Chapter Eighteen Technology
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 ◆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?
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 +x 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)=(6,0,9X3)
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, 9×3)
Production Functions +y denotes the output level. The technology's production function states the maximum amount of output possible from an input bundle. y=f(X1,,Xn)
Production Functions ◆y denotes the output level. ◆The technology’s production function states the maximum amount of output possible from an input bundle. y = f(x , ,xn) 1
Production Functions One input,one output Output Level y f(x)is the production function. y'=f(x')is the maximal 、 output level obtainable from x'input units. X Input Level
Production Functions y = f(x) is the production function. 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 if y≤f(x1,…,xn) The collection of all feasible production plans is the technology set
Technology Sets ◆A production plan is an input bundle and an output level; (x1 , … , xn , y). ◆A production plan is feasible if ◆The collection of all feasible production plans is the technology set. y f(x , ,xn) 1
Technology Sets One input,one output Output Level y f(x)is the production function. y'=f(x')is the maximal output level obtainable from x'input units. y"f(x')is an output level that is feasible from x' input units. Input Level
Technology Sets y = f(x) is the production function. 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 T={(X1,,xn,y)y<f(X1,,xn)and X1≥0，，Xn≥0}
Technology Sets The technology set is T x x y y f x x and x x n n n = {( , , , ) | ( , , ) , , }. 1 1 1 0 0
Technology Sets One input,one output Output Level The technology set 十 Input Level
Technology Sets x’ x Input Level Output Level y’ One input, one output y” The technology set