# pset2_2009_answers - 1 3lnX 2 a Find the Marginal Rate of...

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Economics 420K Problem Set 2 Demand Theory Bronars 1. For the utility function U= X 1 X 2 3 a. Find the Marginal Rate of Substitution b. Derive the demand functions for X 1 , and X 2 , assuming the consumer buys some of both goods c. For I=40, P 1 =1 and P 2 =2, find the consumer’s optimal choices and utility d. Explain what happens to optimal choices and utility if the P 1 were to increase to 2. a. MRS= X2/3X1 b. X1=I/4P1 and X2=3I/4P2 c. X1=10, X2 = 15, U=10*15^3 d. X1=5, X2=15, U=5*15^3 2. For the utility function U= 4X 1 .5 + X 2 a. Find the Marginal Rate of Substitution b. Derive the demand functions for X 1 , and X 2 , assuming the consumer buys some of both goods c. For I=260, P 1 =1 and P 2 =4, find the consumer’s optimal choices and utility d. Explain what happens to optimal choices and utility if the P 2 were to decrease to 2. a. MRS=2/X1^.5 b. X1 = 4(P2/P1)^2 and X2 = (I/P2) – 4(P2/P1) c. X1=64 and X2= 49 and U = 81 d. X1=16 and X2=122 and U = 138 3. For the utility function U= 2lnX
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Unformatted text preview: 1 +3lnX 2 a. Find the Marginal Rate of Substitution b. Derive the demand functions for X 1 , and X 2 , assuming the consumer buys some of both goods c. For I=1000, P 1 =20 and P 2 =15, find the consumer’s optimal choices and utility d. Explain what happens to optimal choices and utility if the P 1 were to decrease to 10. a. MRS=3X2/2X1 b. X1=2I/5P1 and X2=3I/5P2 c. X1=20 and X2=40 and U=2ln(20)+3ln(40) d. X1=40 and X2=40 and U=2ln(40)+3ln(40) 4. For the utility function U= 4X 1 + 2lnX 2 a. Find the Marginal Rate of Substitution b. Derive the demand functions for X 1 , and X 2 , assuming the consumer buys some of both goods a. MRS=2X2/X1 b. X1=2I/3P1 and X2=I/3P2 5. For the utility function U= 20X 1 – X 1 2 + 2X 2 a. Find the Marginal Rate of Substitution b. Derive the demand functions for X 1 and X 2 , assuming the consumer buys some of both goods a. MRS = 10-X1 b. X1=10-P1/P2 and X2 = (I/P2) – 10(P1/P2) – (P1/P2)^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.

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