An investor with an initial endowment of $ 16,000 is confronted with the following productivity curve: C₁=240 (16,000 - Co)0.5 where Co denotes consumption at present, and C₁ consumption in the future. Assume the interest rate (for borrowing and lending) is 20%. The investor's utility function, from which it is possible to derive his indiffere U(CO, C1)=C0C1 How much does the investor borrow or lend in the capital market? O The investor borrowed $13,000 O The investor lent $13,000 The investor borrowed $7,000
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- H3. An investor with an initial endowment of $ 16,000 is confronted with the following productivity curve: C1= 240 (16,000 − C0)0.5 where C0 denotes consumption at present, and C1 consumption in the future. Assume the interest rate (for borrowing and lending) is 20%. The investor's utility function, from which it is possible to derive his indifference curves, is defined as: U(C0, C1) =C0C1 . What is the NPV of the investment chosen by the investor? Show proper step by step calculationAn investor with an initial endowment of $ 16,000 is confronted with the following productivity curve: C1= 240 (16,000 - C0)^0.5 where C0 denotes consumption at present, and C1 consumption in the future. Assume the interest rate (for borrowing and lending) is 20%. The investor's utility function, from which it is possible to derive his indifference curves, is defined as: U(C0,C1) =C0C1 How much will the investor invest in production? A)$16,000 B)$0 C)$10,000 D)$12,000Assume that someone has inherited 2,000 bottles of wine from a rich uncle. He or she intends to drink these bottles over the next 40 years. Suppose that this person’s utility function for wine is given by u(c(t)) = (c(t))0.5, where c(t) is each instant t consumption of bottles. Assume also this person discounts future consumption at the rate δ = 0.05. Hence this person’s goal is to maximize 0ʃ40 e–0.05tu(c(t))dt = 0ʃ40 e–0.05t(c(t))0.5dt. Let x(t) represent the number of bottle of wine remaining at time t, constrained by x(0) = 2,000, x(40) = 0 and dx(t)/dt = – c(t): the stock of remaining bottles at each instant t is decreased by the consumption of bottles at instant t. The current value Hamiltonian expression yields: H = e–0.05t(c(t))0.5 + λ(– c(t)) + x(t)(dλ/dt). This person’s wine consumption decreases at a continuous rate of ??? percent per year. The number of bottles being consumed in the 30th year is approximately ???
- Consider a household with the following utility function representing their preferences over consumption: U = u(Ct) + Bu(C++1) with =- u(C) = exp(-aC), BE (0,1), a > 0 where C and C++1 represent consumption in the current and future periods, respectively. The household faces a two-period decision problem. They receive endowments of Y, and Yt+1 in the current and future periods, respectively. The real interest rate is denoted by rt. Notice: The utility function u(C) takes on negative values for all positive consumption levels. However, in economic models, the absolute value of utility is less important than how utility changes with consumption. A higher level of utility represents a more preferred outcome for the household. Question: Formulate the household's budget constraints for the current and future periods. Com- bine them to derive the household's intertemporal budget constraint. Write down the household's optimization problem (objective function) that they seek to maximize.…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?
- Consider the two period consumption savings problem faced by an individual whose utility is defined on period consumption. This utility function u(c) has the properties that it is strictly increasing and concave, u'(c) > 0, u"(c) < 0 (where u'(c) denotes the first derivative while u"(c) represents the second derivative) and satisfies the Inada condition lim.-→0 u'(c) approaches zero). The individual's lifetime utility is give by u(cı) + Bu(c2). In the first period of life, the individual has y1 units of income that can be either consumed or saved. In order to save, the individual must purchase bonds at a price of q units of the consumption good per bond. Each of these bonds returns a single unit of the consumption good in period 2. Total savings through bond purchases is s1 so that total expenditures on purchasing bonds is qs1. Let c1 denote the amount of consumption in period 1 chosen by the individual. In the second period of life, consumption in the amount c2 is financed out of the…Anna's investment is worth $2.5 million (decreased from $3.5 to $2.5 million) Elsa's investment is worth $2.2 million (increased from $2 to $2.2 million) For each of them write down the reference utility function (First determine the reference point (use a parameter) and derive reference utility function for each).Clare is contemplating her possible consumption patter for this year and next. She know that she will have income of $50,000 this year and $55,000 next yea. Her plan is to consume $40,000 this year (t=0). She is also going to invest 30,000. This investment has a positive NPV of $450. She decides to take the investment; in addition, the return on the investment is 9.62%. What consumption she can expect at t=1? (show a detailed procedure)
- Analysing Utility Function and Household Optimization Consider a household with the following utility function representing their preferences over consumption: with U = u(C) + Bu(C++1) u(C) = exp(-aC), BE (0,1), a>0 where Ct and Ct+1 represent consumption in the current and future periods, respectively. The household faces a two-period decision problem. They receive endowments of Yt and Yt+1 in the current and future periods, respectively. The real interest rate is denoted by rt. Notice: The utility function u(C) takes on negative values for all positive consumption levels. However, in economic models, the absolute value of utility is less important than how utility changes with consumption. A higher level of utility represents a more preferred outcome for the household. Solving for Current Consumption Demand Function Solve for the household's demand function for current consumption (Ct). Express Ct as a function of Yt, Yt+1, rt, and the parameters ẞ and a. Discuss what happens to Ct…An individual’s utility function is given as U (X) = X 0.5 where X represents the money, he has available for spending in a given time period. This individual has income of $225 in each time period and he discounts the future at the rate of 0.7. If he invests his up-front cost is 25 and his return in in the next time period is 35. a. Would this individual consider investing if his investment is financed by borrowing and cost of borrowing is 30%? (Consider two period model to justify your answer) b. Would this individual consider investing if his investment is financed by current savings? (Use two period model to justify your answer). c. Would this individual consider investing if his investment is financed by: $10 from current savings and rest of it from borrowing and the cost of borrowing is 30%? (Use two period model to justify your answer).6. If intertemporal preferences are consistent and the lifetime utility function is additive, then the discount function 8(t) must be (a) bounded (b) exponential (c) hyperbolic (d) linear (e) logarithmic