Ch. 8: Factor Market

1. Ch. 8: Factor Market

2. Derive demand • The demand for any factor of production is a derived demand since it is derived from the demand for the product it helps to produce.

3. Value of Marginal Product • VMP = P x MP Marginal Revenue Product • MRP = MR x MP • If P = MR, VMP = MRP • If P > MR, VMP > MRP

4. Marginal factor cost curve • Marginal factor cost is the cost of employing an additional unit of factor. (vs. MC of output) • Assuming that the firm is a price-taker in the factor market that it cannot affect the prevailing factor price (H). • So the cost in employing each additional unit of factor in a price-taking factor market is the same, equal to H. • MFC = H (=AFC)

5. $ H 0 Factor A Shape of factor supply curve, MFC curve and AFC curve • As the firm cannot affect the factor price, it must faces a horizontal factor supply curve lying at H, which coincides with MFC curve and AFC curve. Factor Supply Curve = MFC curve = AFC curve

6. Marginal revenue product curve Definitions: • Marginal revenue product(邊際生產收入) is the gain from employing an additional unit of factor. (vs. MR of output) • Average revenue product (ARP) is the gain from employing an additional unit of factor in average. • Value of marginal product is equal to marginal product times price. • VMP = MPxP

7. Derivation: • In employing an additional unit of factor, output of a firm increases by MP and its revenue increases by marginal revenue product (MRP) is equal to marginal product times marginal revenue. • MRP = MPx MR • If the firm is a price-taker in the product market, MR = P  MRP (= MP x MR) =VMP (= MP x P) • If the firm is a price-searcher in the product market, MR < P  MRP (= MP x MR) <VMP (= MP x P)

8. Output produced Output produced MRP=MRMP ARP=ARAP AP x AR=ARP MP x MR=MRP AP MP 0 0 Factor A Factor A Shape of MRP curve and ARP curve Derivation of MRP and ARP curve

9. Output produced MRP=MRMP ARP=ARAP Factor A Features: • As MP curve must finally be downward sloping, MRP curve must also be downward sloping. • Similarly, ARP curve must also be downward sloping. • MRP curve passes through the turning point of ARP curve.

10. H1 Derivation of the factor demand curve At the factor price of H1 • MRP (the gain) cannot cover MFC (the cost). • The firm will not employ any unit of factor.

11. M N H2 A1 A2 At the factor price of H2 • However, at A2, ARP < AFC. • So it is not worth for the firm to employ any factor to produce. • At N,MRP curve cuts MFC curve from above. • Either  or  in factor employment reduces wealth. • A2 is wealth-maximizing. • At M,MRP curve cuts MFC curve from below. • Either  or  in factor employment raises wealth. • A1 is wealth-minimizing. MFC = AFC

12. H3 T A3 At the factor price of H3 • At point T, MRP curve cuts MFC curve from above. • At A3, ARP > AFC. • Factor employment at A3 raises wealth.

13. Equilibrium conditions of factor employment • MRP = MFC • MRP curve cuts MFC curve from above • (to determine the max. employment level) • 3. ARP AFC • (to determine if it is worth to employ)

14. Factor Demand Curve • Provided that ARP AFC, the wealth-max. level of factor employment is: MRP=MFC=H • So the factor demand curve of a price-taking firm is the portion of MRP curve lying below the max. point of ARP curve.

15. Market factor demand curve • A factor is demanded by many different firms, e.g., clerks are employed in hospitals, schools, accounting firms, etc. • So the market factor demand curve is equal to the horizontal sum of factor demand curves of all firms in the market.

16. Factor Supply

17. Budget line of a price-taking factor supplier Income N Numerical value of slope = Factor price (Hourly wage rate) M I0 Resources for own use (leisure) R 0 R0 (24 hours)

18. Indifference map of a factor supplier For a resource with reservation use (a good) • Its indifference curves are convex to the origin. Why?

19. I (Income) U3 > U2 > U1 U3 U2 U1 Resource without reservation use (neuter) 0 For a resource without reservation use (a neuter) • Its indifference curves are horizontal line. Why?

20. I* Amount of factor supplied R* Equilibrium of a factor supplier Resource with reservation use (a good)

21. I Resource without reservation use I* U* Resource without reservation use (neuter) Amount of factor supplied R0 0 =R*

22. A2 A1 Substitution effect and income effect of a price change • The effect of a change in price can be decomposed into substitution effect and income effect. Price effect • in price • Budget line tilts upward.

23. S.E. A’ Substitution effect • Factor price  cost of retaining the resource for own use increases  to max. U, an individual supply more units of resource in the factor market • Factor price and quantity supplied are positively related. A1

24. I.E. Income effect • If the resource with reservation use is a superior good • Factor price  an individual earns more  keeps more and supply less resource in the factor market • Factor price and quantity supplied arenegatively related. S.E. A1 A’ A2

25. Backward bending factor supply curve • When factor price is low, the quantity supplied is small. Even if the factor price rises by 10%, the increase in income is rather small. • Moreover, at the beginning, the individual still owns a large amount of the resource. • So, when H rises, the individual is willing to supply more, i.e., substitution effect (A) is larger than income effect (A). The factor supply curve is upward sloping.

26. H’ S.E. > I.E. • When factor price is low, a rise in factor price from H1 to H’ will raise the factor supplied  S.E. > I.E. Upward sloping factor supply curve

27. Backward bending factor supply curve (Con’t) • When factor price is high, the quantity supplied is large. Even a 10% rise in income will raise the income by a very large amount. • Moreover, the individual now owns only a very small amount of the resource. • So, when H rises, he desires to keep more of the resource for own use, i.e., substitution effect (A) is smaller than income effect (A). The factor supply curve is downward sloping.

28. S.E. < I.E. • When factor price is high (above H’), a rise in factor price from H’ to H2 will lower the factor supplied  S.E. < I.E. H’ Backward bending factor supply curve

29. Q13.3 If the resource with reservation use is an inferior good, what will be the shape of the factor supply curve of an individual?

30. Other Points to be Noticed

31. Total receipt (TRP = ARP x L) $ Total payment to labour (WxL ) Total payment to other factors (TRP - WxL) ARP W MFC=AFC MRP Quantity supplied of labour 0 L Functional distribution of income

32. A0 A0+1 Factor employment and marginal revenue product • When the firm employs one more unit of factor A • MPA and MRPA (along the curve)

33. When the firm employs one more unit of factor A, factor B will be used more intensively and productively. • So MRP curve of factor B shifts upward. B0

34. If the factor market is price-searching or the market is controlled by a central authority or an institution, the factor price is no longer determined by market demand and market supply of the factor. • Then, H may not reflect the productivity of the factor, i.e., H  MRP.

35. Transfer Earning • Transfer earning is the minimum amonut that a factor must earn in order to prevent it from transferring to another use.

36. Economic Rent • Economic rent is the return over and above the opportunity costs of the resources employed in alternative uses.

37. Transfer Economic L earningWrent 1 $20 $50 2 30 50 3 40 50 4 50 50 5 60 50 6 70 50 7 80 50

38. P S PL Q

39. P S transfer earning Q

40. P S economic rent Q

41. P S economic rent transfer earning D Q

42. P S transfer earning D Q units of factor of production

43. S P economic rent D Q