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##### Economics problems

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Question;Q1. Suppose we are given the constant returns-to-scale CES production function q = [k + l]1/ where krepresents capital and l represents labora. 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)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 oflabor 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.

Paper#57531 | Written in 18-Jul-2015

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