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)1 and MPl = (q/l)1 . b. Show that RTS = (k/l)1 ; use thi

)1 and MPl = (q/l)1 . b. Show that RTS = (k/l)1 ; use thi

Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.9P
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Q1. Suppose we are given the constant returns-to-scale CES production function q = [k + l]1/ where k represents capital and l represents labora.

a. Show that MPk = (q/k)1 and MPl = (q/l)1 .

b. Show that RTS = (k/l)1 ; use this to show that elasticity of substitution between labor and capital= 1/(1 – ).

c. Determine the output elasticities for k and l; and show that their sum equals

1.Note: Output elasticity measures the response of change in q to a change in any input.

Elasticity of output wrt k is eq,k = %q/%k = (q/k)*(k/q) or (q/k)*(k/q) or lnq/lnkSimilarly for elasticity of output wrt l, eq,ld.

Prove that q/l = (q/l) and hence that ln(q/l) = ln(q/l)

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