Chapter 15 Factor Markets

1. Chapter 15Factor 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

2. Chapter 15 Outline Challenge: Should You Go to College? 15.1 Factor Markets 15.2 Capital Markets and Investing 15.3 Exhaustible Resources Challenge Solution

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?

4. 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)

5. 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.

6. 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.

7. 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).

8. 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 MRPLequation with respect to the wage: • Rearranging terms: • This derivative is negative if the firm is operating where there are diminishing marginal returns to labor.

9. 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.

10. 15.1 Noncompetitive Factor Market • The labor demand curves for different market structures.

11. 15.1 Factor Demand in the Long Run

12. 15.1 A Competitive Firm’s Long Run Factor Demand Curve

13. 15.1 Comparing Short Run and Long Run Labor Demand Curves • LR labor demand is flatter because firms can vary all inputs.

14. 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. 15.1 Firm and Factor Market Demand • Summing individual factor demand curves (with price changes) to derive market demand:

16. 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).

17. 15.2 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.

18. 15.2 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:

19. 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 Rtand cost is Ct, then the firm should invest if:

20. 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.

21. 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 p1this year or p2next 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 )

22. 15.3 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 (pt – m)

23. 15.3 Exhaustible Resources • The gap between resource price and marginal cost, pt – m, grows exponentially with the interest rate.

24. 15.3 Exhaustible Resources • The price of an exhaustible resource will rise if all of the following conditions are met: • Resource is scarce • Resource has a constant marginal cost of extraction over time • Resource is sold in a competitive market • Most exhaustible resources have experienced long period with falling or constant real prices. Why?

25. 15.3 Exhaustible Resources • The real price of an exhaustible resource may fall or remain constant due to: • Abundance • If the good is so abundant that the initial gap between price and marginal cost is zero, the gap does not grow. • Technical progress • The marginal cost of mining has been reduced by technical progress over time. • Changing market power • Changes in market structure can result in either a rise or fall in the price of an exhaustible resource.

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

27. 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.

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