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