Ch 6 Production Theory Monday March 24 2014 4 46 PM 1 Overview a Firm Theory 2 Big Picture of Firm Theory i Trying to maximize objective function with constraints a b How firm makes cost min or profit max production decision Product decision i Production Technology 1 Full info on production tech ex productivity needed inputs ii Cost constraint 1 What are limited resources iii Input Choices 1 Resulting from 1 and 2 A Production Technology 6 1 a Given tech how to evaluate performance B Factors of Production a b Inputs into production Examples i Production Function C Labor raw materials capital machines land etc Show max output produced for combination of inputs f K L i Quantity of inputs Any quantity of output can be less than q a b d c q f K L i Features i Inputs and outputs are flow variables 1 Must have continuous inputs for production of outputs ii q f K L 1 2 Describes given tech If no tech no production iii Given f K L actual output can be q but we assume q 1 Due to competition in the market a b If a firm produces less than q they will not survive All production will be at q 2 If no competition output can be less than q Not efficient eg Government No incentive to improve efficiency a b D Short Run i Long Run E F Total Product a b At least 1 input s Q cannot be changed within this time horizon Suppose K is fixed q L K bar 6L 2 L 3 a All inputs are variable can be changed a b Look at one variable input and get total amount of output TP L q L i Total product of labor given quantity of labor Int Micro Lecture notes Page 1 i Total product of labor given quantity of labor G 2 criteria used to evaluate tech Average Product a i ii TP L L Total product of labor over labor b Marginal Product of input MP L q L q L L q L L derivative of TP i ii iii 1 d TP L d L H Applications a Suppose TP is known how to get AP i ii AP L TP L L Tangent angle at that point b How to get MP i ii iii Tangent line to the curve Derive TP L Or if asked with value of MP q L 1 I Relationships between TP AP MP a If TP L then MP L 0 i At max TP L MP L 0 b If AP L then TP L Since TP L L AP L i c If MP L AP L then AP L i Example 1 2 If average class height is 5 8 Shaq walks in with height 7 1 a b MP 7 1 AP will increase ii i i a b MP L AP L d AP L d L 0 J Law of diminishing marginal returns a If production tech is unchanged Since always leads to higher production function b Then MP of a single factor will eventually decrease At first as it goes up MP up c When all amounts of all other factors stay constant K L There exists a best combination of inputs Labor Productivity a Average product of labor i Output per unit of labor input b Productivity growth Int Micro Lecture notes Page 2 b Productivity growth i ii Ultimately leads to growth in overall consumption standard of living due to factor payments Sources of growth 1 Stock of capital a Total amount of capital available for use in production 2 Technological change a Development of new tech Int Micro Lecture notes Page 3 6 3 Production with 2 variable inputs Sunday March 30 2014 11 55 PM 1 What happens in LR when there are 2 variable inputs Raw materials L K Input Firm Production Function Y f L K Analogous to Consumer Theory Inputs Food clothing Consumer Utility Good Y Output Indifference Curves Curve that shows all combination of inputs to produce same amount of output Y bar f L K c 2 3 a Isoquant a b d 4 MRTS a b Marginal rate of technical substitution Ability of one input to be substituted for another to keep output same Slope of the Isoquant K L 1MP MP c d i ii iii Ability of 1 labor to substitute for capital If L how much less K MP 1 2 Marginal product of labor If one more labor how much output up e Diminishing Marginal Return i MRTS decreasing function of L f Substitute A for B i ii MRS of 1 for 2 MU1 MU2 Two Special Cases g i Perfect Substitutes Int Micro Lecture notes Page 4 i Perfect Substitutes Straight Isoquants MRTS is equal to given constant Q 2K 3L Picture ii Perfect Complements Leontif Production Function Isoquants are L Fixed proportions between 2 inputs Fixed ratio not necessarily 1 1 Picture Example a b c If 2 labor required for 1 capital Y f L K f min 5L K 5 Returns to 1 Factor a b Marginal Productivity K or L on Q 6 Returns to Scale i ii Y f L K What happens if we allow Y to change when L K change proportionally Constant Returns to Scale a i ii iii If production factors changed by then output scales up If f L K f L K Ex Service industries 1 2 Barbers coffee shops Bigger shop as much more production iv Isoquants 1 Equal space between them 1 2 3 4 1 2 3 4 5 2 b Decreasing Returns to Scale i ii iii Due to problems with coordination More people harder to coordinate Ex film industry Increasing Returns to Scale c When large investments can be made Monopolistic firms under regulation Auto Farms electricity 1 i ii iii iv v Usually provided govs If entirely monopolistic will not produce as much as the efficient level Isoquants 1 Become closer Int Micro Lecture notes Page 5 1 Become closer 2 d Exam Question Example i What is impact to Q when K and L increased by 20 if it is decreasing returns to scale 7 Economies of scale i Impact of Q on costs a Unit cost falls as Q grows LRAC falls as Q up i Falls when MC AC b Int Micro Lecture notes Page 6 Returns Econs to Scale Friday April 18 2014 5 20 PM 1 Returns to Scale i ii Y f L K What happens if we allow Y to change when L K change proportionally a Constant Returns to Scale i ii iii If production factors changed by then output scales up If f L K f L K Ex Service industries 1 2 Barbers coffee shops Bigger shop as much more production iv Isoquants 1 Equal space between them b Decreasing Returns to Scale i ii iii Due to problems with coordination More people harder to coordinate Ex film industry Increasing Returns to Scale c When large investments can be made Monopolistic …