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lect05_Demand

# lect05_Demand - Demand Functions Examples of Problems...

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49 Demand Functions Examples of Problems Cobb-Douglas Utility Function U=X 1 a X 2 b or alnX 1 + blnX 2 1. Suppose a consumer has the utility function U(X 1 ,X 2 ) = lnX 1 + 2lnX 2 a. Find the MRS b. Find the demand functions for X 1 and X 2 c. Find the optimal choices and optimal utility if I=900, P 1 =10 and P 2 =30.

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50 2. Suppose a consumer has the utility function (quasi-linear U = aX 1 + bf(X 2 )) U(X 1 ,X 2 ) = X 1 + 5lnX 2 a. Find the MRS b. Find the demand functions for X 1 and X 2 c. Find the optimal choices and optimal utility if I=100, P 1 =4 and P 2 =1.
51 3. Suppose a consumer has the utility function (perfect substitutes U = aX 1 + bX 2 ) U(X 1 ,X 2 ) = 4X 1 + 2X 2 a. Find the MRS b. What should the consumer do if I=60, P 1 =3 and P 2 =4? Why? c. Find the optimal choices and optimal utility when P 1 <2P 2 , for any I.

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