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.
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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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52 Compensated Demand Functions Maximizing utility for a given amount of income I is the same problem as minimizing the cost of achieving a target level of utility U 0 . Consider a consumer that wants to achieve a target level of utility U 0 at the lowest cost. Suppose the consumer’s utility function is given by: U(X 1 ,X 2 ) = X 1 X 2 The graphical solution to this problem is the same as for the utility maximization problem: U 0 X 1 X 2 Budget Line representing lowest cost way of getting to U 0 This Budget Line gets you to U 0 , but at a higher cost E
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53 The 2 equations describing point E are now given by: P 1 /P 2 = MRS And U(X 1 ,X 2 ) = U 0 The solution to the 2 equations and 2 unknowns give us the “Compensated” Demand Functions for X 1 and X 2 .
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This note was uploaded on 09/15/2009 for the course ECON 420 K taught by Professor Bronars during the Fall '09 term at University of Texas at Austin.

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lect05_Demand - Demand Functions Examples of Problems...

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