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Lecture notes 4: Theory of production Hannu Vartiainen HECER Fall 2015 Hannu Vartiainen HECER Production Producer theory Start with a single rm facing given prices Need to describe the technology of the rm Exogenous: prices Endogenous: output and input demands Aim to understand the optimal production decision of the rm No attention to organizational nor stratgic aspects Objective to have a model that can be transferred in it its pure form to the general equilibrium framework Key di¤erence to the consumer model no income e¤ects everything observable Hannu Vartiainen HECER Production Primitives: Firm with one production good in R+ K Input space R The primitive of the model: production function K f : R+ ! R+ describes the output/input combinations that are technologically feasibe Hannu Vartiainen HECER Production Axiom Production function f is continuous, increasing, and quasiconcave By monotonicity, if y y0, then f (y) f (y0) By quasiconcavity, the input requirement set K V(x) = fy 2 R+ : f(y) xg is convex for all x 2 R+ Firms production function can be represented by the production possibility set K+1 Y =f(y,x) 2 R+ : f (y) xg Continuous, increasing, and quasiconcave production function corresponds to a production possibility set Y that is convex: if (y,x),(y0,x0) 2 Y, then λ(y,x)+(1+λ)(y0,x0) 2 Y for all λ monotonic: y 2 V(x) and y0 y imply y 2 V(x) closed Hannu Vartiainen HECER Production
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