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