Economics problems

Economics problems

Question
	
Q1. 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.

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/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)


Q2. Suppose the production of airframes is characterized by a CobbDouglas production function: Q =

LK. The marginal products for this production function are MPL = K and MPK = L. Suppose the price of

labor is $10 per unit and the price of capital is $1 per unit. Find the cost-minimizing combination of labor and capital if the manufacturer wants to produce 121,000 airframes.















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