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- 1. Macroeconomic analysis of technological change Merit course – 2006 Production functions Innovation and employment
- 2. Production functions Today’s substitution possibilities are yesterday’s technological innovations Figure 1. Isoquants showing all possible combinations of production factors that will yield a fixed amount of output
- 3. Characteristics of the production function Returns to scale Decreasing marginal returns These are crucial assumptions in modern economic theory (e.g., without decreasing marginal returns a supply curve would not be upward sloping) Traditional economics does not provide a clear theory of these assumptions would hold; can technology provide the answer?
- 4. Engineering production functions Hollis Chenery, Vernon Smith in 1950s and 1960s An example: heat transfer H1 H0 H L . Tout Tin V St HL , To raise the heat output level, t K we may use insulation of the kS pipe, or produce more heat as Tout Tin H1 H0 . input; these two alternatives are V K substitutable production factors kS 2 280 H1 H0 . 0.01381 0.000595V
- 5. The isoquants Isoquants for the heat transmission process 70 output=10000 BTU/hr 60 insulation material (cubic feet) 50 output=15000 BTU/hr 40 30 output=5000 BTU/hr 20 10 0 0 5000 10000 15000 20000 25000 30000 35000 40000 Heat input (BTU/hr)
- 6. Functional forms of production functions α β = Cobb Douglas (widely used): Constant Elasticity of Substitution (CES): −ρ −ρ − ρ = + Elasticity of substitution: σ= = σ = 1 for Cobb-Douglas, 1/(1+ρ) for CES
- 7. Substitutability and localized technological change Localized technological change (Atkinson & Stiglitz) Figure 3. Isoquants shifting under the influence of localized technological change
- 8. A bias of technological change Bias of technological change (labour-saving or capital-saving) Figure 4. Technological change shifts the isoquant down: neutral technological progress (left), capital saving technological progress (middle) and labour saving technological progress (right)
- 9. Biased technological change – Hicks’ mathematics ∂ ∂ ∂ ∂ = − For Cobb-Douglas a change in A is neutral (B=0) For CES, a change in AK or AL is non-neutral (unless both change in the same proportion) – The CES is a more flexible form than the Cobb- Douglas
- 10. Endogenous bias (Kennedy’s model) Figure 5. Kennedy’s model of an endogenous bias of technology
- 11. Growth accounting Tinbergen/Abramovitz/Solow: dQ dA dK dL f A fK A fL . dt dt dt dt A fK K A fL L ˆˆ ˆ ˆ QA K L. Q Q ˆˆ ˆ ˆ AQ L K. L K Figure 6. Substitution and technological change in the production function A measure of technological change or a measure of our ignorance?
- 12. Growth accounting results (Solow)
- 13. TFP growth for the Netherlands, 1921- 2002 150 140 130 120 110 100 90 80 1920 1940 1960 1980 2000
- 14. Endogenous technological change – R&D Non-military R&D as Total R&D as a % of R&D researchers as a % R&D financed by a % of GDP GDP % of total employment businesses 3.5 3.5 11 75 10 3.0 3.0 70 9 2.5 2.5 65 8 7 2.0 2.0 60 6 1.5 1.5 55 5 4 1.0 1.0 50 EU EU OECD US EU OECD US OECD EU Japan US OECD Japan US Japan Japan Q AR K 1 L ,
- 15. BERD and productivity Country α ρ France 0.860 (0.000) -0.031 (0.273) United Kingdom 0.421 (0.023) 0.395 (0.067) Japan 0.478 (0.000) 0.155 (0.000) United States 0.521 (0.000) 0.237 (0.000) Table 1. Estimations results for the equation including business R&D as a production factor, 1959 - 1999. 2.50 2.00 1.50 1.00 0.50 0.00 1950 1960 1970 1980 1990 2000 2010 France United Kingdom Japan United States
- 16. Issues – Ned Ludd and the Army of Redressers Ricardo: “The opinion, entertained by the labouring class, that the employment of machinery is frequently detrimental to their interests, is not founded on prejudice and error, but is conformable to the correct principles of political economy”
- 17. The demand for labour - Two types of innovation Process innovation: technology replaces labour? Compensation mechanisms: – Lower prices, expanded demand (general equilibrium) – Demand for machinery (investment) Product innovation: expanding demand – New products substitute old ones?
- 18. Labour markets and unemployment Keynesians and neoclassicals: flexible wages or sticky wages? We focus mainly on demand for labour (fall leads to either unemployment or wage pressure)
- 19. Models - Katsoulacos Process innovation and the demand for labour Product innovation (supply-side of the labour market) Structural issues (skills bias)
- 20. Process innovation and the demand for labour Restrictive assumptions: – Homothetic demand – One production factor: homogenous labour – Two sectors/goods Setting: investigate the impact of a change in the labour coefficient (productivity) in one industry
- 21. Goods markets Profit maximization in goods market Qi pi 1 pi (1 ) wai, where . ii pi Qi ii Totally differentiation this w.r.t. time: ( 1) a1 ( ˆ 1 e22) e12 ( 1) a2 ˆ 11 22 22 p1 ˆ , ( 11 1 e11)( 22 1 e22) e12 e21 ( 1) a2 ( 11 1 e11) e21 ( 11 1) a1 ˆ ˆ 22 p2 ˆ , ( 1 e22)( 1 e11) e21 e12 22 11
- 22. Consumers – Utility function Ces functional form: 1 1 1 U C1 C2 , Leads to demand functions: Y d 1 1 Qi , where A p1 p2 , pi A With price elasticities: pi Qi 1 1) s i, 1) sj (i j), where si ( ( ii ij Y 1 1 (pi /pj) Because of homothetic demand: 1 11 12 22 21 12 21 21 12 e 11 e12 , e22 e 21 . 11 22
- 23. Model closure Differentiate demand function: ˆ ˆ ˆd ˆ Li aj Q i ai p ˆ p. ˆ ii i ij j Which leads to: 2 ( )( ( )) ˆˆ 22 22 11 11 22 12 22 11 L a1 . ( )( ) 11 22 22 11 21 11 21 22 Hence everything depends on relative elasticities η11 and η22
- 24. Model conclusions Process innovation leads to an increase in overall demand for labour if the sector where the innovation takes place has a high price elasticity But in the model, price elasticity is an endogenous variable, it depends on the share of a sector in GDP With persistently higher process innovation in a sector, the share of this sector in GDP will grow, and hence it’s price elasticity will decline, hence the impact of process innovation eventually becomes negative
- 25. Product innovation and the demand for labour A similar setup, but – Labour productivity fixed and constant between sectors – Number of goods/sectors is n, and expands as a result of product innovation – Labour supply is modeled explicitly
- 26. Model – consumers and workers Ces utility function 1 1 1 1 U C1 C2 .. Cn . V j = U - ω j, where ω j is worker j’s disutility from work when Vj < 0 (U < ω j), worker j will make the rational decision not to take a job ω j is a random variable distributed uniformly between 0 and ¯ , with total density equal to N (the number of workers)
- 27. Model solution Demand functions become: Y d 1 1 1 Qi , where A p1 p2 .. pn . pi A ( 1) ( 1) , , d c n n Profit maximization condition becomes: 1 p(1 ) w. d This leads to: Each workers that has a job receives w income, which is spent on the n w ( 1) (n 1) . goods. Thus, the budget constraint is w = npC*, where C* is the quantity p (n 1) 1 consumed of each good Substituting in the utility function leads to: 1 1 n ( 1) (n 1) V , (n 1) 1
- 28. Labour supply V*determines labour supply: 1 1 Nn ( 1) (n 1) L . ¯ (n 1) 1 2 1 (1 1/n) n 1 ( L Nn 1) . n ¯ 1)2 (n This derivative is always positive, but it is declining in θ
- 29. Conclusions (in words!) Product innovation (increasing number of products) always leads to a higher labour supply The extent two which this happens declines with the elasticity of substitution between the products In the limit, when products become complete substitutes, there is no effect on labour supply (product innovations completely substitute old products)
- 30. Structural unemployment Industries (Schumpeter’s creative destruction) Skills (skills-bias of technological change and the skills-premium)
- 31. A model of the skills-bias (structural unemployment) A ces production function with skilled and unskilled labour (homogenous output): 1 1 1 QT s (As L s ) u (Au L u) . Profit maximization: 1 1 Aj L j wi 1 Q 1 j Ai T 1 , i, j s,u (i j) i Li Si Li p i Labour demand functions: 1 1 1 Q Li (Ai T) T Ai Aj L j i si . j i Li . Li Q 1 (wi/p) 1 1 1 1 (wi/p) Ai T i
- 32. Model solution From this one may derive: ˆ ˆ ˆˆ Lu /s s T ( /s s 1) As Ls , ˆ ˆ ˆˆ L /s u T ( /su 1) Au Lu, s ˆ ˆˆ ˆˆ Lu > 0 iff /s s (T Au) > Au As , ˆ ˆˆ ˆˆ Ls > 0 iff /su (T A s) > As Au. ˆˆ ˆ Suppose that all three rates of innovation (T, As , Au ) are positive, but that innovation primarily replaces unskilled technical change, i.e., ˆˆ Au > A s . – Then, demand for skilled labour will always increase – But demand for unskilled labour is ambiguous, only when elasticity of substitution is high it may increase
- 33. Conclusions With a skills-bias of technological change, unskilled labour is at a disadvantage (unemployment or skills-premium) But this depends on how easy unskilled labour may substitute for skilled labour

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