Markets for Factors of Production


Here, you want to gain an understanding of how the demand for inputs to production is determined and which factors influence the elasticity of demand for inputs, especially labor. The second key topic is how the market for financial capital establishes the price (interest rate) (or financial capital

Study Session 5

Focus and the factors that influence the supply of and demand for financial capital. Finally, you should gain an understanding of two components of the payments to productive resources, opportunity cost and economic rent.

I .f >S I 1 .2: iixplain why demand for the factors of production is called derived demand, differentiate between marginal revenue and marginal revenue product (JviRi"), and describe how the MP.P determines the demand for labor and the wag! ra«c.

The demand for a productive resource depends on the demand for the final goods that it is being used to produce. Thus, demand for a factor of production is a derived demand.

The marginal product of a resource is the additional output of a final product produced by using one more unit of a productive input (resource) and holding the quantities of other inputs constant. This is measured in output units and is sometimes called the marginal physical product of the resource. The marginal revenue is the addition to total revenue from selling one more unit of output. For a price taker, marginal revenue is equal to price. For a producer facing a downward sloping demand curve, marginal revenue is less than price, since price must be reduced in order to sell additional units of output.

The marginal revenue product (MRP) is the addition to total revenue gained by selling the marginal product (additional output) from employing one more unit of a productive resource. The interpretation of MRP is that it is the addition to total revenue from selling the additional output produced by using one more unit of a productive input, holding the quantities of other inputs constant.

The MRP is downward sloping in an)- range of output for which diminishing marginal returns are realized from using additional units of a productive resource. This downward-sloping MRP curve is in fact the firm's short-run demand curve for the productive resource or input, as illustrated in Figure 1. This is true of any productive input, of which labor is one.

Figure 1: Marginal Revenue Product (Demand for a Productive Resource)

Marginal Revenue Product (Price)

MRP (Demand)


The intuition here is that a profit-maximizing firm will be willing to pay an amount for one more unit of labor (e.g., one more employee day) equal to the addition to total revenue from employing thai additional labor in the production process and selling the resulting additional output. The condition for maximizing profits with respect to hiring additional units of labor is to continue to add additional units of labor until:

Once this condition is met, at any level of production that employed less labor (holding other inputs constant), there would be additional profits to be made. One more unit of labor would cost less than the value of the additional output from hiring an additional unit of labor (the MRPj [ ). For additional units of labor beyond the amount that satisfies MRP,alior = pricc]ahor, each unit of labor costs more than the additional revenue gained from the output of that unit of labor. Thus, the MRP of labor determines the equilibrium wage rate, the highest price a firm will pay to hire an additional unit of labor.

So we can say that a profit-maximizing firm will use additional units of a productive resource as long as its MRP is greater than its price. This supports the conclusion that the MRP curve is a firm's short-run demand curve for a productive resource (short-run, because quantities of other factors are held fixed).

LOS 21.b: Describe the factors that cause changes in the demand for labor and the factors that determine the elasticity of the demand for labor.

Now that we understand how a profit-maximizing firm determines the optimal quantity of an input to employ, we can examine the factors that will influence the firm's demand for labor.

An increase (decrease) in the price of the firm's output will increase (decrease) the demand for labor. An increase in the product price will increase the firm's marginal revenue, which increases the MRP of labor, increasing the demand for labor at each wage level, i.e., the demand curve for labor (the MRP curve) shifts upward. A decrease in the price of the firm's output will have the opposite effect, by the same logic.

The effect on the demand for labor of a change in the price of another factor of production will depend on whether that factor is a complement to labor or a substitute

MRPUb„r = PriceLah, for it. The decrease in the price of computers over time has decreased the demand for many types of labor for which a computer is a substitute (e.g., customer service personnel). The demand for IT professionals, however, has increased tremendously, since they are a complement to computers in the production of the final good.

This example also illustrates the effect of technological improvements on the demand for labor. Demand for some types of labor has increased and the demand for other types of labor has decreased. Over time, the effect of technological improvements has been a net increase in the demand for labor. A rising real wage rate (wage rate adjusted for inflation) over time has provided evidence of this.

Elasticity of Demand for Labor

The demand for labor, like other types of demand, is more elastic in the long run than in the short run. This is simplv because we define the short run in production as a period over which the quantities of other factors of production arc fixed. II the wage rate rises, we will see a greater decrease in the quanntv of labor employed when the firm can substitute (demand) other factors of production for labor (e.g., get more automated mac hiner\').

The elasticity ot labor will be greater for firms with production processes that are more labor-intensive. A warehouse operation that relies heavily on manpower to fill and ship orders will have a relatively elastic demand for labor because labor represents a large proportion of the total cost of the scrvicc it provides. For an airline, on the other hand, labor costs represent a much smaller proportion of total costs. We would expect the airline's demand for pilots to be much less clastic than a warehouse operation's demand for workers.

A third factor affecting the elasticity of demand for labor is the degree to which labor and capital can be substituted. While airplanes may, one day, have the technology to fly themselves, pilots are actually quite difficult to replace with automation (as are flight attendants). In contrast, warehouse operations and manufacturing assembly plants have found man}' ways to substitute capital for labor through automation and robotics. The elasticity of demand for assembly workers is much more elastic than the demand for airline pilots and flight attendants as a result of this difference in the opportunities to substitute capital for labor in production.

LOS 21.c: Describe the factors determining the supply of labor, including ihc substitution and income effects, and discuss the factors related to changes in the supply of labor, including capital accumulation.

Each individual decides whether, and how much, to work. Typically, labor has disutility, people generally prefer less work (and more leisure). Employers must offer a wage rate high enough that workers give up leisure time in favor of employment.

Wages, then, are the opportunity cost of leisure. The higher the wage rate, the more hours of leisure a worker will forego and the more hours of labor he will supply. This is the substitution effect in labor supply: workers substitute labor for leisure to the extent that the wage rate is high enough to give them an incentive to do so.

At some point, however, an individual reaches a maximum amount of labor that he is willing to offer for any wage. Just as labor has disutility, leisure has a positive value. As a worker's income increases, his demand for the things he values also increases, and leisure is one of those things. Thus an income effect limits how much labor a worker is willing to substitute for leisure. For the labor market as a whole, the substitution effect causes the labor supply curve to slope upward, but the income effect makes the curve "bend backward" at some (maximum) quantity of labor supplied.

Factors other than the wage rate that affect the supply of labor (shift the labor supply curve) include the size of the adult population, and capital accumulation in items that increase productivity in the home so that a greater proportion of adults choose to work outside the home.

a»c: ,': ¡a'.K-i- union:- arid :>f monopsony. ;:: to: a market rhar oHcr; n efficient

Labor unions are organized so that workers can bargain for wages and other aspects of employment as a group, a process called collective bargaining. One way to do this is to simplv restrict supply bv refusing to work (striking) until the employer agrees to the new higher wage rate. This is illustrated in Figure 2. Supply of labor curve S(| represents the supply of labor without union bargaining. With collective bargaining the union raav shift the supply curve to S,. The result is that the wage rises from W(, to W^., but fewer workers are employed (Q^, instead of the competitive result, Qc)-

Figure 2: Supply of Labor Restricted by Unionization

In addition to restricting supply through collective bargaining, unions attempt to increase the demand for the labor of their members in various ways. By increasing the demand for union labor, unions can reduce the decline in the quantity of union labor employed caused by the increase in the union wage rate.

One way to increase the demand for the labor of union members is to increase the marginal product of their members through additional training.

Two other ways to increase the demand for union labor are based on increasing the demand for products made by union workers. Advertisements that encourage people to buy products labeled as made by unionized employees are an example of this strategy. Another strategy is to influence trade restrictions on imported goods. Restrictions on imported steel, for example, increase the demand for domestically produced steel, which increases the demand for unionized steel workers.

Other strategies for increasing the demand for union labor are based on reducing the supply (increasing the price) of substitutes for union labor. Unions attempt to get increases in the minimum wage rate for unskilled workers, since unskilled labor may be a substitute for skilled union labor. An increase in the price of a substitute productive resource (input) will increase the demand for a productive resource. Political activity centered on restricting immigrant or guest foreign workers will have the same effect, since less skilled immigrant labor is also seen as a substitute for skilled union labor.

Monopsony refers to a situation where the buver ol a good or productive input has market power, a situation opposite to that of monopolv, where the seller has market power. If an employer pavs a single wage rate, increasing this wage in order to hire additional workers means that all workers receive the increased wage. I he result ot this is that the addition to total cost associated with hiring an additional worker is more that simply the (increased) wage for the additional worker. An employer that is the onlv major emplover in a geographic area can face labor supply and associated marginal costs of hiring additional workers illustrated in Figure 3. A monopsonist employer will hire fewer workers, Q^., compared to the competitive level of employment, Qc. The employer hires workers up to the point where the marginal cost of hiring an addition^; worker is equal to the additional worker's MRP, but pays only the wage necessary to hire that quantity of workers, WM. Compared to the competitive equilibrium, this is inefficient and results in a deadweight loss from underemployment, since the marginal revenue product of an additional worker is greater than the wage rate.

Figure 3: Monopsony in the Market for Labor

If workers are unionized and bargain collectively (as a monopoly supplier) and the employer represents a significant portion of the local demand for labor (acts as a monopsonist), the actual wage rate and employment level will be the result of bargaining between the company and the union. The wage rate will likely be somewhere between the (too high) wage resulting from the union's reduction in the supply of labor and the wage rate (too low) that would result if workers did not negotiate collectively and the employer paid the monopsony wage.

LOS 21.e: Differentiate between physical capital and financial capital, and explain the relation between the demand for physical capital and the demand for financial capital.

Physical capital is the physical assets of a firm, including property, plant, and equipment, as well as its inventory of finished goods and goods in process. The greater the demand for physical capital, the greater the demand for the financial capital (money raised through issuing securities) necessary to purchase the physical capital.

A firm employs physical capital as a factor of production because it is necessary to produce the firm's output and meet customer orders. We can think, in a simple sense, of two primar}- factors of production: labor and physical capital (people, and machines and goods). In this sense, just as a profit-maximizing firm equates the MRPj ijh)i to the watrc rate, it will also equate the MRP, . , to the cost oI capital. Since the production of capital a.sseis comes over many periods, the MRPC. ^ i( is actually a future MRP. The value to the firm of the assets' production is the present value of its future MRP.

The cost ol capital relevant to this decision is the cost of the funds that the firm must raise to buy physical capital. Just think of the MRPj--. ¡[a| as the returns over time (in percentage terms) on the funds necessary to purchase additional physical capital. Viewed in this way, we can sav that the future MRPt- i[a| must equal the interest rate the firm must pay to raise the financial capital in order to maximize profits.

LOS 21.f: Explain the factors that influence the demand and supply of capital.

Similar to the demand for labor, the demand for capital will be a downward sloping curve derived from its MRP curve. A profit-maximizing firm will employ additional physical capital until its MRP is equal to its cost, the interest rate that the firm must pay on the funds (financial capital) necessary to purchase the physical capital. At higher (lower) interest rates, firms will demand less (more) capital, both physical and financial.

Professor's Note: This concept is introduced here but is covered in more detail in the Corporate Finance topic review. Capital budgeting is the process of choosing ^gggP' only those firm investments for which the return on capitaI investment is greater than the firm's cost of investment funds.

We need to add one additional point here to account for an important difference between the MRP of capital and the MRP of labor. The additional output from employing an additional unit of labor is produced at the time that the labor is employed. With physical capital—a bulldozer, for example—the additional output will come over many periods into the future. For this reason, it is actually the present value of the future MRP of capital that will determine the return on a current investment in (physical) capital assets. In any event, the demand for financial capital will be a downward sloping function of the interest rate (the cost of financial capital).

Professor's Note: We saw the concept of net present value of an investment in Quantitative Methods and we will see examples of discounting the value of the future output of an asset to evaluate an investment opportunity in Corporate Finance.

Now that we have explained that the demand for financial capital is derived from the present value of MRP of physical capital in production, we can turn our attention to the supply of financial capital. Since the interest rate is the price of capital, the supply curve will be an upward sloping function of interest rates. The suppliers of capital are savers, and they have the choice of consuming now or saving to consume later. Three primary factors influence savings and the supply of financial capital: interest rates, current incomes, and expected future incomes.

• At higher rates of interest, individuals are willing to save more because they will receive greater future amounts. Savers will save more (forego more consumption now) if thev can consume 10% more next vear than if they are onlv rewarded with 2% more consumption next year for foregoing consumption now.

• Increases in current income induce individuals to save more (increase the supply oi capital), while decreases in current income have the opposite effect.

• If expected future incomes increase, individuals, willingness to trade current consumption for future consumption will decrease. Workers anticipating a decline-in their incomes in retirement are motivated to save more now to smooth out their consumption over time. Thev will save more now (consume less) so that they can consume more in the future when their incomes are lower. College students are in the opposite situation and save little (or go into debt) in anticipation of rising incomes in the future. We can say that, in general, an increase (decrease) in expected future incomes will decrease (increase) the current supply of capital. Changes in current income and expected future income will shift the supply of capital curve; that is, at each interest rate, more or less capital will be supplied.

Equilibrium in the capital market determines interest rates. The interest rate where the quantity of capital supplied equals the quantity of capital demanded is the equilibrium (market) interest rate. Capital market equilibrium is illustrated in Figure 4.

Figure 4: Capital Market Equilibrium

LOS 21.g: Differentiate between renewable and non-renewable natural resources and describe the supply curve for each.

To understand the difference between the supply of renewable and non-renewable resources, assume you own two wells. One well is an oil well and one is a water well. When you take a barrel of oil out of the oil well, it's gone forever—a non-renewable resource. When you take water out of the water well at a sustainable rate, it will be replaced by nature—a renewable resource.

Assuming a competitive market for water, the price will be determined by demand. The supply of renewable resources at a point in time, or per time period, is fixed. Land is also considered a renewable resource—using it now does not mean we cannot use it later, and its quantity is also fixed. The supply of a renewable resource is, therefore, independent of price and is perfectly inelastic.

The quantity of a non-renewable natural resource that has already been discovered is called the known stock of the resource. Though the known stock is fixed at any point in time, it tends to increase over time as technological advances make more resources accessible. The rate at which this resource is supplied, also called "How supply," is perfectly elastic at a price that equals the present value of the expected next-period price.

To understand this concept, assume that the price ol oil is expected to rise at a rate greater than the risk-free interest rate. Oil producing nations would curtail current production and produce more in the next period when the prices are expected to be higher. If the price of oil is expected to rise at a rate less than the risk-free interest rate, oil producing nations are better ofi increasing their current production and investing the proceeds to earn the risk-free rate of return. Based on this principle (the Hotelling Principle), the equilibrium price of oil is expected to rise at a rate equal to the risk-free rate of interest.

Figure 5 illustrates, for a non-renewable resource, that the supply curve is perfectly elastic and the quantity supplied depends only on the demand at that price. For a renewable resource, supply is fixed (perfectly inelastic) and the price is determined by demand.

Figure 5: Equilibrium in Natural Resource Markets

(a) Non-Renewable resource (oil well)

(b) Renewable resource (water well)



(b) Renewable resource (water well)



LOS 21.h: Differentiate between economic rent and opportunity costs.

Differences in incomes are due to differences in workers' marginal revenue products. An actor who can star in a movie and fill theaters has a high marginal revenue product. A worker in a car wash has a low marginal revenue product.

The opportunity cost of an employee is what he could make in his next highest-paying alternative employment. For the worker in the car wash, this may be very close to the wage rate at the car wash. There are many opportunities for employment in low skill/low marginal revenue product jobs.

The difference between what successful actors earn and what they could earn in their next highest-paying alternative may be quite large. This difference between a factor of production's earnings and opportunity cost is called economic rent. For many successful actors, a very large part of what they earn is economic rent.

Kelsey Grammer (star of a U.S. television show) earned $1.6 million per hall-hour episode. .Assuming that Grammer s opportunity cost for a week of work (his weekly earnings in his next highest-paving alternative occupation) was considerably less, he would have continued to be a television actor even if the weekly pay were considerably less than SI.6 million. We can think of the opportunity cost as the amount required to induce a person to do particular work or, alternatively, as the amount necessary to bid a factor of production away from its next highest-valued alternative use.

Economic rent is similar to the concept of producer's surplus and depends to a large extent on die shape of the supply curve for the resource. When the supply curve is perfectly elastic, as it is with a non-renewable resource, there is no economic rent. When the supply is perfectly inelastic, as it is with a renewable resource, the entire payment for the factor is economic rent. For an upward sloping supply curve economic rent is part of the total paid for the factor of production. These cases are illustrated in Figure 6.

If the factor of production is relatively easy to create or supply, economic rent is reduced by competition. If a factor of production is very difficult to supply or reproduce (like the skills of a professional athlete or musical performer), and the factor has a high marginal revenue product, the factor will receive significant economic rent. Scarcity is not enough. The skill of a top-flight curling player may be in very short supply, but they do not receive anywhere near the rent that a soccer star does.

Figure 6: Economic Rent to Factors of Production

(a) Perfectly elastic supply

(b) Perfectly inelastic supply (c) Upward sloping supply curve



\ c








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  • selamawit
    How to figure the marginal physical product of an actor?
    8 years ago

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