Ch18 Technology.ppt

Chapter Eighteen,Technology,Technologies,A technology is a process by which inputs are converted to an output.E.g.labor,a computer,a projector,electricity,and software are being combined to produce this lecture.,Technologies,Usually several technologies will produce the same product-a blackboard and chalk can be used instead of a computer and a projector.Which technology is“best”?How do we compare technologies?,Input Bundles,xi denotes the amount used of input i;i.e.the level of input i.An input bundle is a vector of the input levels;(x1,x2,xn).E.g.(x1,x2,x3)=(6,0,93).,Production Functions,y denotes the output level.The technologys production function states the maximum amount of output possible from an input bundle.,Production Functions,y=f(x)is theproductionfunction.,x,x,Input Level,Output Level,y,y=f(x)is the maximal output level obtainable from x input units.,One input,one output,Technology Sets,A production plan is an input bundle and an output level;(x1,xn,y).A production plan is feasible ifThe collection of all feasible production plans is the technology set.,Technology Sets,y=f(x)is theproductionfunction.,x,x,Input Level,Output Level,y,y”,y=f(x)is the maximal output level obtainable from x input units.,One input,one output,y”=f(x)is an output level that is feasible from x input units.,Technology Sets,The technology set is,Technology Sets,x,x,Input Level,Output Level,y,One input,one output,y”,The technologyset,Technology Sets,x,x,Input Level,Output Level,y,One input,one output,y”,The technologyset,Technicallyinefficientplans,Technicallyefficient plans,Technologies with Multiple Inputs,What does a technology look like when there is more than one input?The two input case:Input levels are x1 and x2.Output level is y.Suppose the production function is,Technologies with Multiple Inputs,E.g.the maximal output level possible from the input bundle(x1,x2)=(1,8)isAnd the maximal output level possible from(x1,x2)=(8,8)is,Technologies with Multiple Inputs,Output,y,x1,x2,(8,1),(8,8),Technologies with Multiple Inputs,The y output unit isoquant is the set of all input bundles that yield at most the same output level y.,Isoquants with Two Variable Inputs,y 8,y 4,x1,x2,Isoquants with Two Variable Inputs,Isoquants can be graphed by adding an output level axis and displaying each isoquant at the height of the isoquants output level.,Isoquants with Two Variable Inputs,Output,y,x1,x2,y 8,y 4,Isoquants with Two Variable Inputs,More isoquants tell us more about the technology.,Isoquants with Two Variable Inputs,y 8,y 4,x1,x2,y 6,y 2,Isoquants with Two Variable Inputs,Output,y,x1,x2,y 8,y 4,y 6,y 2,Technologies with Multiple Inputs,The complete collection of isoquants is the isoquant map.The isoquant map is equivalent to the production function-each is the other.E.g.,Technologies with Multiple Inputs,x1,x2,y,Technologies with Multiple Inputs,x1,x2,y,Technologies with Multiple Inputs,x1,x2,y,Technologies with Multiple Inputs,x1,x2,y,Technologies with Multiple Inputs,x1,x2,y,Technologies with Multiple Inputs,x1,x2,y,Technologies with Multiple Inputs,x1,y,Technologies with Multiple Inputs,x1,y,Technologies with Multiple Inputs,x1,y,Technologies with Multiple Inputs,x1,y,Technologies with Multiple Inputs,x1,y,Technologies with Multiple Inputs,x1,y,Technologies with Multiple Inputs,x1,y,Technologies with Multiple Inputs,x1,y,Technologies with Multiple Inputs,x1,y,Technologies with Multiple Inputs,x1,y,Cobb-Douglas Technologies,A Cobb-Douglas production function is of the formE.g.with,x2,x1,All isoquants are hyperbolic,asymptoting to,but nevertouching any axis.,Cobb-Douglas Technologies,x2,x1,All isoquants are hyperbolic,asymptoting to,but nevertouching any axis.,Cobb-Douglas Technologies,x2,x1,All isoquants are hyperbolic,asymptoting to,but nevertouching any axis.,Cobb-Douglas Technologies,x2,x1,All isoquants are hyperbolic,asymptoting to,but nevertouching any axis.,Cobb-Douglas Technologies,Fixed-Proportions Technologies,A fixed-proportions production function is of the formE.g.with,Fixed-Proportions Technologies,x2,x1,