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 , so he will choose the °rst 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
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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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