VI. Competing technologies

1. VI. Competing technologies

2. A naïve question • What if the old technology can be used along with the new one? • Would not that prevent the wages of any worker from falling? • The answer is no: The two technologies compete for mobile factors

3. How can 2 technologies be used? • The new technology dominates the old but is costly to learn (imperfect mobility) • The new technology does not dominate the old

4. The Caselli “technological revolution” model • The economy is in a LR steady state • A new, superior, unbiased technology is introduced • The first generation of workers has to pay a learning cost to use it • The learning cost differs across workers • More skilled = lower learning cost • Capital can freely move between the two

5. The initial steady state:

6. The technological revolution • New production function • Learning cost • Critical worker • Allocation of labor • Allocation of capital

7. The impact on the distribution of income • We want to know how the TR affects the wages • Two categories of workers: old tech/new tech • Wages are given by marginal product conditions • Because of capital mobility, wage ratio only depends on TFP ratio

9. The basic results • Inequality clearly must increase • The old tech must earn less • In fact, they earn less than if technology 1 had not been introduced

10. 3 possibilities: • ROR goes down, and both wages increase • ROR goes up, and one wage increases, the other falls • ROR goes up even higher, and both wages fall

11. r FPF1 FPF0 w1 w0 w Figure 4.1: The determination of wages in each technology

12. rN r FPF1 FPF0 w1 wN w0 w Figure 4.2: Configuration I: both wages go up

13. r rN FPF1 FPF0 w0 wN w1 w Figure 4.3: Configuration II: wage divergence

14. r FPF1 rN FPF0 w0 w1 wN w Figure 4.4: Configuration III: both wages fall

15. Both wages can’t go up • Otherwise, K/L must go up in old tech • To compensate, it falls in new tech • But then, ROR goes down in old tech and up in new tech • That is incompatible with RIR equalization

16. Both wages can’t go down • Otherwise, K/L must go down in technology 0 • To compensate, it must go up in technology 1 • But then, wages go up in technology 1 • That is a contradiction

17. Theorem • Upon introducing the new technology, wages fall for the workers who go on using the old technology • Wages are higher than before for the workers who use the new technology • Thus, workers who do not “adapt” lose from technical progress

18. What is going on? • More productive technology generates a greater return to capital • Capital moves there, leaving workers in old tech with less capital per worker • Labor movement cannot compensate for that • Otherwise, K/L would be unchanged in both sectors, and ROR would be higher in new tech

19. Gainers and losers • Old tech workers necessarily lose • New tech workers have higher wages • But they have to pay the training cost • Therefore, they do not necessarily gain on net • There are cases where all workers lose • All gains then accrue to owners of capital

20. An example • Only two learning costs • All we need is that the marginal worker has cost eL • It is easy to construct such an equilibrium

21. De-skilling technical change • What if new technology suddenly easier to learn? • We can show that wages fall in both technologies • At the same time, more workers learn the higher paying new technology

22. What is going on? • The equilibrium wage ratio only depends on the technological parameters  both wages move in the same direction • K/L must fall in both technologies, because resources move to the new one, which has a higher K/L • Therefore, wages must fall in both technologies

23. K O’ K1 II E K0 I O L L1 L0 Figure 4.5: de-skilling technical progress moves the economy to region I

24. Conclusion • The introduction of a new technology may harm the unskilled who are at a disadvantage at learning it • Its popularization jeopardizes the rents of those who already master it • These effects are likely to be transitory on income distribution

25. Competing technologies with different factor intensities • The economy is originally in steady state • One can now use a new technology • The new technology is more intensive in skilled labor • Both technologies can co-exist if the new technology does not entirely dominate the old one

26. 3 possibilities, depending on the economy’s factor endowment • Old technology not used at all (H/L low) (A) • Both technologies used simultaneously (H/L intermediate) (C) • Old technology abandoned in favor of new one (B)

27. ω A C B’ FPF1 C0 B FPF0 w Figure 4.6: introducing a skill-intensive technology

28. The effect of the new technology on factor prices • If new technology is used, then the wages of the unskilled fall and those of the skilled go up • MRS more favorable to H in new technology • Workers left with old technology work with less H per workers • If both technologies are used, factor prices are pinned down at the intersection, independent of factor endowments

29. Asymmetrical TP • TP in the skilled-intensive technology harms the low skilled • By raising MPs, both factors move to the new technology • New technology has a higher H/L ratio • To maintain aggregate H/L ratio constant, H/L ratio has to fall in both technologies • Thus, w falls and ωgoes up

30. ω C’ C FPF’1 FPF1 FPF0 w Figure 4.7: technical progress in the skill-intensive technology

31. A reinterpretation • Using the two technologies makes H and L more substitutable • Asymmetric technical progress indirectly affects the MRS between H and L • That makes it equivalent to skilled-biased technical change (FPF and isoquants are globally flatter)

32. H A Isoquant-1 E B Isoquant-0 L Fig 4.8: representing the two technologies in the (L,H) plane

33. I0’ H A I1 A’ I1’ E B B’ I0 L Fig 4.9: Technical progress in the skill-intensive technology in the (L,H) plane.

34. VII. Supply effects and competing technologies

35. The standard view • An increase in the skill premium should induce people to invest in H • Accordingly, the relative supply of skills should go up • That should dampen the initial increase in the skill premium

36. The alternative view • A greater supply of skilled workers may lead to further SBTC • Two potential mechanisms • The skilled-intensive technology is used more • New skilled-biased technologies are introduced • Let us study the first mechanism

37. The supply of skills in the 2-tech model • If only one of the two technologies is used, then an increase in H/L reduces ω/w • If both technologies are used, then an increase in H/L increases the use of the skilled-intensive tech

38. H’ H E E’ L Figure 5.2: impact of human capital accumulation on the technology mix

39. 1 0 H/L Figure 5.3: the evolution of the employment share of the new technology

40. Effect on the distribution of income • Factor prices are unaffected, since they do not depend on H/L • Thus, supply response does not dampen initial rise in inequality • But it does not worsen it either • Can we change the model to get what we want?

41. Two ideas • Factor prices are pinned down by a 2 x 2 system; if we introduce capital, they are no longer pinned down • If greater use of skilled-intensive technology drives enough capital away from old technology, w may fall as in Caselli • Let’s see what we get with a 3-factor, 2-tech model

42. The model • 2 technologies, Old (O), New (N) • 3 factors H, K, L • Factor prices ω, r, w • Cost functions and • We only look at the regime where both technologies are in use • = amount of factors used in old technology • “ ^ ” = unit input requirement

43. Solving the model

44. Road map • The preceding equations determine factor prices and the allocation of factors • We will make assumptions on the nature of each technology • We then derive predictions on how changes in the factor endowments H,K,L affect the distribution of wages, under these assumptions

45. Technological assumption #1 • N is more intensive in labor, relative to human capital, than H

46. Comovements between factor prices • The vector of factor prices must be on the intersection between the two FPF • That defines a 1-dimensional locus • Locally, any shock will move that vector in a single direction • That direction may be computed and its properties depends on the technological assumptions

48. Two pairs of alternatives

49. Three cases

50. To summarize: • The most intensive factors are substitutes • The intermediate factor is complement with the others • This pattern does not depend on complementarities and substitutabilities within each technology