Problem Set 5 - Solution

Problem Set 5 - Solution - revealed to be preferred to the...

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Econ 313-1 TA: Tian Liang Solutions to Problem Set 5 1. (a) max c 1 ;c 2 c 3 1 c 2 s.t. c 1 > 0 ; c 2 > 0 1 : 1 c 1 + c 2 = 1 : 1 5000 + 5000 3 c 2 c 1 = 1 : 1 1 : 1 c 1 + c 2 = 10500 = ) c 1 = 7159 : 1 c 2 = 2625 (b) To determine which grant he will choose, we only need to compare the value of ((1 + r ) m 1 + m 2 ) . The grant with a greater value of ((1 + r ) m 1 + m 2 ) has a greater endowment and a higher budget line. 1 : 1 5000 + 5000 = 10500 , 1 : 1 3900 + 6200 = 10490 grant. (c) If r = 0 , then we need to compare the value of ( m 1 + m 2 ) . 5000 + 5000 = 10000 , 3900 + 6200 = 10100 , so he will choose the second grant. 2. (a) Both the income and substitution e/ects on c 1 are negative. 1
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(b) The income e/ect on c 1 is positive, and the substitution e/ect is negative. (c) The e/ect is not possible. If the consumer remains a lender after the decrease in interest rate, his utility must have decreased. The new optimal bundle was in the original budget set but was not chosen, so the original optimal bundle was
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Unformatted text preview: revealed to be preferred to the new one. Therefore the consumer must be worse o/. The income e/ect on c 1 is negative, and the substitution e/ect is positive. 2 (d) If the consumer is better o/ as shown above, then both the income and substitu-tion e/ects are positive. If the consumer is worse o/ as shown above, then the income e/ect is negative and the substitution e/ect is positive. 3 3. If the 5 yearly payments start right now, then the present value of the 5 payments is 5000 + 5000 1 + 0 : 05 + 5000 (1 + 0 : 05) 2 + 5000 (1 + 0 : 05) 3 + 5000 (1 + 0 : 05) 4 = 22730 : So the consumer prefers paying in 5 yearly payments if X > 22730 . 4...
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This note was uploaded on 06/27/2008 for the course ECON 3130 taught by Professor Masson during the Spring '06 term at Cornell.

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Problem Set 5 - Solution - revealed to be preferred to the...

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