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? 15.1Factor Markets 15.2Capital Markets and Investing 15.3Exhaustible Resources Challenge Solution

Copyright ©2014 Pearson Education, Inc. All rights reserved.15-3 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?

Copyright ©2014 Pearson Education, Inc. All rights reserved 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)

Copyright ©2014 Pearson Education, Inc. All rights reserved 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.

Copyright ©2014 Pearson Education, Inc. All rights reserved Factor Market in Short Run The marginal revenue product of labor (MRP L ), 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 MRP L shows the maximum wage that a firm is willing to pay to hire a given number of workers.

Copyright ©2014 Pearson Education, Inc. All rights reserved Competitive Factor Market in the Short Run The profit-maximizing number of workers is given by the intersection of supply and demand (MRP L ).

Copyright ©2014 Pearson Education, Inc. All rights reserved 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 MRP L 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.

Copyright ©2014 Pearson Education, Inc. All rights reserved 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.

Copyright ©2014 Pearson Education, Inc. All rights reserved Noncompetitive Factor Market The labor demand curves for different market structures.

Copyright ©2014 Pearson Education, Inc. All rights reserved Factor Demand in the Long Run

Copyright ©2014 Pearson Education, Inc. All rights reserved A Competitive Firm’s Long Run Factor Demand Curve

Copyright ©2014 Pearson Education, Inc. All rights reserved Comparing Short Run and Long Run Labor Demand Curves LR labor demand is flatter because firms can vary all inputs.

Copyright ©2014 Pearson Education, Inc. All rights reserved 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.

Copyright ©2014 Pearson Education, Inc. All rights reserved Firm and Factor Market Demand Summing individual factor demand curves (with price changes) to derive market demand:

Copyright ©2014 Pearson Education, Inc. All rights reserved 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).

Copyright ©2014 Pearson Education, Inc. All rights reserved Capital Markets and Investing 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.

Copyright ©2014 Pearson Education, Inc. All rights reserved Capital Markets and Investing 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:

Copyright ©2014 Pearson Education, Inc. All rights reserved 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 R t and cost is C t, then the firm should invest if:

Copyright ©2014 Pearson Education, Inc. All rights reserved 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.

Copyright ©2014 Pearson Education, Inc. All rights reserved 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 p 1 this year or p 2 next year, then when should you sell it? Sell it all this year if p 1 – m > (p 2 – m) / (1+ i ) Sell it all next year if p 1 – m < (p 2 – m) / (1+ i ) Sell it either year if p 1 – m = (p 2 – m) / (1+ i )

Copyright ©2014 Pearson Education, Inc. All rights reserved Exhaustible Resources 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 (p t – m)

Copyright ©2014 Pearson Education, Inc. All rights reserved Exhaustible Resources The gap between resource price and marginal cost, p t – m, grows exponentially with the interest rate.

Copyright ©2014 Pearson Education, Inc. All rights reserved Exhaustible Resources 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 time 3.Resource is sold in a competitive market Most exhaustible resources have experienced long period with falling or constant real prices. Why?

Copyright ©2014 Pearson Education, Inc. All rights reserved Exhaustible Resources 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.

Copyright ©2014 Pearson Education, Inc. All rights reserved Challenge Solution Individuals may choose to invest in education in order to raise their productivity and future earnings.

Copyright ©2014 Pearson Education, Inc. All rights reserved 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.

Copyright ©2014 Pearson Education, Inc. All rights reserved Figure 15.6 First-Year Price in a Two-Period Model