No Such Thing as a Free Lunch: Principles of Economics (Part 49)

"Advertising is, actually, a simple phenomenon in terms of economics. It is merely a substitute for a personal sales force - an extension, if you will, of the merchant who cries aloud his wares."

Rosser Reeves

Input Demand: The Labor and Land Markets

(Part E)

by

Charles Lamson

The Firm's Profit-Maximization Condition in Input Markets

Thus far we have discussed the labor and land markets in some detail. Although we will put off a detailed discussion of capital until a few posts in the not-so-distant future, it is now possible to generalize about competitive demand for factors of production. Every firm has an incentive to use variable inputs as long as the revenue generated by those inputs covers the cost of those inputs at the margin. More formally, firms will employ each input up to the point that it's price equals its marginal revenue product. This condition holds for all factors at all levels of output:

Hiring more labor drives down the marginal product of labor, and using less capital increases the marginal product of capital. This means that the ratios can come back to equality as the firm shifts out of capital and into labor.

So far we have used very general terms to discuss the nature of input demand by firms in competitive markets, where input prices and output prices are taken as given. The most important point here is that demand for a factor depends on the value that the market places on its marginal product. The next few posts explore the forces that determine the shapes and positions of input demand curves. 

*CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., P. 209*

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No Such Thing as a Free Lunch: Principles of Economics (Part 48)

"How great, my friends, is the virtue of living upon a little!"

Horace

Input Demand: The Labor and Land Markets

(Part D)

by

Charles Lamson

Land Markets

Unlike labor and capital, land has a special feature that we have not yet considered: it is in strictly fixed (perfectly inelastic) supply in total. The only real questions about land thus center around how much it is worth and to what use it will be put.

Because land is fixed in supply, we say that its price is demand determined. In other words, the price of land is determined exclusively by what households and firms are willing to pay for it. The return to any factor of production in fixed supply is called pure rent.

Thinking of the price of land as demand determined can be confusing because all land is not the same. Some land is clearly more valuable than other land. What lies behind these differences? As with any other factor of production, land will presumably be sold or rented to the user who is willing to pay the most for it. The value of land to a potential user may depend on the characteristics of the land itself or on its location. For example, more fertile land should produce more farm products per acre and thus command a higher price than less fertile land. A piece of property located at the intersection of two highways may be of great value as a site for a gas station because of the amount of traffic that passes the intersection daily.

A numerical example may help to clarify our discussion. Consider the potential uses of a corner lot in a suburb of Kansas City. Alan wants to build a clothing store on the lot. He anticipates that he can earn economic profits of $10,000 per year because of the land's excellent location. Bella, another person interested in buying the corner lot, believes that she can earn $35,000 per year in economic profit if she builds a drugstore there. Bella will be able to outbid Alan, and the land owner will sell (or rent) to the highest bidder.

Because location is often the key to profits, landowners are frequently able to "squeeze" their renters. One of the most popular locations in the Boston area, for example, is Harvard Square. There are dozens of restaurants in and around the square, and most of them are full most of the time. Despite this seeming success, most Harvard Square restaurant owners are not getting rich. Why? Because they must pay very high rents on the location of their restaurants. A substantial portion of each restaurant's revenues goes to rent the land that (by virtue of its scarcity) is the key to unlocking those same revenues.

Although Figure 6 shows that the supply of land is perfectly inelastic (a vertical line), the supply of land in a given use may not be perfectly inelastic or fixed. Think, for example, about farmland and land available for housing developments. As a city's population grows, housing developers find themselves willing to pay more and more for land. As land becomes more valuable for development, some farmers sell out, and the supply of land available for development increases. This analysis would lead us to draw an upward-sloping supply curve (not a perfectly inelastic supply curve) for land in the land for development category.

Nonetheless, our major point---that land earns a pure rent is still valid. The supply of land of a given quality at a given location is truly fixed in supply. Its value is determined exclusively by the amount that the highest bidder is willing to pay for it. Because land cannot be reproduced, supply is perfectly inelastic.

Rent and the Value of Output Produced on Land

Because the price of land is determined, rent depends on what the potential users of the land are willing to pay for it. As we have seen, land will end up being used by whoever is willing to pay the most for it. What determines this willingness to pay? Let us now connect our discussion of land markets with our earlier discussions of factor markets in general.

As our example of two potential users bidding for a plot of land shows, the bids depend on the land's potential for profit. Alan's plan would generate $10,000 a year; Bella's would generate $35,000 a year. Nevertheless, these profits do not just materialize. Land in a popular downtown location is expensive because of what can be produced on it. Note that land is needed as an input into the production of nearly all goods and services. All restaurants located next to a popular theater can charge a premium price because it has a relatively captive clientele. The restaurant must produce a quality product to stay in business, but the location alone provides a substantial profit opportunity.

It should come as no surprise that the demand for land follows the same rules as the demand for inputs in general. A profit-maximizing firm will employ an additional factor of production as long as its marginal revenue product exceeds its market price. For example, a profit-maximizing firm will hire labor as long as the revenue earned from selling labor's product is sufficient to cover the cost of hiring additional labor which for perfectly competitive firms equals the wage rate. The same thing is true for land:

Just as the demand curve for labor reflects the value of labor's products as determined in output markets, so the demand for land depends on the value of land's product in output markets. The profitability of the restaurant located next to the theater results from the fact that the meals produced there command a price in the marketplace.

The allocation of a given plot of land among competing uses thus depends on the trade-off between competing products that can be produced there. Agricultural land becomes developed when its value in producing housing or manufactured goods, or providing space for a mini mall, exceeds its value in producing crops. A corner lot in Kansas City becomes the site of a drug store instead of a clothing store because the people in that neighborhood have a greater need for a drug store.

One final word about land: because land cannot be moved physically, the value of any one parcel depends to a large extent on the uses to which adjoining parcels are put. A factory belching acrid smoke will probably reduce the volume of adjoining land, while a new highway that increases accessibility may enhance it. 

*CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., PP. 207-209*

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No Such Thing as a Free Lunch: Principles of Economics (Part 47)

"There is much of economic theory which is pursued for no better reason than its intellectual attraction; it is a good game. We have no reason to be ashamed of that, since the same would hold for many branches of mathematics."

John Hicks

Input Demand: The Labor and Land Markets

(Part C)

by

Charles Lamson

A Firm Employing Two Variable Factors of Production in the Short and Long Run

You have seen that inputs can be complementary or substitutable. Land, labor, and capital are used together to produce outputs. The worker who uses a shovel digs a bigger hole than one with no shovel. Add a steam shovel and that worker becomes even more productive. When an expanding firm adds to its stock of capital, it raises the productivity of its labor, and vice versa. Thus, each factor complements the other. At the same time, though, land, labor, and capital can also be substituted for one another. If labor becomes expensive, some labor-saving technology---robotics, for example---may take its place.

In firms employing just one variable factor of production, a change in the price of that factor affects only the demand for the factor itself. When more than one factor can vary, however, we must consider the impact of a change in one factor price on the demand for other factors as well.

Substitution and Output Effect of a Change in Factor Price Table 2 presents data on a hypothetical firm that employs variable capital and labor. Suppose that the firm faces a choice between two available technologies of production---technique A, which is capital-intensive, and technique B, which is labor intensive. When the market price of labor is $1 per unit and the market price of capital is $1 per unit, the labor-intensive method of producing output is less costly. Each unit cost only $13 to produce using technique B, while the unit cost of production using technique A is $15. If the price of labor rises to $2, however, technique B is no longer less costly. Labor has become more expensive relative to capital. The unit cost rises to $23 for labor-intensive technique B, but to only $20 for capital-intensive technique A.

Table 3 shows the impact of such an increase in the price of labor on both capital and labor demand when a firm produces 100 units of output. When each input factor costs $1 per unit, the firm chooses technique B and demands 300 units of capital and 1000 units of labor. Total variable cost is $1,300. An increase in the price of labor to $2 causes the firms to switch from technique B to technique A. In doing so, it substitutes capital for labor. The amount of labor demanded drops from 1,000 to 500 units. The amount of capital demanded increases from 300 to 1,000 units, while total variable cost increases to $2,000.

TABLE 3

The tendency of firms to substitute away from a factor whose relative price has risen and toward a factor whose relative price has fallen is called the factor substitution effect. The factor substitution effect is part of the reason that input demand curves slope downward. When an input, or factor of production, becomes less expensive, firms tend to substitute it for other factors and thus buy more of it. When a particular input becomes more expensive, firms tend to substitute other factors and buy less of it.

The firm described in Tables 2 and 3 continued to produce 100 units of output after the wage rate doubled. An increase in the price of a production factor, however, also means an increase in the costs of production. Notice that total variable cost increased from $1,300 to $2,000. When a firm faces higher costs, it is likely to produce less in the short run. When a firm decides to decrease output, its demand for all factors declines---including, of course, the factor whose price increased in the first place. This is called the output effect of a factor price increase.

A decrease in the price of a factor of production, in contrast, means lower costs of production. If their output price remains unchanged, firms will increase output. This, in turn, means that demand for all factors of production will increase. This is the output effect of a factor price decrease.

The output effect helps explain why input demand curves slope downward. Output effects and other substitution effects work in the same direction. Consider, for example, a decline in the wage rate. Lower wages mean that a firm will substitute labor for capital and other inputs. Stated somewhat differently, the factor substitution effect leads to an increase in the quantity of labor demanded. Lower wages mean lower costs, and lower costs lead to more output. This increase in output means that the firm will hire more of all factors of production, including labor itself. This is the output effect of a factor price decrease. Notice that both effects lead to an increase in the demand for labor when the wage rate falls.

Many Labor Markets

Many labor markets exist. There is a market for baseball players, for carpenters, for chemists, for college professors, and for unskilled workers. Still other markets exist for taxi drivers, assembly line workers, secretaries, and corporate executives. Each market has a set of skills associated with it and a supply of people with requisite skills.

If labor markets are competitive the wages in those markets are determined by the interaction of supply and demand. As we have seen, firms will hire workers only as long as the value of their product exceeds the relevant market wage. This is true in all competitive labor markets. 

*CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., PP. 205-207*

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No Such Thing as a Free Lunch: Principles of Economics (Part 46)

"The notion that big business and big labor and big government can sit down around a table somewhere and work out the direction of the American economy is at complete variance with the reality of where the American economy is headed. I mean, it's like dinosaurs gathering to talk about the evolution of a new generation of mammals."

Bruce Babbitt

Input Demand: The Labor and Land Markets

(Part B)

by

Charles Lamson

Labor Markets

Let us begin our discussion of input markets simply by discussing a firm that uses only one variable factor of production.

A Firm Using Only One Variable Factor of Production: Labor

Demand for an input depends on that input's marginal revenue product and its unit cost, or price. The price of labor, for example, is the wage determined in the labor market. (At this point we are continuing the example of the sandwich shop from last post, and we assume that the sandwich shop uses only one variable factor of production---labor. Remember that competitive firms are price takers in both output and input markets. Such firms can hire all the labor they want to hire as long as they pay the market wage.) We can think of the hourly wage at the sandwich shop as the marginal cost of a unit of labor.

A profit-maximizing firm will add inputs in the case of labor, it will hire workers as long as the marginal revenue product of that input exceeds the market price of that input---in the case of labor, the wage.

Look again at the figures for the sandwich shop in Table 1 (from last post and reintroduced below), column five. Now suppose that the going wage for sandwich makers is $4 per hour. A profit-maximizing firm would hire three workers. The first worker would yield $5 per hour in revenues and would yield $7.50, but they each would cost only $4 per hour. The third worker would bring in $5 per hour, but still cost only $4 in marginal wages. The marginal product of the fourth worker, however, would not bring in enough revenue ($2.50) to pay this workers salary. Total profit is thus maximized by hiring three workers.

TABLE 1

Figure 3 presents the same concept graphically. The labor market appears in Figure 3(a); Figure 3(b) shows a single firm that employs workers. This firm, incidentally, does not represent just the firm's single industry. Because firms in many different industries demand labor, the representative firm in figure 3(b) represents any firm in any industry that uses labor.

The firm faces a market wage rate of $10. We can think of this as the marginal cost of a unit of labor. (Note that we are now discussing the margin in units of labor; in previous posts, we talked about marginal units of output.) Given a wage of $10, how much labor would the firm demand?

Thus the curve in Figure 3(b) tells us how much labor a firm that uses only one variable factor of production will hire at each potential market wage rate. If the market wage falls, the quantity of labor demanded will rise. If the market rises, the quantity of labor demanded will fall. This description should sound familiar to you---it is, in fact, the description of a demand curve. Therefore we can now say that when a firm uses only one variable factor of production, that factor's marginal revenue product curve is the firm's demand curve for that factor in the short run.

Comparing Marginal Revenue and Marginal Cost to Maximize Profits In parts 34 through 38 of this analysis, we saw that a competitive firm's marginal cost curve is the same as its supply curve. That is, at any output price, the marginal cost curve determines how much output a profit-maximizing firm will produce. We came to this conclusion by comparing the marginal revenue that a firm would earn by producing one more unit of output with the marginal cost of producing that unit of output.

In both cases, the firm is comparing the cost of production with potential revenues from the sale of product at the margin. In parts 34 through 38 of this analysis, the firm compared the price of output (P, which is equal to MR in perfect competition) directly with cost of production (MC), where cost was derived from information on factor prices and technology. (Review the derivation of cost curves in parts 34 through 38 if this is unclear.) Here, information on output price and technology is contained in the marginal revenue product curve, which is compared with information on input price to determine the optimal level of input to demand.

The assumption of one variable factor of production makes the trade-off facing firms easy to see. Figure 5 shows that in essence firms weigh the value of labor as reflected in the market wage against the value of the product of labor as reflected in the price of output.

Assuming that labor is the only variable input, if society values a good more than it costs firms to hire the workers to produce that good, the good will be produced. In general, the same logic also holds for more than one input. Firms weigh the value of outputs as reflected in output price against the value of inputs as reflected in marginal costs.

Driving Input Demands For the small sandwich shop, calculating the marginal product of a variable input (labor) and marginal revenue product was easy. Although it may be more complex, the decision process is essentially the same for both big corporations and small proprietorships.

When an airline hires more flight attendants, for example, it increases the quality of its service to attract more passengers and sell more of its product. In deciding how many to hire, the airline must figure out how much new revenue the added flight attendants are likely to generate relative to their wages.

At the sandwich shop, diminishing returns set in at a certain point. The same holds true for an airplane. Once a sufficient number of attendants are on a plane, additional attendance adds little to the quality of service, and beyond a certain level might even give rise to negative marginal product. Too many attendants could bother the passengers and make it difficult to get to the restrooms.

In making your own decisions, you, too, compare marginal gains with input costs in the presence of diminishing returns. Suppose you grow vegetables in your yard. First, you save money at the grocery store. Second, you can plant what you like, and the vegetables taste better fresh from the garden. Third, you simply like to work in the garden.

Like the sandwich shop and the airline, you also face diminishing returns. You have only 625 square feet of garden to work with, and with land as a fixed factor in the short run, your marginal product will certainly decline. You can work all day everyday, but your limited space will produce only so many string beans. The first few hours you spend each week watering, fertilizing, and dealing with major weed and bug infestations probably have a high marginal product. However, after five or six hours, there is little else you can do to increase yield. Diminishing returns also apply to your sense of satisfaction. The farmers markets are now full of cheap fresh produce that taste nearly as good as yours. Once you have been out in the garden for a few hours, the hot sun and hard work start to lose their charm.

Although your gardening does not involve a salary (unlike the sandwich shop and the airline, which pay out wages), the labor you supply has a value that must be weighed. When do returns diminish beyond a certain point, you must weigh the value of additional gardening time against leisure and the other options available to you.

Less labor is likely to be employed as the cost of labor rises. If the competitive labor market pushed the daily wage to $6 per hour, the sandwich shop would hire only two workers instead of three (see Table 1).

In the "new economy" there is a common example of what may seem to be an exception to the rule that workers will only be hired if the revenues they generate are equal to or greater than their wages. Many startup companies pay salaries to workers before they begin to take in revenue. How does a company pay workers if it is not earning any revenues? The answer is that the entrepreneur, or the venture capital fund supporting the entrepreneur, is betting that the firm will earn substantial revenues in the future. Workers are hired because the entrepreneur expects that their current efforts will produce future revenues greater than their wage costs. 

*CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., PP. 201-205*

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No Such Thing as a Free Lunch: Principles of Economics (Part 45)

"Call a thing immoral or ugly, soul-destroying or a degradation of man, a peril to the peace of the world or to the well-being of future generations; as long as you have not shown it to be ''uneconomic'' you have not really questioned its right to exist, grow, and prosper."

F. Schumacher

Input Demand: The Labor and Land Markets

(Part A)

by

Charles Lamson

All business firms must make three decisions: (1) how much to produce and supply in output markets; (2) how to produce that output---that is, which technology to use; and (3) how much of each input to demand. So far, our discussion of firm behavior has focused on the first two questions. In parts 30 through 44 of this analysis, it is explained how profit-maximizing firms choose among alternative technologies and decide how much to supply in output markets.

We now turn to the behavior of firms in perfectly competitive input markets, going behind input demand curves in much the same way that we went behind output supply curves in the previous posts mentioned above. When we look behind input demand curves, we discover the exact same set of decisions that we saw when we analyzed output supply curves. In a very real sense, we have already talked about everything covered in the next few posts. It is the perspective that is new.

The three main inputs are labor, land, and capital. Transactions in the labor and land markets are fairly straightforward. Households supply their labor to firms that demanded it in exchange for a salary or wage. Landowners sell or rent land to others. Capital markets are a bit more complex but are conceptually very similar. Households supply the resources used for the production of capital by saving and giving up present consumption. Savings flow through financial markets to firms that use these savings to procure capital to be used in production. Households receive interest, dividends, or profits in exchange. The next few posts discuss input markets in general, while focusing on the capital market in some detail. Figure 1 outlines the interactions of households and firms in the labor and capital markets.

Input Markets: Basic Concepts

Before we begin our discussion of input markets, it will be helpful to establish some basic concepts: derived demand, complementary and substitutable inputs, diminishing returns, and marginal revenue product.

Demand for Inputs: A Derived Demand

A firm cannot make a profit unless there is a demand for its product. Households must be willing to pay for the firm's output. The quantity of output that a firm produces (in both the long and the short run) thus depends on the value placed by the market on the firm's product. This means that demand for inputs depends on the demand for outputs. In other words, input demand is derived from output demand.

The value attached to a product and the input needed to produce that product define the input's productivity. Normally, the productivity of an input is the amount of output produced per unit of that input. When a large amount of output is produced per unit of an input, the input is said to be highly productive. When only a small amount of output is produced per unit of the input, the input is said to exhibit low productivity.

Inputs are demanded by a firm if and only if households demand the good or service produced by that firm.

Prices in competitive input markets depend on firms' demand for inputs, households' supply of inputs, and interaction between the two. In the labor market, for example, households must decide whether to work and how much to work. The opportunity cost of working for a wage is either the leisure or the value derived from unpaid labor---working in the garden, for instance, or raising children. In general, firms will demand workers as long as the value of what those workers produce exceeds what they must be paid. Households will supply labor as long as the wage they receive exceeds the value of leisure or the value that they derive from nonpaid work.

Inputs: Complementary and Substitutable

Inputs can be complementary or substitutable. Two inputs used together may enhance, or compliment, each other. For example, a new machine is useless without someone to run it. Machines can also be substituted for labor, or less often perhaps labor can be substituted for machines.

All this means that a firm's input commands are highly linked to one another. An increase or decrease in wages naturally causes the demand for labor to change, but it may also have an effect on the demand for capital or land. If we are to understand the demand for inputs, therefore, we must understand the connections among labor, capital, and land.

Diminishing Returns

If you have been following along, you will recall that the short run is the period during which some fixed factor of production limits a firm's capacity to expand. Under these conditions, the firm that decides to increase output will eventually encounter diminishing returns. Stated more formally, a fixed scale of plant means that the marginal product of variable inputs eventually declines.

In parts 30 through 33 of this analysis, we talked at some length about declining marginal product at a sandwich shop. The first two columns of Table 1 reproduce some of the production data from that shop. You may remember that the shop has only one grill, at which only two or three people can work comfortably. In this example, the grill is the fixed factor of production in the short run. Labor is the variable factor. The first worker can produce 10 sandwiches per hour, and the second can produce 15 (see column 3 of Table 1). The second worker can produce more because the first is busy answering the phone and taking care of customers, as well as making sandwiches. After the second worker, however, marginal product declines. The third worker adds only 10 sandwiches per hour, because the grill gets crowded. The fourth worker can squeeze in quickly while the others are serving or wrapping, but adds only five additional sandwiches each hour, and so forth.

TABLE 1

In this case, the grill's capacity ultimately limits output. To see how the firm might make a rational choice about how many workers to hire, we need to know more about the value of the firm's product and the cost of labor.

Marginal Revenue Product

The marginal revenue product (MRP) of a variable input is the additional revenue a firm earns by employing one additional unit of that input, ceteris paribus. If labor is the variable factor, for example, hiring an additional unit will lead to added output (the marginal product of labor). The sale of that added output will yield revenue. Marginal revenue product is the revenue produced by selling the good or service that is produced by the marginal unit of labor. In a competitive firm, marginal revenue product is the value of a factor's marginal product. 

*CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, PP. 197-201*

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