1. Production functions

3. Production? 09/13/11

6. 09/13/11 Production Function Q= f(x 1 , x 2 , x 3 , x 4 , . . . . . . . X n ) Where x 1 = labour x 2 = land x 3 = capital x 4 = organization tools, machines, infrastructure, transport, electricity, fuel, time, advertisement, supervision, planning, control and coordination, leadership, managerial talent, R&D, government policies - licenses, tax, rules, and regulations etc.

7. 09/13/11 Factors of production

11. The law of variable proportions 09/13/11 K L Q AP L = Q/L MP L = Δ Q/ Δ L 10 0 0 - - 10 1 10 10 10 10 2 30 15 20 10 3 60 20 30 10 4 80 20 20 10 5 95 19 15 10 6 108 18 13 10 7 112 16 4 10 8 112 14 0 10 9 108 12 -4 10 10 100 10 -8

12. 09/13/11 Example - law of diminishing returns Yield of wheat under different fertilizer rates, 1989-90, q/ha Annual Report, Agricultural Research Station, Arjia, Bhilwara, Rajasthan, 1990 N- Nitrogen, P2O5- Phosphorus pentoxide

13. Thomas Malthus (1766-1834) 1798 -1826 six editions An Essay on the Principle of Population The law of diminishing returns and the food crisis Index of world food consumption (per capita) 09/13/11 Year Index 1948-1952 100 1955 109 1960 115 1965 116 1970 123 1978 128 1987 133 1991 142

14. Determining optimal input proportions – long run analysis 09/13/11

16. 09/13/11 Production table

22. 09/13/11 Profit maximization maximize  = TR - TC = PQ – P L .L - P K .K where  = profit P = product price Q = 549.92 +12.98L + 26.72K + 0.196 LK - 0.104L 2 - 0.319K 2 maximize  = (0.1585) (549.92 + 12.98L + 26.72K + 0.196LK- 0.104L 2 - 0.319K 2 ) - 0.75L - 0.50K L,K  0

23. 09/13/11 Unconstrained max. problem for which two first - order partial derivatives be zero d  /dL = (0.1585) (12.98 + 0.196K – 0.208L) – 0.75 = 0 d  /dK = (0.1585) (26.72 + 0.196L – 0.638K) – 0.50 = 0 Simplifying these we get (0.1585) (12.98 + 0.196K – 0.208L) = 1 0.75 And (0.1585) (26.72 + 0.196L – 0.638K) = 1 0.50 Yields profit max. input combination L =103 K = 68

24. Q = 549.92 + 12.98 (103) + 26.72 (68) + 0.196 (103)(68) – 0.104 (103) 2 – 0.319 (68) 2 = 2498 profit max. output corresponding max. profit  = (0.1585)(2498) – 0.75(103) – 0.50(68) = 395.9 – 111.2 = 284.7 09/13/11

26. 09/13/11 Energy consumption (in thousand Btu) per dollar of value added in selected industries Source: U.S. Department Of Commerce, Bureau Of The Census, Statistical Abstract Of The United States: 1981 (Washington, D.C.:U.S. Government Printing Office, 1981). Sectors Year All Manufacturing Paper Organic Chemicals Petroleum Refining Steel Aluminum 1971 52.5 316.2 277.9 631.4 314.7 418.5 1977 42.3 308.7 193.9 573.4 282.7 379.9 Percent -19.4 -2.4 -30.2 -9.2 -10.2 -9.2 Change Prices rose 1971-80 Crude oil 240%, natural gas 347%, coal 113%

28. Exercise - Returns to scale 09/13/11 L K Q I 1 1 5 II 2 2 31 III 3 3 59 IV 4 4 72 V 6 6 107

33. 09/13/11 Introduced to relate output in manufacturing industries from 1899-1922 to labor and capital inputs Q = AK  L   Q = A(2K)  (2L)   Q = 2  2  (AK  L  ) but Q= AK  L  . Hence the factor  = 2  +  and will be less than 2, equal to 2, or greater than 2, depending on  +  Cobb-Douglas production function

37. 09/13/11 Estimates of  1 ,  2 ,  3 for selected industries 1963-80 Q = AL  1 K  2 M  3 L - labor K - capital M - raw material

39. 09/13/11 Factor productivity Single factor productivity (SFP) - ratio of volume of output to the quantity of the factor of production for which productivity is to be estimated.

43. 09/13/11 0 10 20 L 8 11 K B A 500

45. Relative contribution of factors in TFP in India 1960-80 09/13/11 Trivedi, 2002, Managerial Economics,Tata McGraw, p 288 Industry type TFP K (%) L(%) O(%) All selected 1.1385 15.7 47.8 36.5 Basic goods 1.1070 5.5 63.7 30.8 Intermediate goods 1.1591 25.5 45.9 28.6 Consumer goods 1.1357 39.5 36.5 24.0