Advanced Microeconomic (lecture l production theory I Ye Jianliang(叶建亮)
Advanced Microeconomics (lecture 1: production theory I) Ye Jianliang(叶建亮)
Summary o textbook Varian, Hal R, 1992, Microeconomics Analysis, 3rd ed Mas-Colella m Whinston and j, green 1995, microeconomics Theory assignments. twice a week Team work Deliver on the class o 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 Supply Demand Market echnology 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=(y,y2, .,n) o Production set Y: all technological feasible yY={y∈界": y are technologically feasible o Restricted production set Y(=) 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 v in y are negative, let them bex (then X is positive), and the rest yi to be q So,x∈+andq∈,andy=(q,-x)∈ the input requirement set is v(q)={x∈界:(q,-x)∈Y} 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 o Transformation function T:9-)9 and satisfied {y:7(y)=0 Y={y∈界":7(y)≤0} if and only if y is technologically efficient then T(y)=0 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 se O Production function: fO=land[=n-1, then g=f(x) when T(9, -x)=0 means:f(x)={q≥q:(q,-x)∈Y} Isoquant Q(q)={(x)=q:(q,-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"sy,andy"∈ Y means y∈Y o No free lunch:Y∩c{0 SOee the fo. o Free disposal: y-RTCY Oee thene 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, and yEY, then y+y∈Y Convexity yeY, and y'EY, then ay+(1-a)y∈Y, here a∈[0,1 o Proposition: if Y is convex, so is v(q) o Proposition 2 if V(g) 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]