高级微观经济学Summary.ppt

1、Advanced Microeconomics(lecture 1: production theory I),Ye Jianliang(叶建亮),lecture 1,for Chu Kechen Honors College,Summary,textbook: Varian, Hal R., 1992, Microeconomics Analysis, 3rd ed. Mas-Colell, A., M. Whinston, and J. Green, 1995, Microeconomics Theory. assignments: twice a week; Team work; Del

2、iver on the class. examinations: Mid-term: by the assignments; Final-term: 80% of the questions coming from the assignments.,lecture 1,for Chu Kechen Honors College,The Basic Framework of Microeconomics,Technology,Preference,Choice (production),Choice (purchase),Supply,Demand,Market Equilibrium,lect

3、ure 1,for Chu Kechen Honors College,Technology,Contain: “production (possibilities) set” (PS) and “production function”; Properties of the “PS”; Technical rate of substitution; Returns to scale.,lecture 1,for Chu Kechen Honors College,1. Production set,Production plan (production vector, or input-ou

4、tput vector): Production set Y: all technological feasible y. Restricted production set Y (z): Some of yi in y are restricted on z . Short-run production set.,lecture 1,for Chu Kechen Honors College,1. Production set,Input requirement set: All yi in y are negative, let them be x (then x is positive)

5、, and the rest yj to be q . So, and , and the input requirement set is :,lecture 1,for Chu Kechen Honors College,1. Production set,Transformation function: and satisfied if and only if y is technologically efficient, then,y2,y1,lecture 1,for Chu Kechen Honors College,1.Production set,Production func

6、tion: If O = 1,and I = n - 1, then: means: Isoquant: Question1: calculate the PS, RS, TF, PF, Isoquant of Cobb-Douglas technology and Leontief technology.,lecture 1,for Chu Kechen Honors College,2.Properties of PS.,Y is nonempty: we have something to do. Y is close: Y contain its boundary, No free l

7、unch: See the fig. Free disposal: See the fig.,lecture 1,for Chu Kechen Honors College,2.Properties of PS.,Additive (free entrance) : Convexity: See the fig. Proposition1: if Y is convex, so is V(q). Proposition2: if V(q) is convex, f(x) is quasi-concave.,lecture 1,for Chu Kechen Honors College,3.Te

8、chnical rate of substitution,Marginal rate of transformation (MRT) of good j for good i at y and T(y)=0. T(y)=0, we got: See the fig.,lecture 1,for Chu Kechen Honors College,3.Technical rate of substitution,one production: the marginal rate technical of substitution at x* . As x changes , we got tec

9、hnical rate of substitution,lecture 1,for Chu Kechen Honors College,3.Technical rate of substitution,The elasticity of substitution: the curvature of the isoquant. Question2: calculate the “TRS” and the “elasticity of substitution” of Cobb-Douglas technology and CES technology.,lecture 1,for Chu Kec

10、hen Honors College,4.Returns to scale,Nonincreasing returns to scale: Nondecreasing returns to scale: Constant return to scale:,lecture 1,for Chu Kechen Honors College,4.Returns to scale,Proposition 3: Y is constant returns to scale if Y is both “additive” and “convexity”. Proposition 4: single prod

11、uction, if and only if f(.) is homogenous of degree 1, Y is constant returns to scale.,lecture 1,for Chu Kechen Honors College,4.Returns to scale,Why we assume that Y is non-increasing (or decreasing for usual) returns to scale? Suppose Y is decreasing returns to scale, and its PF f(x), now we intro

12、duce new input z, and difine a new PF: F(.) is homogenous of degree 1.,lecture 1,for Chu Kechen Honors College,4.Returns to scale,Homogeneous and homothetic tech. Homogeneous of degree k: Homothetic function: Elasticity of scale:,lecture 1,for Chu Kechen Honors College,Assignment,Textbook: ex.1.1, ex.1.3, ex.1.7. ex.1.9,lecture 1,for Chu Kechen Honors College,Properties of PS.,y2,y1,Free lunch,lecture 1,for Chu Kechen Honors Colle