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Suppose we are given the constant returns-to-scale CES production function q = [k + l]1/ where k represents capital and l represents labor
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.
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/lnk Similarly for elasticity of output wrt l, eq,l
d. Prove that q/l = (q/l) and hence that ln(q/l) = ln(q/l)
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