exchange value of the dollar. Most of the effects of these policies were favorable, even if somewhat disappointing compared to what the administration predicted.

Economic growth increased from a 2.8 percent annual rate in the Carter administration, but this is misleading because the growth of the working-age population was much slower in the Reagan years. Real GDP per working-age adult, which had increased at only a 0.8 annual rate during the Carter administration, increased at a 1.8 percent rate during the Reagan administration. The increase in productivity growth was even higher: output per hour in the business sector, which had been roughly constant in the Carter years, increased at a 1.4 percent rate in the Reagan years.

Productivity in the manufacturing sector increased at a 3.8 percent annual rate, a record for peacetime. Most other economic conditions also improved. The unemployment rate declined from 7.0 percent in 1980 to 5.4 percent in 1988.

The inflation rate declined from 10.4 percent in 1980 to 4.2 percent in 1988. The combination of conditions proved that there is no long-run trade-off between the unemployment rate and the inflation rate (see Phillips Curve). Other conditions were more mixed.

The rate of new business formation increased sharply, but the rate of bank failures was the highest since the thirties. Real interest rates increased sharply, but inflation-adjusted prices of common stocks more than doubled. Economy experienced substantial turbulence during the Reagan years despite favorable general economic conditions.

This was the “creative destruction” that is characteristic of a healthy economy. At the end of the Reagan administration, the U. Economy had experienced the longest peacetime expansion ever.

The “stagflation” and “malaise” that plagued the U. Economy from 1973 through 1980 were transformed by the Reagan economic program into a sustained period of higher growth and lower inflation. In retrospect the major achievements of Reaganomics were the sharp reductions in marginal tax rates and in inflation.

Moreover, these changes were achieved at a much lower cost than was previously expected. Despite the large decline in marginal tax rates, for example, the federal revenue share of GDP declined only slightly. Similarly, the large reduction in the inflation rate was achieved without any long-term effect on the unemployment rate.

One reason for these achievements was the broad bipartisan support for these measures beginning in the later years of the Carter administration. Reagan’s first tax proposal, for example, had previously been endorsed by the Democratic Congress beginning in 1978, and the general structure of the Tax Reform Act of 1986 was first proposed by two junior Democratic members of Congress in 1982. Similarly, the “monetarist experiment” to control inflation was initiated in October 1979, following Carter’s appointment of Paul Volcher as chairman of the Federal Reserve Board.

The bipartisan support of these policies permitted Reagan to implement more radical changes than in other areas of economic policy. Reagan failed to achieve some of the initial goals of his initial program. The federal budget was substantially reallocated—from discretionary domestic spending to defense, entitlements, and interest payments—but the federal budget share of national output declined only slightly.

Both the administration and Congress were responsible for this outcome. Reagan supported the large increase in defense spending and was unwilling to reform the basic entitlement programs. Similarly, neither the administration nor Congress was willing to sustain the momentum for deregulation or to reform the regulation of health, safety, and the environment.

Reagan left three major adverse legacies at the end of his second term. First, the privately held federal debt increased from 22.3 percent of GDP to 38.1 percent and, despite the record peacetime expansion, the federal deficit in Reagan’s last budget was still 2.9 percent of GDP. Second, the failure to address the savings and loan problem early led to an additional debt of about $125 billion.

Third, the administration added more trade barriers than any administration since Hoover. The share of U. Imports subject to some form of trade restraint increased from 12 percent in 1980 to 23 percent in 1988.

There was more than enough blame to go around for each of these problems. Reagan resisted tax increases, and Congress resisted cuts in domestic spending. The administration was slow to acknowledge the savings and loan problem, and Congress urged forbearance on closing the failing banks.

Reagan’s rhetoric strongly supported free trade, but pressure from threatened industries and Congress led to a substantial increase in new trade restraints. The future of Reaganomics will depend largely on how each of these three adverse legacies is resolved. Restraints on spending and regulation would sustain Reagonomics.

But increased taxes and a reregulation of domestic and foreign trade would limit Reaganomics to an interesting but temporary experiment in economic policy. The Regan economic program led to a substantial improvement in economic conditions, but there was no “Reagan revolution.” No major federal programs (other than revenue sharing) and no agencies were abolished.

The political process continues to generate demands for new or expanded programs, but American voters continue to resist higher taxes to pay for these programs. A broader popular consensus on the appropriate roles of the federal government, one or more constitutional amendments, and a new generation of political leaders many be necessary to resolve this inherent conflict in contemporary American politics. The comparison between the economies of Canada and the United States is generally far more of a concern to Canadian than to American.

Canada is under constant pressure to remain competitive with the United States. IF it dows not then forces such as the brain drain will occur, where the top Canadians emigrate to the U.S. If Canada falls behind corporations will also leave for the United States. The U.S. has far less to fear as any losses to Canada can be easily managed.

Despite the contrasts listed below Canada and the United States are extremely similar economically. They are both developed countries and are thus vastly closer to each other than to the majority of the world’s countries. Canada also is by almost all economic indices closer to the United States than it is to Europe.

Boom and bust cycles in Canada and the United States are closely linked as are many indices such as inflation and interest rates. Demographic patterns are also similar, with a slightly higher birth rate in the U.S. and a higher immigration rate in Canada. In its quest to remain competitive Canada starts at an immediate disadvantage.

Canada’s harsh climate lead to high costs for such things as heating. Workers are less likely to immigrate to Canada and the wealthy are more likely to leave for tropical climates. The climate of Canada also contributes to higher transportation costs as planes, trains, and automobiles are all more expensive to operate than in much of the United States.

Canada’s low population density also makes transportation costs higher. More of a historical concern was that much of the country lacks natural river systems that could be easily used for transportation. Canada’s terrain is also somewhat more rugged than the United States.

The Rocky Mountains are more of an obstacle, and the mass of the Canadian Shield provides a formidable barrier to any links between Ontario and Manitoba. Canada does have some distinct geographic advantages. The large river systems in the north are sources of cheap hydro-electric power.

The main advantage is Canada’s vast supplies of natural resources. While the United States has large supplies of resources, these are not enough to meet domestic demands and they are forced to import many raw materials, a great deal of which come from Canada. By contrast Canada is a net exporter of resources.

This leads to an important difference as increases in the price of resources boosts the Canadian economy while hurting the American. For example a rise in oil prices generally causes a fall in the Dow Jones but an increase in the TSX. Differences between government intervention in the economies of the two countries is most closely examined in Canada, because some feel that policies that more closely emulate the U.S. are preferable, while others disagree.

The average tax rate in Canada is higher than in the United States. In Canada total tax revenue for every level of government equals about 36.8% of GDP, in the U.S. this is closer to 30%. There is some regional variation, however.

A resident of oil rich Alberta pays less in taxes than a resident of high tax Massachusetts. The taxes are applied differently as well. Canada’s tax system is more heavily biased against the highest income earners, thus while Canada’s tax rate is higher on average, the bottom fifty percent of the population is more lightly taxed than in the United States.

Canada also has a national sales tax of 7% on all purchases, while the U.S. federal government relies almost entirely on income taxes. Canada has no inheritance tax while the United States still does, but the U.S. tax is currently scheduled to be abolished. For its higher taxes Canada has a more complete system of social programs than the United States.

These differences include having all major universities receive government funding, having a national broadcaster in the CBC and, most notably, having a fully government-funded health care system. The United States, however, spends far more on military than Canada. The greatest difference in social programs is in health care.

The United States spends far more of its per capita GDP on health care than does Canada. Canadians, h

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