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Unformatted text preview: Theory of the Firm Moshe BenAkiva 1.201 / 11.545 / ESD.210 Transportation Systems Analysis: Demand & Economics Fall 2008 Outline Basic Concepts Production functions Profit maximization and cost minimization Average and marginal costs 2 Basic Concepts Describe behavior of a firm Objective: maximize profit ( ) max = R a ( ) C a s t . . a 0 R, C, a revenue, cost, and activities, respectively Decisions: amount & price of inputs to buy amount & price of outputs to produce Constraints: technology constraints market constraints 3 Production Function Technology: method for turning inputs (including raw materials, labor, capital, such as vehicles, drivers, terminals) into outputs (such as trips) Production function: description of the technology of the firm. Maximum output produced from given inputs. q = q ( X ) q vector of outputs X vector of inputs (capital, labor, raw material) 4 Using a Production Function The production function predicts what resources are needed to provide different levels of output Given prices of the inputs, we can find the most efficient (i.e. minimum cost) way to produce a given level of output 5 Isoquant For twoinput production: Labor (L) Capital (K) q 1 K L q=q(K,L) q 2 q 3 6 Production Function: Examples CobbDouglas : InputOutput: q = x 1 a x 2 b q = min( ax 1 , bx 2 ) x 2 q 1 x 1 Isoquants q 2 q 2 q 1 x 1 x 2 7 Rate of Technical Substitution (RTS) Substitution rates for inputs Replace a unit of input 1 with RTS units of input 2 keeping the same level of production x 2 x 2 q x 1 RTS = = x q x 2 1 q ' x 2 q slope=RTS ' x 1 x 1 8 RTS: An Example CobbDouglas Technology q = x 1 a x 2 b q = ax 1 a 1 x 2 b x 1 x q 2 = bx 1 a x 2 b 1 x RTS = 2 = a x 2 x b x 1 1 q 9 Elasticity of Substitution The elasticity of substitution measures the percentage change in factor proportion due to 1 % change in marginal rate of technical substitution ( x 2 / x 1 ) RTS s = [ RTS ] ( x 2 / x 1 ) ln( x 2 / x 1 ) s = ln( RTS ) For CobbDouglas: ( x 2 / x 1 ) = [ RTS ] 1 s = ( b / a ) ( a / b ) ( x 2 / x 1 ) = 1 [ RTS ] 1 ( x 2 / x 1 ) a b ( x 2 / x 1 ) = = b a 10 Other Production Functions...
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 Fall '08
 MosheBenAkiva

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