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Chapter 3

Chapter 3. The Demand For Labor. Objectives. Consumers maximize utility subject to a budget constraint Firms maximize profits subject to cost and production constraints. Two types of demand to consider:. Consumer’s demand for goods and services derived from utility maximization

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Chapter 3

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  1. Chapter 3 The Demand For Labor

  2. Objectives Consumers • maximize utility subject to a budget constraint Firms • maximize profits subject to cost and production constraints

  3. Two types of demand to consider: Consumer’s demand for goods and services • derived from utility maximization Firm’s demand for inputs (labor, capital) • derived from profit maximization

  4. We will make the following assumptions: • All firms wish to maximize profits. • Firms employ only two homogeneous inputs - Capital (K) and Labor (L). • The only cost of labor is the hourly wage (W) • The only cost of capital is the hourly rental cost (C) • Perfectly competitive labor and product markets

  5. What rule do firms follow to maximize profits? Marginal Revenue = Marginal Cost MR = MC

  6. Why? Suppose that MR > MC. What should the firm do? • The firm should expand output because the unit is worth more to the firm (in terms of additional revenue) than it costs the firm to produce Suppose that MC > MR. What should the firm do? • The firm should reduce output because the last unit cost the firm more to produce than it is worth (in terms of additional revenue)

  7. Since a firm can only expand or contract output by changing its level of inputs, we can think of the profit-maximization decision in terms of employment of inputs:

  8. If the revenue generated by hiring an additional unit of an input > additional expense of hiring that unit, the firm should add that unit (because it will increase profit) • If the revenue generated by hiring an additional unit of an input < additional expense of hiring that unit, the firm should reduce employment of that input (because that unit will decrease profit) • If the revenue generated by hiring an additional unit of an input = additional expense of hiring that unit, no further changes in that input should be made (profits are maximized)

  9. Short-Run Demand for Labor

  10. Let’s do an example: The Short-Run Demand for Labor When Both the Product Market and the Labor Market Are Perfectly Competitive

  11. Definition of the Short-Run: • Capital is fixed at K* • Note that the length of the short-run will vary across different firms

  12. What happens to output as we add more labor? • Marginal Product of Labor • MPL = DQ/DL

  13. Suppose we are running an apple farm • Two inputs: capital (fixed at K*) and labor • Apples sell in a competitive market for $4/bushel • We hire apple pickers in a competitive labor market for $8/hour (This implies that the Marginal Expense [MEL] of hiring a worker is equal to $8.) • HOW MANY WORKERS DO WE HIRE?

  14. Output for Apple Farm L (#pickers) Q (bushels/hour) 0 0 1 7 2 12 3 15 4 17 5 18

  15. L Q 0 0 1 7 2 12 3 15 4 17 5 18 MPL ---- 7 5 3 2 1 Measuring Output of Labor

  16. Law of Diminishing Marginal Returns • after some point, each additional unit of labor will result in smaller increases in output • eventually, marginal product can become negative (implying that hiring an additional unit of input will result in a decrease in output) • this is true for any input in the short-run (because at least one other input is fixed)

  17. How much is that additional output worth? We need to include information on the price of apples.

  18. Valuing Output of Labor L Q MPL P 0 0 ---- 4 1 7 7 4 2 12 5 4 3 15 3 4 4 17 2 4 5 18 1 4

  19. We can use information on MPL and P to calculate the Marginal Revenue Product of Labor (MRPL) • MRPL is the additional revenue a firm earns by hiring an additional unit of labor • MRPL = MPL X MR (general case) • MRPL = MPL X P (competitive output market)

  20. L Q MPL P 0 0 ---- 4 1 7 7 4 2 12 5 4 3 15 3 4 4 17 2 4 5 18 1 4 MRPL ---- 28 20 12 8 4 Valuing Output of Labor

  21. L Q 0 0 1 7 2 12 3 15 4 17 5 18 MPL P MRPL ---- 4 ---- 7 4 28 5 4 20 3 4 12 2 4 8 1 4 4 So, how many workers would we hire if we have to pay them a wage of $8/hour?

  22. We would hire workers up to the point where the last worker adds nothing to profits. • That is where the additional revenue from hiring that worker equals the addition to total costs (“expense”) of hiring him/her • The firm hires workers to the point where MRPL = MEL MRPL = MEL

  23. Since the labor market is competitive (in our example): • MEL = w Since the product market is competitive (in our example): • MRPL = P * MPL

  24. MRPL = MEL is the same thing as MRPL = w which is the same thing as P X MPL = w Dividing both sides by P, we get: MPL = w/P

  25. Thus, we can express the profit-maximization decision in terms of the nominal wage: MRPL = w Or in terms of the real wage: MPL = w/P

  26. Let’s do another example:

  27. Competitive firm producing ping-pong balls that sell for $0.50 each. Hourly output: K* L Q 10 0 0 10 1 14 10 2 46 10 3 84 10 4 116 10 5 130 10 6 140

  28. K* L Q 10 0 0 10 1 14 10 2 46 10 3 84 10 4 116 10 5 130 10 6 140 MPL ---- 14 32 38 32 14 10 Let’s calculate MPL:

  29. K* L Q MPL 10 0 0 ---- 10 1 14 14 10 2 46 32 10 3 84 38 10 4 116 32 10 5 130 14 10 6 140 10 P MRPL 0.50 ---- 0.50 7 0.50 16 0.50 19 0.50 16 0.50 7 0.50 5 Now, let’s calculate MRPL. We need to include information on price:

  30. K* L Q MPL 10 0 0 ---- 10 1 14 14 10 2 46 32 10 3 84 38 10 4 116 32 10 5 130 14 10 6 140 10 P MRPL 0.50 ---- 0.50 7 0.50 16 0.50 19 0.50 16 0.50 7 0.50 5 If the wage is $7/hour, how many workers do we hire?

  31. Let’s graph MRPL:

  32. The firm’s demand for labor curve is the downward sloping portion of the MRPL curve.

  33. The market demand for labor is a horizontal summation of the firms’ demand for labor.

  34. Monopoly • What happens to the firm’s short-run labor demand when the firm is a monopoly in its output market?

  35. A monopoly has the same goal as a competitive firm. It wishes to maximize profit. • However, P  MR (indeed, MR < P at all output rates except Q=1) • This means that we must use the general formula to calculate MRPL. MRPL = MR X MPL

  36. For a monopoly, MR always lies below P. P D Q MR

  37. The rule to find the profit-maximizing level of labor hired is the same for all firms (whether the product market perfectly competitive or not): • Hire labor up to the point where MRPL = w For a monopolist: MR X MPL = w For a competitive firm: P X MPL = w

  38. Since MR < P for a monopolist: • MRPL for a monopolist will be lower than MRPL for a competitive firm • this implies that the monopolist’s demand for labor would lie below (or to the left) of the competitive firm’s demand for labor

  39. Since the labor demand curve for a monopolist lies below and to the left of the labor demand curve for a competitive firm, then at any given wage the monopolist will hire less labor than the competitive firm.

  40. Therefore, just as output is lower for a monopolist, so is the level of employment.

  41. Let’s do an example: • Suppose we own the only pizzeria in town • Thus, we face the market demand curve for pizza (which is downward-sloping) • We do, however, hire labor in a competitive labor market • Let’s see how we would decide how many workers to hire

  42. Output per day as the amount of labor varies: L Q 0 0 1 45 2 75 3 95 4 102 5 105 6 106

  43. L Q 0 0 1 45 2 75 3 95 4 102 5 105 6 106 MPL ---- 45 30 20 7 3 1 Let’s calculate MPL:

  44. L Q MPL 0 0 ---- 1 45 45 2 75 30 3 95 20 4 102 7 5 105 3 6 106 1 P TR MR ---- ---- ---- 4.75 213.75 4.75 4.50 337.50 4.13 4.30 408.50 3.55 4.15 423.30 2.11 4.05 425.25 0.67 4.00 424.00 -1.25 Now let’s add information and calculate MR:

  45. L Q MPLP TR MR 0 0 ---- ---- ---- ---- 1 45 45 4.75 213.75 4.75 2 75 30 4.50 337.50 4.13 3 95 20 4.30 408.50 3.55 4 102 7 4.15 423.30 2.11 5 105 3 4.05 425.25 0.67 6 106 1 4.00 424.00 -1.25 MRPL ---- 213.75 123.90 71.00 14.77 2.00 -1.25 Now let’s calculate MRPL:

  46. L Q MPLP TR MR 0 0 ---- ---- ---- ---- 1 45 45 4.75 213.75 4.75 2 75 30 4.50 337.50 4.13 3 95 20 4.30 408.50 3.55 4 102 7 4.15 423.30 2.11 5 105 3 4.05 425.25 0.67 6 106 1 4.00 424.00 -1.25 MRPL ---- 213.75 123.90 71.00 14.77 2.00 -1.25 Again, we should be able to determine how many workers we would hire at different values of the daily wage

  47. So far, we have been assuming that the labor market is competitive. But, what if it is not? • Remember that profit-maximization requires the firm to hire labor until MRPL = MEL • We have used the rule: MRPL = w because we have assumed a perfectly competitive labor market (MEL = w).

  48. MONOPSONY • exists when only one firm is the buyer of labor in a particular market • Some examples may include coal mining and nursing

  49. If the firm is the only buyer of labor, it faces the entire labor supply curve. • No longer can the firm hire all of the labor it chooses at the going market wage • Since the market labor supply curve is upward-sloping, the firm must raise the wage to hire additional workers • Thus, when hiring an additional worker, labor costs rise in 2 parts: (a) the additional worker’s wages and (b) the increase in wages paid to all workers

  50. Let’s do an example: Suppose we are running a coal mine which is the major employer of the region

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