An individual lives for two periods (1 young, 2 = old). His/her preferences over the con- sumption streams in the two periods are defined as follows U(c1,c2) = log(c1)+Blog(c2) (1) where B measures the degree of patience of the individual. The individual receives incomes yı and y2 respectively in the two periods, and can freely borrow and lend at the interest rate r. Please express the optimal (c1,c2) in terms of y1, y2, r,

An individual lives for two periods (1 young, 2 = old). His/her preferences over the con- sumption streams in the two periods are defined as follows U(c1,c2) = log(c1)+Blog(c2) (1) where B measures the degree of patience of the individual. The individual receives incomes yı and y2 respectively in the two periods, and can freely borrow and lend at the interest rate r. Please express the optimal (c1,c2) in terms of y1, y2, r,

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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1
Given the following utility functions, check if the utility function is homogeneous and if MRS is diminishing: (1) U(x, y) = Vr + y (2) U(x,y) = (x +y")/5.851
solve this all these three subparts early i upvote
Consider a consumer who can borrow or lend freely at an interest rate of 100% per period of time (think of the period as being, say, 30 years, a bit like with a mortgage). So r = 1.0, or 100%. The consumer's two-period utility function is: U = In(ct) + (1/2)In(Ct+1) The consumer earn Y=100 each period, so Y₁=100 and Yt+1 also equals 100. If this consumer is behaving optimally, trying to maximize her lifetime utility subject to the IBC, what's her consumption in period t?
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Q7
At a company, 20 employees are making contributions for a retirement gift. Each of the 20 employees is choosing how many dollars to contribute from the interval [0,20]. The manager of these 20 employees announces that she will contribute dd dollars for every dollar that an employee contributes. The payoff to employee ii who makes contribution of xixi dollars is bi(1+d)xi−xi, where bi>0.bi(1+d)xi−xi, where bi>0. Assume that d=4d=4, bi=0.25bi=0.25 for i=1,2,…,10i=1,2,…,10, andbi=0.5bi=0.5 for i=11,12,…,20i=11,12,…,20 What is the best contribution level of any employee ii for i=1,2,…,10i=1,2,…,10. At a company, 20 employees are making contributions for a retirement gift. Each of the 20 employees is choosing how many dollars to contribute from the interval [0,20]. The manager of these 20 employees announces that she will contribute dd dollars for every dollar that an employee contributes. The payoff to employee ii who makes contribution of xixi dollars is bi(1+d)xi−xi,…
Emma has a utility functionU(x1, x2, x3) = logx1+ 0.8logx2+ 0.72logx3 incomes x1 , x2, x3 in the next three years. This is an example of (A) expected value; (B) quasi-hyperbolic utility function; (C) standard discounted utility; (D) none of the above.
A widely used utility function in the economics literature is the constant rate of risk aversion utility function. It is given by: utc) = c*(1-n) (1-n) Assume that an agent lives tor three periods (t-0,1,2) and discounts future utity at rate B (per period), The agent is born with asset level ag and his/her labour market income is yo and y, for periods O and 1 respectively, the agent retire in the last period (no labour income). The interest rate in this economy is Please answer the following questions based on the information displayed here. Choose the best option avallable. Select one: O a. The budget constrain in period te2 is given by: C2 + ay = az(1+r) O b. The budget constrain in period te2 is given by: c2= az{1+1) O G. The budget constrain in period t=2 is glven by: ute, )+ ag = a;(1+1) +ya d. The budget constrain in period t=2 is given by: C2= az(1+r) +y3 e. The budget constrain in period te2 is given by: c, + ag = az(1+) +ya
For a certain Utility function, which is a simple sifted parabolic equation, the maximum utility is 10 for n=5. Determine the mathematical expression of this Utility function. Hint: look up (h,k) values for a parabola. Multiple Choice 10n + 5 10n + 5n - 2n2 +10n + 5 - (n-5)2+10
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