北京大学：《微观经济学》Chapter Eighteen Technology 技术

Chapter eighteen Technology 技术

Chapter Eighteen Technology 技术

Structure Describing technologies O Production set or technology set ● Production function ● Isoquant ◆ Marginal product ◆ Returns to scale e Technical rate of substitution e Well-behaved technologies Long run and short run

Structure ◆ Describing technologies ⚫Production set or technology set ⚫Production function ⚫Isoquant ◆ Marginal product ◆ Returns to scale ◆ Technical rate of substitution ◆ Well-behaved technologies ◆ Long run and short run

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 o 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 xi denotes the amount used of input i; i,e, the level of input i P An input bundle is a vector of the input levels; 1 25

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 )

Production functions(生产函数) cy 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 (生产函数） ◆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 y function y'=f(x)is the maximal output level obtainable from xinput units X 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;( X,,..., Xng y) ◆ A production plan is feasib|e(可行)if y≤f(X n The collection of all feasible production plans is the production set(生产集)or technology set(技术集)

Technology Sets ◆ A production plan is an input bundle and an output level; (x1 , … , xn , y). ◆ A production plan is feasible （可行）if ◆ The collection of all feasible production plans is the production set (生产集) or technology set （技术集）. y  f(x , ,xn) 1 

Technology sets One input, one output Output Level y f(x) is the production y function y'=f(x,)is the maximal output level obtainable from x' input units y y =f(x)is an output level that is feasible from x' input units X X 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 production set or technology set is T={(x1,…,Xn,y)|y≤f(x1,…,Xn)and X1≥0,,Xn≥0

Technology Sets The production set or technology set is T x x y y f x x and x x n n n =    {( , , , ) | ( , , ) , , }. 1 1 1 0 0   