3. Anya has a two-period horizon. She has the utility function u(c1, c2) = 2ln(cı) + In(c2),where c; is her consumption in period j. Her income is Mj in period j. Assume that M1 =7,000 and M2 = 9,600. The interest rate at which she can borrow and lend is 20%.(i) Find the equation for Anya's budget line.(ii) Find her optimal bundle.(iii) Explain whether her utility would rise or fall if the interest rate were to fall slightly.(iv) NowExplain why her optimal bundles here and in (ii) are related as they are!əsoddnsthat the interest rate is again 20% and Anya has M1 = 0 and M2 = 18,000.

Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Answered: 3. Anya has a two-period horizon. She…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Anya has a two-period horizon. She has the utility functionu (c1,c2) = 2ln(c1) + ln(c2), where cj is her consumption in period j. Her income is Mj in period j. Assume that M1= 7,000 and M2=9,600. The interest rate at which she can borrow and lend is 20%. (i) Find the equation for Anya’s budget line. (ii) Find her optimal bundle. (iii) Explain whether her utility would rise or fall if the interest rate were to fall slightly. (iv) Now suppose that the interest rate is again 20% and Anyahas M1= 0 and M2= 18,000.Explain why her optimal bundles here and in (ii) are related as they are. *just answer part iv.
Anya has a two-period horizon. She has the utility functionu (c1,c2) = 2ln(c1) + ln(c2), where cj is her consumption in period j. Her income is Mj in period j. Assume that M1= 7,000 and M2=9,600. The interest rate at which she can borrow and lend is 20%. (i) Find the equation for Anya’s budget line. (ii) Find her optimal bundle. (iii) Explain whether her utility would rise or fall if the interest rate were to fall slightly. (iv) Now suppose that the interest rate is again 20% and Anyahas M1= 0 and M2= 18,000.Explain why her optimal bundles here and in (ii) are related as they are.
Holly's utility function is U(c1, c2) = c/21 + 0.87d/22, where cq is her consumption in period 1 and c2 is her consumption in period 2. In period 2, her income is twice as large as her income in period 1. At what interest rate will she choose to consume the same amount in period 2 as in period 1? (Choose the closest answer.) Group of answer choices 0.30 0.08 0.23 0.15
Patience has a utility function where c₁ is her consumption in period 1 and c2 is her consumption in period 2. Her income in period 1 is 3 times as large as her income in period 2. At what interest rate will she choose to consume the same amount in period 1 as in period 2? 20% 13% 25% 1/2 1/2 U(c1, c2) = ¹/² +0.80c¹/² 0% 80%
Assume Marjeri lives for only two periods and has the utility function U(C1, C2) = In C1 + 0.9 In C2 She can save or borrow any amount at an interest rate of 8%. Her income in each period is $10,000. How much should she consume in each period in order to maximize her utility? How much will she save or borrow?
Suppose you have the option of spending $[x] now or saving it until next year. If you save it, the bank will pay you an interest rate of 9.8%. Your utility function is u(w) = w. What does your discount factor & need to be for you to be indifferent between spending the money now and saving it? Round your answer to 3 decimal places (so an answer might be, for example, 0.476).
John has the following utility function U(C₁, C2) = min{c₁ + ac2, C2}, where C₁ and c₂ are his consumption in periods 1 and 2, respectively and a is some positive constant. Suppose John has $100 income in period 1 and $105 income in period 2. Prices in both periods are $1. Question 2 Part al Suppose a = 2. If John can freely borrow and lend at 5% interest rate what would be his optimal consumption in both periods? 1 Question 2 Part a2 Suppose a = 2. Now, John can lend at 5% interest rate, but can't borrow at all. What would be his optimal consumption in both periods? Question 2 Part bl Suppose a 0.5. If John can freely borrow and lend at 5% interest rate what would be his optimal consumption in both periods? Question 2 Part b2 Suppose a 0.5. Now, John can lend at 5% interest rate, but can't borrow. What would be his optimal consumption in both periods?
Dr Issac Parish will live for two periods only. His utility function is U(c1, c2) = c1c2, where c1 is consumption in period 1 and c2 is consumption in period 2. He will have no income in period 2. His income in period 1 is £40,000. If the interest rate rises from 10 to 14%: Select one: a. his savings will not change but his consumption in period 2 will increase by £800. b. his savings will increase by 4% and his consumption in period 2 will increase. c. his consumption in period 1 will decrease by 14% and his consumption in period 2 will increase. d. his consumption in both periods will decrease. e. his consumption in both periods will increase.
Patience has a utility function 1/2 1/2 U(cl, c2) = c? + 0.80c/? where c is her consumption in period 1 and c is her consumption in period 2. Her income in period 1 is 3 times as large as her income in period 2. At what interest rate will she choose to consume the same amount in period 1 as in period 2? a. 2 b. 0.13 c. 0.25 d. 0 е. О.38 20% 13% 25% 0%
Dr Issac Parish will live for two periods only. His utility function is U(c1, c2) = c1c2, where c1 is consumption in period 1 and c2 is consumption in period 2. He will have no income in period 2. His income in period 1 is £40,000. If the interest rate rises from 10 to 14%: Select one: O a. his savings will not change but his consumption in period 2 will increase by £800. b. his consumption in both periods will decrease. c. his savings will increase by 4% and his consumption in period 2 will increase. O d. his consumption in period 1 will decrease by 14% and his consumption in period 2 will increase. e. his consumption in both periods will increase.
Suppose Jack lives for two periods. Period one is his working life, during which he earns income $50,000; period two is his retirement, during which he earns nothing. During retirement he consumes from the savings during his working life. The rate of interest on his savings is 10%. His consumption during his working life is Cw, and his consumption during his retirement life is Cr. Assume that Jack's utility function is a standard utility function exhibiting diminishing marginal rate of substitution between Cw and Cr. His current consumption during the working life is 75% of his earned income. a. Using the intertemporal choice model, draw a well labeled graph that details all the information discussed above. Notably, indicate the slope of the budget constraint, the intercepts of the budget constraint on both axes, the value of current and future consumptions, and the current savings. Keep in mind that no tax has been imposed on the saver, yet. b. Now the government taxes interest…
Assume a consumer has current-period income y = 200, future-period income y′ = 150, current and future taxes t = 40 and t′ = 50, respectively, and faces a market real interest rate of r = 0.05, or 5% per period. The consumer would like to consume according to the following utility function: U (c, c′ ) = ln(c) + ln(c′ ). Show mathematically the lifetime budget constraint for this consumer. Find the optimal consumption in the current and future periods and optimal saving. Suppose that instead of r = 0.05 the interest rate is r = 0.1. Repeat parts (a) and (b). Does the substitution effect or the income effect dominate?

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