An individual has preferences over contingent consumption in two states of nature {a, b}, given by u (x(a), x(b)) = logx(a) +2logx(b), and current income m = sured in units of consumption. The prices of contingent contracts for deliveries of a unit of consumption in the two states of nature are (p(a), p(b)) = (1,4). Find the optimal consumption plan (x*(a), x*(b)) of this individual and answer: compute the value of the consumption plan in state a, i.e., p(a)x* (a). 6, mea-

An individual has preferences over contingent consumption in two states of nature {a, b}, given by u (x(a), x(b)) = logx(a) +2logx(b), and current income m = sured in units of consumption. The prices of contingent contracts for deliveries of a unit of consumption in the two states of nature are (p(a), p(b)) = (1,4). Find the optimal consumption plan (x(a), x(b)) of this individual and answer: compute the value of the consumption plan in state a, i.e., p(a)x* (a). 6, mea-

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Rodrigo is taking a year between high school and college to work and save up. His utility from consumption each year is U(c) = discounts future utility by B. Rodrigo is going to make $I his year of working, and whatever he doesn't consume from that income will a savings account which will earn return r before he consumes next year. He has to pay for school expenses E in year two, before he consumes (but after return has been realized). 1-o and he go into
A consumer's consumption-utility function for a two period horizon is 0.5 U(Cg,G) =C,G" he consumer's earned income stream is given by mo, m1 and the market rate of interest is r. a) Write the intertemporal budget constraint in present value terms. If the consumer does not consume anything in peripd 0, what is the most she can consume in period 1? b) Draw a graph that shows optimal consumption in each period co* and c1*. What is the slope of her budget line? c) Solve the problem for optimal consumption in each period co* and c;*. d) Suppose mọ is S50 and mị is S110 and r = 0.1. Is the consumer a borrower or a lender? Show this outcome by drawing co*. C1*, mo, mį, and bond-holdings on your graph.
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 has endowment 1500 now and 500 later. Internet rate is 2.0%. She prefers smooth consumption to time (i.e., u0=u1=u). a. Assume utility function, u(c)= log c. What are the optimal consumption c0and c1if Anna's beta=1, and she wants to maximize her utility? b. Now assume that the utility function, u(c)=c0.5. If everything else remains the same as Problem 1(a), what are the optimal consumption c0and c1if Anna wants to maximize her utility?
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.…
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?
The utility maximization problem is given by 0-1 Ө-1\0-1 max uf = Cit,C2t,St 0 + a, (c2t) subject to Cit + St = Wt + e C2t = (1+ rt+1)s, By solving the maximization problem, characterize the saving function depending on the value of 0, i.e., there are three cases.
DEFINE Limit of consumption options
Assume 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 an economy with two periods (interpreted as “when young” and “when old” periods)and two consumers, Gillian Davis and Joana Wolinsky. Gillian is a star ballet dancer with a lifetime income given by ωG= (400,0). Joana is an Econ Ph.D. student with incomeωJ= (0,400). Gillian and Joana have identical utility functions given by Ui(x1,x2) = 6 lnx1+ 3 lnx2 for i=G, J a) Plot an Edgeworth box and mark the initial endowment point. b) Write the general definition of Pareto efficient allocation (one sentence) and give the equivalent condition in terms of MRS (give formula). Check if this condition is satisfied for initial endowments. c) Derive the contract curve (write down the appropriate conditions and solve for the curve) and depict it in the Edgeworth box. d) Suppose Gillian and Joana can “trade” consumption in both periods at pricesp1,p2. Find the competitive equilibrium (6 numbers) and depict the equilibrium allocation in the Edgeworth box. e) Using the MRS condition from part b),…
Seung's utility function is given by U - C^(1/2), where C is consumption and C^(1/2) is the square root of consumption. She makes $50,625 per year and enjoys jumping out of airplanes. There's a 5% chance that in the next year, she will break both legs, incur medical costs of $30,000, and lose an additional $5,000 from missing work. a. What is Seung's expected utility without insurance? b. Suppose Seung can buy insurance that will cover the medical expenses but not the forgone part of her salary. How much would an actuarially fair policy cost, and what is the expected utility if she buys it? Policy cost: $___ Expected utility: ___ c. Suppose Seung can buy insurance that will cover her medical expenses and foregone salary. How much would such a policy cost if it's actuarially fair, and what is her expected utility if she buys it? Policy cost: $___ Expected Utility: ___
Suppose a household has the following lifetime utility function: U=c1/2 + ẞc¹/2 12tt+1 A) Find expressions for the partial derivatives of lifetime utility, U, with respect to period t and period t + 1 consumption. Is marginal utility of consumption in both periods always positive? B) Find expressions for the second derivatives of lifetime utility with respect to period t and t+1 consumption, i.e., 2U and a 20_Are these second derivatives always negative for ac²²+1 any positive values of period t and t+1 consumption? C) Derive an expression for the indifference curve associated with lifetime utility level Uo (i.e., derive an expression for C++₁ as a function of U₁ and c). What is the slope of the indifference curve? How does the magnitude of the slope vary with the value of c?