4. Suppose you had to eat a cake over 3 days. The share of cake consumed in period t is Ct, so that Σ1Ct ≤ 1. Instantaneous utility is derived as u(ct) = log(Ct). a) = Find the optimal consumption path for an exponential discounter with a daily discount rate of p 0.1. b) Find the consumption path for a naïve hyperbolic discounter with a discount factor of 1 in the current day and B (1) for utility delayed by 7 days, where ß = 0.7 and p = 0.1. c) Discuss what a sophisticated hyperbolic discounter should do on the first day.

4. Suppose you had to eat a cake over 3 days. The share of cake consumed in period t is Ct, so that Σ1Ct ≤ 1. Instantaneous utility is derived as u(ct) = log(Ct). a) = Find the optimal consumption path for an exponential discounter with a daily discount rate of p 0.1. b) Find the consumption path for a naïve hyperbolic discounter with a discount factor of 1 in the current day and B (1) for utility delayed by 7 days, where ß = 0.7 and p = 0.1. c) Discuss what a sophisticated hyperbolic discounter should do on the first day.

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

Gina is at a toy store and is buying toy T-Rex's (x), which cost på, and toy yaks (y), which cost py. Her income is I. She likes 3 T-Rex's as much as she likes 4 yaks. These toys are perfect substitutes for her.
1. A consumer wishes to maximize the utility U(X1, X2) = (X1 + 20)(X2 + 30) subject to the available income (M= 600) and prices (pi = 5, p2 = 4). Find the optimal consumption levels and marginal utility of income. ASsuming a local maximum is attained, prove that it is also a unique global maximum.
urgent
Given the utility function U (x1, x2) = x³x2.7 select all that are true. a) 30% of the budget is spent on good 1. ○b) V (p, I) = 30.370.7 I 10 P1P2 c) If P2 = 2 and I = 60, then $18 is spent on good 21. d) If P1 = 9, P2 = 2, and I = 60 then the consumer enjoys 1.81 utils of utility. e) Half the budget is spent on good 1 and the other half is spent on 2.
Given the total utility function for a consumer, consuming two goods is U = x+2y + xy+2 the prices of x and y are 4 TL and 6 TL respectively (Px = 4 and Py = 6), and the total budget of the consumer (B) is 130 TL; a) Write the constraint ( budget) function. b) Write the lagrangian function. c) What are the first-order conditions for utility maximization? d) Find the critical values of x, y and \lambda (x*,y*and \lambda *) according to the first order conditions. e) is the second order suficent condition for maximum utility satisfied 2 4 10 [ [:] 8 Write the appropriate commands to create A and d matrixes in R software. A-1. din R language? Given A = 1 3 And d = How can you formulate the equation X =
Emma has a utility functionU(x1, x2, x3) = logx1+ 0.8 logx2+ 0.72 logx3over her 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. Emma’s preferences can exhibit which of the following behavioral patterns?(A) preference for flexibility;(B) context effects;(C) time inconsistency;(D) intransitivity.
image attached
The utility derived by a consumer from the consumption of two commodities is given by the function U (A, B) = 0.5In (A) + 0.5 In (B) where A are the number of units of the first commodity consumed and B are the number of units of the second commodity consumed each month. A unit of the first commodity costs $8 and a unit of the second commodity costs $ 4 using the Lagrange multiplier method determine the optimal quantity of each of the commodities consumed each month given that consumer has $32 to spend on both commodities each month
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?
A consumer has the following utility function: U(x.y)=x(y+1), where x and y are quantities of two consumption goods whose prices are Px and Py, respectively. The consumer also has a budget of B. Therefore, the Lagrangian for this consumer is x(y + 1) + X(B – Prx – Py) (a) Verify that this is a maximum by checking the second-order conditions. By substituting x* and y* into the utility function, find an expression for the indirect utility function U* = U(Pr, Py, B) and derive an expression for the expenditure function E = E(Pr, Py, U*) (b) This problem could be recast as the following dual problem Min Prx + Pyy Subject to æ(y + 1) = U* Find the values of x and y that solve this minimization problem and show that the values of x and y are equal to the partial derivatives of the expenditure function, ðE/ðP, and ðE/ðP, respectively.
Suppose a utility function is given by u(x1, x2) = x12 + x2. Graph the indif- ference curve for utility level 100 and 400. What is wrong about the shape of the indifference curves? Does the utility function describe reasonable preferences? Now suppose prices are p1 = 2, p2 = 1 and I = 10. Determine the optimal consumption graphically.
Merge the two budget constraints into a single lifetime budget constraint by eliminating savings from the system of two constraints.