TechnologyProduction function：from input to outputY=f (X1,...., Xn) single output=f (input bundle) single input: Double input:Anisoquant is the set of all possible combinations of inputs 1 and 2 that are just sufficient to producea given amount of output. (similar indifference curves)The complete collection of isoquants is called isoquant map.Here’s a fancy picture:Examples oftechnologies and theirisoquants:1. Fixed proportionEg. f (X1, X2)= min{X1, X2} Just like thecase of perfectcomplements2. Perfect substitutesEg. f (X1, X2)= X1 +X2) Just like the case of perfect substitutes3. Cobb-Douglas Eg. f (X1, X2)= AXa1Xb2 Just like ............. Note that parameters do matter here.Marginal product of factor:When the marginal product of input igets smaller as the level of input iincreases, we say the MP is diminishing. Simply take thesecond derivative How to interpret MP1/MP2 ?Technical rate of substitution similar the themarginal rate ofsubstitutionThree types of returns-to-scale:Constant returns-to-scale f (kX1, kX2,....kXn) = kf (X1, X2, ....Xn)Diminishing returns-to-scale f (kX1, kX2,....kXn) ： kf (X1, X2, ....Xn)Increasing returns-to-scale f (kX1, kX2,....kXn) ： kf (X1, X2, ....Xn)It is perfect possible for a technology to exhibit constant/increasing returns to scale anddiminishing marginal product to each factor. Returns to scale describes what happens when youincrease all inputs, while diminishing marginal product describes what happens when you increaseon of the inputs and hold the others fixed.The long run and the short runIn the short run, there will be some factors of production that are fixed at predetermined levels.In the long run, all the factors can be varied.Additions:Technology constraints: only certain combination of inputs are feasible ways to produce a givenamount of outputA production plan is feasible if Y≤f (X1,...., Xn), and the technology set is the set of all feasibleplans.The combination of inputs and outputs that comprise a feasible way to produce is calledproduction set.A well-behaved technology is monotonic and
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