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- A consumer's income in the current period is y = 100 and income in the future period is y'= 120. He or she pays lump-sum taxes t=20 in the current period and t'= 10 in the future period. The real interest rate is 0.1, or 10%, per period. (a) Determine the consumer's lifetime wealth. (b) Suppose that current and future consumptions are perfect complements for the con sumer and that he or she always wants to have equal consumption in the current and future periods. Draw the consumer's indiffer ence curves. (c) Determine what the consumer's optimal current-period and future-period consump tions are, and what optimal saving is, and show this in a diagram with the consumer's budget constraint and indifference curves. Is the consumer a lender or a borrower?Bora's income in the current period is y=200, and income in the future period is y'=250. He pays lump-sum taxes t=30 in the current period and t'=10 in the future period. The real interest rate is 5%, per period.Suppose that Bora will always choose current consumption, c and the future consumption, c′ in a constant proportion:c=32c′ a) Determine the optimal current-period and future-period consumption for Bora. b) Determine the optimal saving for Bora, and show this in a diagram with his budget constraint and indifference curves, and also determine if Bora is a lender or a borrower?Assume a set of well-behaved (i.e. strictly monotone and strictly convex) intertemporal indifference curvesbetween period 1 and 2. Then suppose that the nominal interest rate r decreases. Explain what happens to thenew interior solution if current and future consumption are normal and inferior goods, respectively.
- 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?A university student was bequeathed $2,000 upon graduation at age 20 years. This person was hired by one of the largest global tech companies soon after graduation with an expected annual income of $250. Assume that the retirement age is 65 years and life expectancy is 85 years in the country in which the student resides. Given that this country has zero real interest rate and consumption smoothing is optimal for all individuals: Derive an expression for the person’s lifetime resources clearly describing each term. Calculate the value of the person’s lifetime resources. Derive an expression for the person’s consumption function clearly describing any new terms included. Derive an expression for the person’s average propensity to consuming. State the theory on which you based the calculations in parts i., ii. and iii. above.Suppose that a consumer/investor has an initial endowment only for the current period, which is Eo =450. She may consume today or in the next period only (two-period model). The interest rate for borrowing and lending in the capital market is 5% (a)Depict the budget constraint for the investor in an inter-temporal consumption diagram! What is the maximum amount the consumer is able to consume in the next period? (b)The consumption preferences of the consumer/investor are best described by a square root function, defined over current and future consumption. What is his optimal consumption plan? Show your calculations! Depict the results in appropriate diagram. Which amount is invested in the capital market?
- Consider an individual who lives for two periods and has utility of lifetime consumption U = log(C1) + 1/1+δ log(C2), where C1 and C2 are the consumption levels in the first and second period respectively, and δ, 0 1 > 0 in the first period and no income in the second period, so Y2 = 0. He can transfer some income to the second period at a before-tax rate of return of r, so saving $S in the first period gives $[1 + r]S in the second period. The government levies a capital tax at rate τ on capital income received in the second period. The tax proceeds are paid as a lump-sum transfer to the following generation. The present generation does not care about the next one. a. What is the lifetime consumption profile of this individual? What is his lifetime indirect utility function expressed as a function of Y1 and b. Evaluate the change in initial income Y1 that is required to compensate the individual for the welfare loss due to the capital income tax τ. c. What is…A consumer's current income (y) is 200 and the future income ( t.') is 240. A current lump sum tax (t) of 10 is paid and the tax in the next period (t') is 15. The real interest rate is 20% for each period. Please assume that current and future consumption are complements. and the consumer always prefers to have one unit of current consumption and two units of consumption in the future.Calculate the consumer's lifetime wealth.Calculate the optimal current and future consumption and the optimal current and future savings. Is the consumer a lender or a borrower? How does he she. as a lender or a borrower. affect the future consumption?Consider the following 2-period model U(C1,C2) = min{3C1,4C2} C1 + S = Y1 – T1 C2 = Y2 – T2 + (1+r)S Where C1 : first period consumption C2 : second period consumption S : first period saving Y1 = 20 : first period income T1 = 5 : first period lump-sum tax Y2 = 50 : second period income T2 = 10 : second period lump-sum tax r = 0.05 : real interest rate Find the optimal saving, S*
- A consumer's income in the current period is y = 100 and income in the future period is y'= 120. He or she pays lump-sum taxes t=20 in the current period and t'= 10 in the future period. The real interest rate is 0.1, or 10%, per period. (a) Determine what the consumer's optimal current-period and future-period consump tions are, and what optimal saving is, and show this in a diagram with the consumer's budget constraint and indifference curves. Is the consumer a lender or a borrower? (b) Now suppose that instead of y = 100 the consumer has y = 140 Again, determine optimal consumption in the current and future periods and optimal saving, and show this in a dia gram. Is the consumer a lender or a borrower? (c) Explain the differences in your results be tween parts (a) and (b).APPLIED ECONOMICS Topic: Intertemporal Choice Levinn’s utility function is expressed as the following: U= C1 C2 0.3 where C1 is his first periodconsumption and C2 is his second period consumption. His income in the first period is$2500 and interest rate is at 10%. If at equilibrium, Levinn is neither a borrower nor a lender,then what is his expected income in the second period? Do not copy from othersA consumer's current income (y) is 200 and the future income ( t.') is 240. A current lump sum tax (t) of 10 is paid and the tax in the next period (t) is 15. The real interest rate is 20% for each period. Please assume that current and future consumption are complements. and the consumer always prefers to have one unit of current consumption and two units of consumption in the future. Calculate the optimal current and future consumption and the optimal current and future savings. Is the consumer a lender or a borrower? How does he she. as a lender or a borrower. affect the future consumption?