1. Consider the two-period endowment economy discussed in class.The economy is populated by m consumers. The lifetime utilityfunction of each consumer is time separable and is given byU (c, c') = u(c) + Bu(c) 0 (c) Suppose the government runs a redistributive tax scheme. Thatis, the government redistributes income across the two groupsby setting t₁ = = ¹ and to = −ÿ in the current period andt' = and t₁ = y in the future period. Find the equilibriumlevel of the real interest rate under this tax scheme. Is there anylending in equilibrium? Explain your results intuitively.(d) Use a graphical analysis to analyse the effects of the introductionof the new tax scheme on the consumer choice of group b.(e) Does the new tax scheme imply a Pareto improvement comparedto the initial situation with no taxes? Explain, also intuitively,why or why not.

The real interest rate effect refers to the impact of changes in interest rates on economic…

Answered: Consider the two-period endowment…

Economics:

10th Edition

ISBN:9781285859460

Author:BOYES, William

Publisher:BOYES, William

Chapter21: Demand: Consumer Choic

Section: Chapter Questions

Problem 15E

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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
Q1. Consider a consumer with a lifetime utility function U(c, c') = u(c) + Bu(c) that satisfies all the standard assumptions listed in the book. The period 1 and 2 budget constraints are c+s=y c+sy+(1+r)s (a) What is the optimal value of s'? Impose this optimal value and derive the life-time budget constraint.
While individuals face trade-offs in consumption, as shown by the budget constraint. there is no such trade-off for society in terms of production or consumpotion True False
1. Suppose that the representative consumer has a utility function defined over consumption over two dates of the form U(C₁, C₂) = c₁²c₂². The general form of the slope of the indifference curve for the representative consumer is - C₂/C₁. Moreover, remember that c₁ = y₁ − S and C₂ = y₂ + s(1 + r). a. Assume that the representative consumer has an endowment of consumption goods in the two periods of y₁ = 20 and y₂ = 10. Assuming an interest rate r = 1, compute the equilibrium allocation and the implied savings. b. Suppose that, because of an attack of pessimism, the representative consumer assumes that future income will drop so that y₂ = 0. What happens to the savings s in the first period? c. In the previous part, the interest rate remained at 1. Now, consider the savings function, that is, the relationship between the real rate of interest and the amount saved. The equilibrium interest rate is then determined as a market price in the Saving-Investment diagram. Given the typical shape…
What is a lifetime utility function, and in what sense does it exhibit diminish-ing returns?
Suppose an individual makes consumption and savings decisions in two time periods (1 and 2). Its utility function is given by: U = In addition, the prices and income of said individual and the interest rate he faces are known: P1 = 1, P2=3; M1 = 100, M2 = 200 r=0.23 Determine: a) The budget constraint and plot b) Optimal demand functions c) The savings supply function d) In equilibrium, will the individual be a lender or a borrower?
Task 4: leisure or work? The consumer choice is not restricted to the choice of consumption goods. In fact, it can apply to all our decisions that involve trade-offs. Suppose Mary has a wage per hour of 10 euros. With her earned income she consumes. That is, C = wH per day. She also decides how many hours to work of take leisure time each day. H = 24 – N, where H is work and N is leisure. Her utility is given by C1-o U(C, N) + B log(N) 1- o (a) Solve for the optimal decision of labor/leisure. Plot the budget constraint and the indif- ferent curve. What is the labor supply function? (b) If o > 1, what is the shape of the labor supply? How does it relate with the income and
1. Harvey Habit's utility function is U (C₁, C2) = min {c₁, c2}, where c₁ is his consumption of bread in period 1 and c₂ is his consumption of bread in period 2. The price of bread is $1 per loaf in period 1. The interest rate is 21%. Harvey earns $2,000 in period 1 and he will earn $1,100 in period 2. (a) Write Harvey's budget constraint in terms of future value. (b) How much bread does Harvey consume in the first period and how much money does he save?
A possible explanation for the indecency might be the fact that the consumers are not all alive at the same time and therefore some mutually advantageous trades cannot occur. Consider an economy where consumer t receives an endowment of 1 unit of the single consumption good at time t and obtains utility only from consumption at times t and t + 1. All consumers meet at time 0 to trade. What is the equilibrium? Is exigency restored?
3. Consider a parent who is altruistic towards her child, but also cares about her own consumption. The parent's utility over her own consumption and that of her child is up = log(co) +a log(ci) where c is the child's consumption, and a > 0 is the degree of parental altruism. Suppose that the parent can invest in the child's human capital by spending money (e) on her education; education generates human capital h /() and human capital is paid at rate w. The parent has a total income of (a) Write down an expression for the child's future consumption in terms of the parent's choice of e. (b) Now write down the Lagrangian for the parent's decision problem.
Zeynep is at the supermarket buying her bi-weekly groceries. As she arrived at the store right before closing, not much is left on the shelves; so her purchases are limited to beef, B, and an assortment of organic vegetables, V. Beef costs £50/kg and vegetables Ł10/kg. Her utility function is expressed as U(B,V) = B0-6v0.3. She has ±150 to spend. Please answer the following questions using this information: A) Given the vegetables cost less than beef, explain why Zeynep would not only buy vegetables. B) Write Zeynep's constrained maximization problem (objective function subject to her budget constraint). C) Using the Lagrangian technique, find how much beef and vegetables would Zeynep buy? D) Show that for the preferences represented as above, demand for beef is a function of only its own price, pg, and income, m, but not the price of vegetables, py. Note: Rather than using the given prices and income, use PB, Py and m. Find and comment on the comparative statics, i.e., how do changes…
= 5. Consider an economy with a single (representative) agent with utility function u(x, lc) = x¹/514/5 and an endowment of 0 units of x and 10 units of time, which the agent can use as leisure (c) or labor (L) (i.e., L + lc = 10). The agent owns a firm that produces good x using L as an input, with technology of production given by x(L) = 3√L. Let the price of x be p = 1 and let w denote the price of time (i.e., the price of leisure and the wage). Find the competitive price of time w and the competitive allocation.

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Consider the two-period endowment economy discussed in class. The economy is populated by m consumers. The lifetime utility function of each consumer is time separable and is given by U(c, c') = u(c) + Bu(c) 0