chapter 15 factor markets work is of two kinds: first, altering the position of matter at or near...

Chapter 15

Factor Markets

Work is of two kinds: first, altering the position of matter at or near the earth’s surface relative to other matter; second, telling other people to do so.

Bertrand Russell

Copyright ©2014 Pearson Education, Inc. All rights reserved. 15-2

Chapter 15 Outline

Challenge: Should You Go to College?15.1 Factor Markets15.2 Capital Markets and Investing15.3 Exhaustible Resources

Challenge Solution


Challenge: Should You Go to College?

• Background: • Going to college is expensive.• In the 2011–2012 school year, half of all

18 to 24-year-old undergraduate students borrowed money to pay for college.

• Question: • Is going to college worth it?


15.1 Factor Markets

• Factor markets refer to the markets where labor (L) and capital (K) are bought and sold or rented.

• Factor markets are competitive when there are many small sellers and buyers.

• Factor markets from earlier chapters:• Labor supply determination via labor-leisure model (Ch. 5)• Firm input choices via profit maximization (Chs. 6 & 7)• Competitive supply determination for general firm (Ch. 8)


15.1 Factor Market in Short Run

• A firm’s SR production function can be expressed solely in terms of labor, q = q(L), because capital is fixed in the SR.

• Revenue is a function of production and the firm’s objective is to maximize profit by choosing L in the SR:

• FOC:

• Simplifies:

• The firm chooses L so additional revenue from employing last worker equals wage paid to that last worker.


15.1 Factor Market in Short Run

• The marginal revenue product of labor (MRPL), sometimes called the value of the marginal product, is the additional revenue generated by the last unit of labor.

• In a competitive market:

• This is the firm’s SR labor demand function.

• The MRPL shows the maximum wage that a firm is willing to pay to hire a given number of workers.


15.1 Competitive Factor Market in the Short Run

• The profit-maximizing number of workers is given by the intersection of supply and demand (MRPL).


15.1 Competitive Factor Market in the SR: Effect of Wage Change

• Graphically, we can see that more workers are hired as the wage falls.

• Mathematically, we prove this result with comparative static analysis.

• Differentiate MRPL equation with respect to the wage:

• Rearranging terms:

• This derivative is negative if the firm is operating where there are diminishing marginal returns to labor.


15.1 Noncompetitive Firm’s SR Factor Demand Curve

• How does market power in the output market affect factor market equilibrium?

• Less of a factor is sold than if all firms were competitive.

• Accounting for market power, the marginal revenue product of labor function is:

• For an identical MPL curve, a Cournot dupoly firm’s labor demand curve lies above that of a monopoly, but below that of a competitive firm.


15.1 Noncompetitive Factor Market• The labor demand curves for different market structures.


15.1 Factor Demand in the Long Run


15.1 A Competitive Firm’s Long Run Factor Demand Curve


15.1 Comparing Short Run and Long Run Labor Demand Curves

• LR labor demand is flatter because firms can vary all inputs.


15.1 Competitive Factor Markets

• A factor market demand curve is the horizontal sum of the factor demand curves of the various firms that use the input.

• Inputs such as capital and labor are used in many markets.

• Derive the labor demand curve for each output market and then sum across output markets to obtain the factor market demand curve.


15.1 Firm and Factor Market Demand

• Summing individual factor demand curves (with price changes) to derive market demand:


15.2 Capital Markets and Investing

• When renting durable goods or workers’ services, a firm chooses a quantity that equates current marginal cost and current marginal benefit.

• If the capital good must be bought or built rather than rented, then a firm must compare current cost of capital to future higher profits associated with the investment.• Such comparisons involve both stocks and flows.• A stock is measured independently of time (e.g.

wealth).• A flow is measured per unit of time (e.g. income).



• An interest rate is the percentage more that must be repaid to borrow money for a fixed period of time.

• People value having a dollar today more than having a dollar in the future, so some future offering would have to be inflated:

• A discount rate reflects the relative value an individual places on future consumption compared to current consumption.



• Many people and firms pay for a new purchase by making monthly payments over time.

• One way to evaluate this investment is to compare the present value (PV) of the flow of payments to the PV of the item purchased, the stock.

• If the firm makes a future payment of f per year for t years at an interest rate i, the PV of this flow of payments is:


15.2 Net Present Value Approach

• A firm should make an investment only if the PV of the expected return exceeds the PV of the costs.• A firm should make an investment only if the net present

value is positive: NPV = R – C > 0.

• If in year t of T years, revenue is Rt and cost is Ct, then the firm should invest if:


15.2 Internal Rate of Return Approach

• The internal rate of return (irr) is the discount rate such that the net present value of an investment is zero.

• Solve the following for irr:

• where f is a steady stream of profit paid forever

• It pays the firm to borrow to make the investment if the internal rate of return on that investment exceeds that of the next best alternative: irr > i.


15.3 Exhaustible Resources

• Discounting plays an important role in decision making about how fast to consume exhaustible resources, nonrenewable natural assets that can only be depleted.• Examples: oil, gold, copper, uranium

• If the cost of mining an exhaustible resource is m and it could be sold for p1 this year or p2 next year, then when should you sell it?• Sell it all this year if p1 – m > (p2 – m) / (1+ i )

• Sell it all next year if p1 – m < (p2 – m) / (1+ i )

• Sell it either year if p1 – m = (p2 – m) / (1+ i )



• How does the price of an exhaustible resource change over time?

• The price of an exhaustible resource changes from year to year according to:

• In order to be indifferent between selling the resource this year and next, this year’s price must be higher.• It must be higher by a specific amount.• That amount is the value of selling today and investing

the proceeds: i (pt – m)



• The gap between resource price and marginal cost, pt – m, grows exponentially with the interest rate.



• The price of an exhaustible resource will rise if all of the following conditions are met:1.Resource is scarce 2.Resource has a constant marginal cost of extraction

over time3.Resource is sold in a competitive market

• Most exhaustible resources have experienced long period with falling or constant real prices. Why?



• The real price of an exhaustible resource may fall or remain constant due to:1.Abundance• If the good is so abundant that the initial gap between price

and marginal cost is zero, the gap does not grow.

2.Technical progress• The marginal cost of mining has been reduced by technical

progress over time.

3.Changing market power• Changes in market structure can result in either a rise or fall in

the price of an exhaustible resource.


Challenge Solution

• Individuals may choose to invest in education in order to raise their productivity and future earnings.


Challenge Solution

• If the discount rate is less than 10.42%, then the present value of earnings for a college grad is greater than that of a high school grad.


Figure 15.6 First-Year Price in a Two-Period Model

chapter 15 factor markets work is of two kinds: first, altering the position of matter at or near...

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