Business Economics 06 Theory of Production

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Business Economics 06 Theory of Production

  1. 1. Production functions
  2. 2. Firm, production, optimal input combination <ul><li>Coverage </li></ul><ul><li>The concept of production function </li></ul><ul><li>Properties of the production functions </li></ul><ul><li>Conditions for achieving peak production efficiency and for optimizing the mix of resource inputs in short and long run </li></ul><ul><li>Technical and economic efficiency </li></ul>09/13/11
  3. 3. Production? 09/13/11
  4. 4. Production <ul><li>Any activity which creates value is production. </li></ul><ul><li>e.g. – transporting sand, collecting tax, operating a jeweler store, drilling for oil, recruiting new employees, driving a garbage truck, designing a system to measure air pollution. </li></ul>09/13/11
  5. 5. Production process <ul><li>An integrated system of activities by which inputs are transformed into the production of goods and services over some period of time. </li></ul><ul><li>Production processes composed of sequentially organized phases e.g.; </li></ul><ul><li>Adding labor–saving equipment > material specifications and modifying skill levels of labor > procurement pattern and hiring and training programmes </li></ul>09/13/11
  6. 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. 7. 09/13/11 Factors of production
  8. 8. Factor definitions <ul><li>Land- all natural resources, including the sea and outer space. Fixed supply and a factor in its unimproved state </li></ul><ul><li>Labour- number of people and physical and intellectual skills and efforts </li></ul><ul><li>Capital- capable of generating incomes, holding stored value means it represents deferred consumption or use </li></ul><ul><li>Organizer or entrepreneur- who perceives market opportunities in uncertainty. Involved in risk taking, invention </li></ul>09/13/11
  9. 9. <ul><ul><ul><li>Inputs – fixed and variable </li></ul></ul></ul><ul><ul><ul><li>Time periods- market, short and long </li></ul></ul></ul><ul><ul><ul><li>Rational producer </li></ul></ul></ul><ul><ul><ul><li>Productivity- evaluates the effectiveness of production process </li></ul></ul></ul><ul><ul><ul><li>Measurements of productivity– total production (TP), average production (AP), marginal production (MP) </li></ul></ul></ul>09/13/11
  10. 10. Short run production function The law of diminishing returns or The law of variable proportions <ul><li>Q = f (L, K) </li></ul><ul><li>Where L = labour </li></ul><ul><li>K = capital </li></ul><ul><li>As the use of one input increases keeping other inputs fixed, a point will eventually be reached at which the resulting additions to output decrease. </li></ul>09/13/11
  11. 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. 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. 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. 14. Determining optimal input proportions – long run analysis 09/13/11
  15. 15. 09/13/11 <ul><li>maximize output for a given cost </li></ul><ul><li>minimize cost for a given output </li></ul><ul><li>produce output that max. profit </li></ul>Production function for long run - three options
  16. 16. 09/13/11 Production table
  17. 17. Isoquants or Isoproduct curve <ul><li>A line showing all the alternative combinations of two factors that can produce a given level of output. </li></ul>09/13/11
  18. 18. Characteristics of an Isoquant <ul><li>all rational combinations of inputs lie on negatively sloped and convex to the origin portion </li></ul><ul><li>nonintersecting </li></ul><ul><li>higher isoquant gives higher output </li></ul><ul><li>inputs are imperfectly substitutable </li></ul>09/13/11
  19. 19. MRTS <ul><li>The rate at which firm is able to substitute labor for capital </li></ul><ul><li>Loss in Q due to decline in K </li></ul><ul><li>= ΔK.MP K </li></ul><ul><li>Gain in Q due to increase in L </li></ul><ul><li>= ΔL.MP L </li></ul><ul><li>Loss = Gain </li></ul><ul><li>- ΔK.MP K = ΔL.MP L </li></ul><ul><li>ΔK/ ΔL = MP L / MP K </li></ul><ul><li>Imperfect substitution, perfect substitution and perfectly complimentary </li></ul>09/13/11
  20. 20. Isocost curve or cost constraint <ul><li>TC = P L .L + P K . K </li></ul><ul><li>Slope of isocost </li></ul><ul><li>= TC/P K /TC/P L = - P L /P K </li></ul><ul><li>the rate at which firm is economically able to substitute labor for capital </li></ul>09/13/11
  21. 21. 09/13/11 <ul><li>The optimum mix of resource inputs </li></ul><ul><li>Least-cost input combination - Optimization where isocost and isoquent are tangential </li></ul><ul><li>MRTS LK = - P L /P K </li></ul><ul><li>MP L /MP K = P L /P K </li></ul><ul><li>Maximum-output input combination </li></ul><ul><li>Maximum-profit input combination - the expansion path </li></ul>
  22. 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. 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. 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
  25. 25. <ul><li>Ridge lines </li></ul><ul><li>The impact of change in resource price </li></ul><ul><li>Cost effect = substitution effect + output effect </li></ul>09/13/11
  26. 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%
  27. 27. Returns to scale <ul><li>Refers to the character of changes in output when all resource inputs are changed in equal proportions. </li></ul><ul><li>increasing returns to scale-short range(b>a) </li></ul><ul><li>constant returns to scale- lengthy range(b=a) </li></ul><ul><li>decreasing returns to scale- (b<a) </li></ul><ul><li>L + K = Q </li></ul><ul><li>aL + aK = bQ </li></ul><ul><li>RTS is reflection on TFP </li></ul>09/13/11
  28. 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
  29. 29. Factors responsible for returns to scale <ul><li>Economies Diseconomies </li></ul><ul><li>Internal Internal </li></ul><ul><ul><ul><ul><li> External External </li></ul></ul></ul></ul>09/13/11
  30. 30. Factors for increasing returns to scale <ul><li>labor economies, division of labor, specialization </li></ul><ul><li>indivisibility of factors of production - technical economies </li></ul><ul><li>dimensional economies </li></ul><ul><li>economies of mass production – low cost, less spare parts </li></ul><ul><li>managerial economies </li></ul><ul><li>marketing economies </li></ul><ul><li>financial economies </li></ul><ul><li>economies of risk spreading </li></ul><ul><li>external economies </li></ul>09/13/11
  31. 31. <ul><li>Factors for constant returns to scale </li></ul><ul><li>producing in the most efficient plant size </li></ul><ul><li>Factors for decreasing returns to scale </li></ul><ul><li>diseconomies related to management, labor, transport </li></ul>09/13/11
  32. 32. All input elasticity of output <ul><li>Responsiveness of output to the change in all inputs </li></ul><ul><li>E Q,I = % ΔQ/%Δ in all inputs </li></ul><ul><li>=DQ/Di.I/Q </li></ul><ul><li>=ΔQ/ΔI.I/Q </li></ul><ul><li>E Q,I > 1  Increasing RTS </li></ul><ul><li>E Q,I = 1  Constant RTS </li></ul><ul><li>E Q,I < 1  Decreasing RTS </li></ul>09/13/11
  33. 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
  34. 34. <ul><li>sum of exponents returns </li></ul><ul><li>(  +  ) to scale </li></ul><ul><li>less than one decreasing </li></ul><ul><li>equal to one constant </li></ul><ul><li>greater than one increasing </li></ul><ul><li>Q = 10K 0.5 L 0.6 </li></ul><ul><li> +  = 0.5+0.6 = 1.1 > 1 </li></ul><ul><li>increasing return to scale </li></ul>09/13/11
  35. 35. 09/13/11 Case on C-D function <ul><li>Agricultural economist E O Heady conducted an experiment on 302 pigs weighing between 34-250 pound </li></ul><ul><li>G = 1.60P .30 C .53 for the weight interval 34-75 pounds </li></ul><ul><li>G = 0.71P .14 C .77 for 75-150 pounds </li></ul><ul><li>G = 0.46P .09 C .86 for 150-250 pounds </li></ul>
  36. 36. <ul><li>where G is weight gain, P is input of soybean oil meal (protein), and C is input of corn (carbohydrate) all measured in pounds per pig. </li></ul><ul><li>Source: E O Heady, “An econometric investigation of the technology of agricultural production functions”. </li></ul><ul><li>Econometrica, V25 (April, 1957) </li></ul>09/13/11
  37. 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
  38. 38. Economies of Scope <ul><li>Savings when two or more products are produced jointly </li></ul><ul><li>S = 50,000+30,000 – 70,000 </li></ul><ul><li>------------------------------ = 0.14 </li></ul><ul><li>70,000 </li></ul>09/13/11
  39. 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.
  40. 40. <ul><li>AP L = Q/L </li></ul><ul><li>200/10=20, 240/11=21.8 </li></ul><ul><li>Whether labour productivity has increased by 9%? </li></ul><ul><li>No consideration for capital used </li></ul>09/13/11
  41. 41. Multi factor (or total factor) productivity (MFP or TFP) <ul><li>Ratio of volume of output to a weighted sum of the inputs used in the production process </li></ul><ul><li>TFP tries to circumvent the problem encountered in interpretation of SFP estimates due to changing factor intensities </li></ul><ul><li>Broadest measure of productivity and efficiency in resource use </li></ul><ul><li>Decomposes changes in Q due to changes in quantity of inputs used and changes in all the residual factors </li></ul><ul><li>Also called as ‘index of ignorance’ (ABROMOVITZ, 1986) </li></ul>09/13/11
  42. 42. TFP = Q/r.K + w.L <ul><li>Case 1 Q=500 K 1 =8 L 1 =20 r 1 =4 w 1 =2 </li></ul><ul><li> K 2 =11 L 2 =10 r 2 =2 w 2 =4 </li></ul>09/13/11 16.13% increase in TFP in terms of output per rupee of inputs  2 = 500/ 2(11) + 4(10) = 8.06
  43. 43. 09/13/11 0 10 20 L 8 11 K B A 500
  44. 44. <ul><li>Case 2 Q 1 =500 K 1 =20 L 1 =40 r 1 =2 W 1 =4 </li></ul><ul><li>Q 2 =600 K 2 =22 L 2 =43 </li></ul>09/13/11 11.2% increase in TFP
  45. 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
  46. 46. 09/13/11 The impact of technological advance upon production function <ul><li>Several forms of technical efficiency </li></ul><ul><li>a new production process permits same amount of resources combined differently to yield more. </li></ul><ul><li>a new process uses same type of inputs but less of one or several inputs and no more of others to produce same type of output. </li></ul><ul><li>a new process may require inputs or yield output, that are of a kind not used until now or available at all. </li></ul><ul><li>. </li></ul>
  47. 47. Economic efficiency <ul><li>Any change that harms no one and improves the lot of some people, if all such changes are carried out and thus no opportunity to make such changes remains - situation is termed as economic efficient </li></ul>09/13/11

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