# Unit 7: Factor Markets

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1 Unit 7: Factor Markets

2

3 Factor Market Markets in which the factors of production are bought and sold. A factor input is either land, labor, capital, or entrepreneurship Entrepreneurship is not purchased in an easily identifiable factor market like the other three.

4 Derived Demand It results from (that is, derived from) the demand for the output being produced. If the demand for a product rises or falls, then the demand for the factors used for producing that product will rise or fall respectively.

5 Wage (W), Rental Rate (R*) Price (P) Circular Flow Diagram Competitive Market S (Firms) P 1 P E E E 1 Q E Q 1 Quantity (Q) D 1 D (Households) Competitive Market S (Households) W 1 W E E E 1 L E L 1 D 1 Quantity of Inputs (L, Q*Land, Q*Capital) D (Firms) Derived Demand

6 Labor Demand for a Perfectly Competitive Firm We will start our analysis under the assumption that the factor market is perfectly competitive We will further assume that the product market is perfectly competitive This provides a benchmark against which to compare other labor markets or product markets that are not perfectly competitive

7 Labor Demand for a Perfectly Competitive Firm Assumptions Each employer is one of a very large number of employers Workers do not need special skills Workers are free to move from one employer to another The firm is a price taker in the labor market

8 Distinguishing Between Competitive Markets and Firms Competitive Market Competitive Firm S MC = S (above AVC) P E E P MR = D D Q E Q (MR=MC) Competitive Market Competitive Firm S W E E W MFC = S D MRP = VMP = D L E L (MRP = MFC)

9 Marginal Revenue Product (MRP) (perfect competition) The additional revenue generated by employing one more unit of that factor input. *Important - (perfect competition) implies we are assuming the firm is competitive both in the market in which it is a seller (goods/services) and the market in which it is a buyer (factor inputs). MRP = MR x MP or TR / Q of Factor

10 Marginal Revenue Product (MRP) (perfect competition) \$50 \$90 \$120 \$140 \$150 \$50 \$40 \$30 \$20 \$10 MRP = MR x MP or TR / Q of Factor

11 Marginal Revenue Product Curve Shows how the value of the marginal product of the factor depends on the quantity of the factor employed. The MRP curve shows the various quantities of the factor the firm is willing to buy at different prices, which is what a demand curve shows. The MRP curve is the firm's factor demand curve. The MRP slopes downward because of diminishing returns of the input used in production.

12 Marginal Revenue Product Curve MRP (Table taken from MRP slide)

13 Value of the Marginal Product (VMP) The price of the good/service multiplied by the marginal product of the factor input. *Important: Is VMP = MRP? Only if P = MR This occurs in perfect competition VMP = P x MP

14 Firms Demand for Labor (perfect competition) A firms demand for labor (MRP L ) will change (curve will shift) as a result of three main causes: 1) Change in the price of goods (derived demand) 2) Change in the supply of other factors 3) Changes in prices of other resources

15 Firms Demand for Labor (perfect competition) \$40 \$32 \$24 \$16 \$8 \$80 \$64 \$48 \$32 \$16 MRP = MR x MP

16 Firms Demand for Labor If Could the price the MRPL of the product curves also is \$6 \$8 \$4 be how labeled many as workers VMPL curves? will the Why firm or hire why if not? the wage is \$48? Yes, because P = MR 20 3 (perfect competition) MRPL3 MRPL2

17 Firms Demand for Labor (perfect competition) 2) Change in the supply of other factors Demand for labor will increase if Labor becomes more productive, either with more resources available, better technology, or a higher quality workforce. Demand for labor will decrease if Labor becomes less productive, either with fewer resources available, lessened technology, or a lower quality workforce.

18 Firms Demand for Labor (perfect competition) 2) Change in the supply of other factors Can improved technology ever decrease factor demand? Yes. Consider horses, which were once an important factor of production. The development of substitutes for horse power, such as automobiles and tractors, greatly reduced the demand for horses.

19 Firms Demand for Labor (perfect competition) 2) Change in the supply of other factors Can improved technology ever decrease factor demand? However, even though there have been persistent fears that machinery would reduce the demand for labor, over the long run the U.S. economy has seen both large wage increases and large increases in employment, suggesting technological progress has greatly increased labor demand. Technological progress tends to increase the demand for a given factor, because it usually raises the marginal product of the factor.

20 Firms Demand for Labor (perfect competition) 3) Change in prices of other resources Substitute Resources Substitution effect (SE): If the price of a substitute resource (machine vs labor) decreases demand for labor will decrease. Output effect (OE): Lower resource prices lower production costs. This will cause the firms MC curve to shift to the right and production to increase. To increase production more labor may be needed. Demand for labor will increase if OE > SE Demand for labor will decrease if SE > OE

21 Firms Demand for Labor (perfect competition) 3) Change in prices of other resources Complementary Resources Resources that are used together. Demand for labor will increase if The price of a complementary resource falls. Demand for labor will decrease if The price of a complementary resource rises.

22 Marginal Factor Cost (MFC) (perfect competition) The additional cost incurred by employing an additional factor unit. Factor Price Taker: A firm that can buy all of a factor it wants at the equilibrium price. It faces a horizontal (flat, perfectly elastic) supply curve of factors. Total Factor Cost / Factor or ( TC / L) if TC is only changing due to labor.

23 Marginal Factor Cost (MFC) (perfect competition) \$30 \$60 \$90 \$120 \$150 \$30 \$30 \$30 \$30 \$30 Total Factor Cost / Factor

24 Marginal Factor Cost Curve (MFC) (perfect competition) Shows how the cost of the marginal cost of the factor depends on the quantity of the factor employed. The MFC curve is the firm's factor supply curve.

25 Marginal Factor Cost Curve (MFC) (perfect competition) Even though the MFC, or factor supply, curve for a single factor price taker is horizontal, the market supply curve is upward sloping. This is because the firm is too small relative to the industry to drive up the price of the factor. This is similar to the situation for a perfectly competitive firm where the firm's demand curve is horizontal but the market demand curve is downward sloping. But in factor markets we are talking about the supply side of the market instead of the demand side.

26 Distinguishing Between Competitive Markets and Firms Competitive Market Competitive Firm S P E E P MR = D D Q E Competitive Market Competitive Firm S W E E W MFC = S D L E

27 Marginal Factor Cost Curve (MFC) (perfect competition) MFC SFactor

28 Optimal Factor Purchase (Profit Maximization for firm) (perfect competition) In the factor market, a firm buys the factor quantity at which marginal revenue product equals marginal factor cost. MRP = MFC

29 Optimal Factor Purchase (Profit Maximization for firm) (perfect competition) If the factor being examined is labor, how would you label the vertical and horizontal axis? MFC What if the factor was land or capital? MRP Wage rate (W) Q of labor (workers) Rental rate (R*Land) Q of land Rental rate (R*Capital) Q of capital

30 Marginal Productivity Theory Firms in a competitive, or perfect product and factor markets, pay factors their marginal revenue product. For Labor this implies W = MRP (perfect competition)

31 Marginal Productivity Theory Logic: 1. For a factor price taker, MFC is constant and equal to price. For the firm that implies MFC=W, where W is the wage rate. 2. Firms hire the factor quantity at which MRP=MFC. 3. If MFC = W & MRP=MFC, then W=MRP. If A = B & C = A, then B = C 4. Additionally, if a firm is a perfect competitor then MRP=VMP. (perfect competition) 5. If W=MRP & MRP=VMP, then W=VMP.

32 Market Supply and Demand (perfect competition) The bubonic plague killed roughly one-third of the population in Europe during the 14th-century. Adjust the markets for labor and land accordingly by drawing the new supply or demand curve. Explain your answer. Labor explanation: Land explanation:

33 Effects of the Black Death W 1 R*Land 1 L 1 S 1 D 1 Reduced population decreased the supply of labor. Resulting in an increase in wages. With a smaller supply of workers, the marginal product of labor rises (diminishing marginal product in reverse). Labor is a complementary resource for land. If the price of labor increases, the demand for land will decrease. Resulting in lower rental rates. With fewer workers available to work the land, the marginal product of land fell.

34 Effects of the Black Death Both predictions are consistent with the historical evidence. Wages approximately doubled during this period Rents declined 50% or more Thus, the Black Death led to economic prosperity for the peasant classes (if lucky enough to survive) and reduced income for the landed classes.

35 Imperfect Competition Monopsonist: A single buyer in a factor market. Monopsony: A market similar to a monopoly except that a large buyer not seller controls a large proportion of the market and drives the prices down. People have accused Ernest and Julio Gallo (the big wine makers) of being a monopsony. They had such power buying grapes from growers, that sellers had no choice but to agree to their terms.

36 Difference between perfect and imperfect factor markets: Demand In perfectly competitive markets firms are product price takers P = MR making VMP = MRP, where VMP = P x MP & MRP = MR x MP. Whereas in imperfect markets P > MR making VMP > MRP. This means the VMP curve will be above the MRP curve. Supply In perfectly competitive markets firms are factor price takers P = MFC, where P = price of factor (wage or rental rate). Therefore, MFC curve = supply curve Whereas in imperfect markets P < MFC. This means the MFC curve will be above the market supply curve.

37 Difference between perfect and imperfect factor markets:

38 Imperfect Competition Why is MFC > P (wage rate)? In order to hire more of a resource, such as labor, the firm must raise the wage and pay everyone more. Making the cost of hiring another worker higher than the wage rate.

39 Imperfect Competition MP = TP / L

40 Imperfect Competition TR = P x Q \$45 \$72 \$84 \$84

41 Imperfect Competition MR = TR / Q \$45 \$72 \$84 \$84 \$9 \$6.75 \$4 \$0

42 Imperfect Competition VMP = P x MP 5 \$45 \$9 \$45 4 \$72 \$6.75 \$32 3 \$84 \$4 \$21 2 \$84 \$0 \$12

43 Imperfect Competition MRP = MR x MP 5 \$45 \$9 \$45 \$45 4 \$72 \$6.75 \$32 \$27 3 \$84 \$4 \$21 \$12 2 \$84 \$0 \$12 \$0 Q: Why is VMP > MRP? A: P > MR because the firm must lower price to sell more.

44 Imperfect Competition \$15 \$40 \$75 \$120 \$15 \$25 \$35 \$45

45 Imperfect Competition Reminder: In the factor market, a firm buys the factor quantity at which marginal revenue product equals marginal factor cost. Therefore, Q is determined by where the MRC & MRP curves intersect. The factor price (wage/rental rate) however, is determined by following Q vertically until it reaches the supply curve.

46 Imperfect Competition How is the employment wage rate determined? level determined? Where the employment level intersects with supply. MRP = MFC MFC S W* L* D, MRPL

47 Least-Cost Rule A firm minimizes costs by buying factors in combination at which the MP-to-price ratio for each is the same. If the marginal product of labor per dollar is greater than the marginal product of capital per dollar, then the firm will employ more labor and less capital. Which results in a decrease in the marginal product of labor, and an increase in the marginal product of capital. Until the marginal product of labor per dollar is equal to the marginal product of capital per dollar.

48 Least-Cost Rule Example #1: Given that the most recent worker hired by a firm produces 30 products per hour, & the last automated technology it employed produced 70 products per hour; how could it minimize costs if they pay \$10/hr for labor and \$35/hr to run their technology? Employ more labor and less capital. 30 / \$10 = 3 > 70 / \$35 = 2 MP L / P L = MP K / P K marginal product of labor per dollar marginal product of capital per dollar or MP L / MP K = P L / P K

49 Least-Cost Rule Example #2: Assume a firm pays \$10 an hour for labor and \$20 for each hour of capital employed.

50 Least-Cost Rule Steps to solving Example #2: Step 1: Identify if you are working with an output or cost constraint. i.e. finding the best way to produce 100 units is an output constraint, whereas told you can only spend \$250 is a cost constraint. Step 2: Find all possibilities where MP L / MP K = P L / P K

51 Least-Cost Rule Steps to solving Example #2: Step 3: Of the found possibilities choose the one that produces the desired output or cost constraint. If working with an output constraint, calculate total product for each possibility. Choose the possibility that produces the desired TP (output constraint). If working with a cost constraint, calculate total cost for each possibility. Choose the possibility that produces the desired TC (cost constraint).

52 Least-Cost Rule Example #2: Step 1: Output constraint Step 2: MP L / MP K = P L / P K L = 1 & K =1 P L / P K = 1/2 Assume a firm pays \$10 an hour for labor and \$20 for each hour of capital employed. What is the least-cost combination of labor and capital when trying to produce a total product of 360? 1 Identify if you are working with an output or cost constraint. L = 2 & K =3 L = 3 & K =4 2 Find all possibilities where MP L / MP K = P L / P K

53 Least-Cost Rule Example #2: Step 1: Output constraint Step 2: MP L / MP K = P L / P K L = 1 & K =1 L = 2 & K =3 L = 3 & K =4 Step 3: P L / P K = 1/2 Assume a firm pays \$10 an hour for labor and \$20 for each hour of capital employed. What is the least-cost combination of labor and capital when trying to produce a total product of 360? 3 If Identify working if with you are an output working with an 1 constraint, output or cost calculate constraint. total product for each possibility. Find all possibilities where 2 MP L / Choose MP K = the P L / P K TP = = 150 possibility that produces the desired TP = ( ) + ( ) = 360 TP (output The firm will employ 2 units of labor and 3 units of capital. constraint).

54 Least-Cost Rule Example #2: Step 1: Cost constraint Step 2: MP L / MP K = P L / P K L = 1 & K =1 P L / P K = 1/2 Assume a firm pays \$10 an hour for labor and \$20 for each hour of capital employed. What is the highest level of output that can be produced if you can only spend \$110 per hour? 1 Identify if you are working with an output or cost constraint. L = 2 & K =3 L = 3 & K =4 2 Find all possibilities where MP L / MP K = P L / P K

55 Least-Cost Rule Example #2: Step 1: Cost constraint Step 2: MP L / MP K = P L / P K L = 1 & K =1 L = 2 & K =3 L = 3 & K =4 Step 3: P L / P K = 1/2 Assume a firm pays \$10 an hour for labor and \$20 for each hour of capital employed. TC = \$10 + \$20 = \$30 TC = (\$10 x 2) + (\$20 x 3) = \$80 TC = (\$10 x 3) + (\$20 x 4) = \$110 The firm will employ 3 units of labor and 4 units of capital. What is the highest level of output that can be produced if you can only spend \$110 per hour? 3 If Identify working if with you are a cost working with an 1 constraint, output or cost calculate constraint. total cost for each possibility. Find Choose all possibilities the where 2 MP L / possibility MP K = P L that / P K produces the desired TC (cost constraint).

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