The Homothetic (Cobb-Douglas) utility function is given by U (Q1, Q2)= Q 1 a Q 2

Question

The Homothetic (Cobb-Douglas) utility function is given by

U (Q1, Q2)= Q1a Q2b , where assume a +b =1.

a) What is the marginal rate of substitution?

Then, Use the lagrangian method to find value of Q1and Q2 . The income is I. The price for good Q1 and good Q2 are P1 and P2 (Show all the works and steps)

b) What is the objective function and first order conditions for Utility maximization

c) What are these three first-order equations for Q1 and Q2.

d) What is the uncompensated demand for each good when face price P1=2 and P2=3 with income M=200. Assume a=b=0.5

Explanation / Answer

The Homothetic (Cobb-Douglas) utility function is given by U (Q1, Q2)= Q 1 a Q 2

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