Advanced icroeconomic (lecture Is production theory I Ye Jianliang (叶建亮)
Advanced Microeconomics (lecture 1: production theory I) Ye Jianliang(叶建亮)
Summary o textbook, Varian, HaIR 1992, Microeconomics Analysis, 3rd ed Mas-Colell M. Whinston, and ], green 1995, microeconomics Theory assignments: twice a weeK, Team work; Deliver 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
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; – Deliver on the class. • examinations: – Mid-term: by the assignments; – Final-term: 80% of the questions coming from the assignments
The Basic Framework of Microeconomics pply Demand Market ITechnology Preference Equilibrium Choice Choice (production) (purchase) lecture 1 for Chu Kechen Honors College
lecture 1 for Chu Kechen Honors College The Basic Framework of Microeconomics Technology Preference Choice (production) Choice (purchase) Supply Demand Market Equilibrium
Technology o 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
lecture 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
1. Production set Production plan(production vector, or input-output vector): y=(,y2," ...,yn) Production set Y: all technological feasible 艺Y={y∈界?" y are technologically feasible} o 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
lecture 1 for Chu Kechen Honors College 1. Production set • Production plan (production vector, or input-output 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. 1 2 ( , , , ) n y = y y y { : are technologically feasible} n Y y y =
1. Production set Input requirement set All y in y are negative, let them be -x(then x is positive), and the rest yi to be q S0,x∈界andq∈9,andy=(q,x)∈9 the input requirement set is T(q)={X∈界:(q,-x)eY} lecture 1 for Chu Kechen Honors College
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), and the rest yj to be q . – So, and , and – the input requirement set is : I + x O q+ ( ) n = + y q, -x ( ) { : ( , ) } I V q x q x Y = − +
1. Production set Transformation function T:界R"→>9R and satisfied Y={y∈9":(y)≤0} if and only if y is technologically efficient, then T(y)=0 VI Y={y∈界":7(y)≤0} lecture 1 for Chu Kechen Honors College
lecture 1 for Chu Kechen Honors College 1. Production set • Transformation function: and satisfied • if and only if y is technologically efficient, then : n T → { : ( ) 0} n Y y y = T T( ) 0 y = y2 y1 { : ( ) 0} n Y y y = T { : ( ) 0} y y T =
1. Production set → Production function IfO=I,andi=n-1 then q=f(x) when T(q-x)=0 means:f(x)={q≥q:(q2-x)∈Y} o Isoquant Q(q)={(x)=q:(q2-x)∈Y Question calculate the PS, rs, tE PF isoquant of Cobb-Douglas technology and Leontief technology lecture 1 for Chu Kechen Honors College
lecture 1 for Chu Kechen Honors College 1.Production set • Production function: – 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. q f T q = − = ( ) when ( , ) 0 x x f q q q ( ) ={ : ( , ) } x x Y − Q q f q q ( ) { ( ) : ( , ) } = = − x x Y
2. Properties Of PS Y is nonempty. we have something to do Y is close: Y contain it's boundary, the array y"→>y,andy"∈ Y means y∈Y No free lunch:Y∩?c{0} the o Free disposal: y-RlCY See thet lecture 1 for Chu Kechen Honors College
lecture 1 for Chu Kechen Honors College 2.Properties of PS. • Y is nonempty: we have something to do. • Y is close: Y contain it’s boundary, • No free lunch: See the fig. • Free disposal: See the fig. the array , and means y y y Y y Y n n → {0} n Y + n − + y Y
2. Properties Of PS Additive(free entrance) y∈Y, andy'EY, then y+y∈Y o Convexity y∈ Y, and y'∈Y, then ay+(1-ay∈Y, here a∈[0,1 Proposition: if Y is convex, so is V(q) o Proposition2 if V(q) is convex, f(x)is quasi concave lecture 1 for Chu Kechen Honors College
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 quasiconcave. y Y y Y y y Y + ,and , then y Y y Y y y Y + − ,and , then (1 ) , here [0,1]
