3.4Let c represent calories (or cigarettes), with u the strictly concave (immediate) utility ofconsumption and v the strictly convex (delayed) cost of consumption. Let the consumer havepreferences described by the (intertemporal) utility functionU(-1,C,C+1+2)= [u(c)-v(c-1)]+ B8[u(C1+1) = v(ct)]+882[u(+2) v(c+1)],where 0 B1 and 0 < 8≤1.<a. Calculate the optimal level of consumption from the perspective of date 1.b. Assuming that B1, show that c, C++1c. Assuming that ẞ<1, show that c> +1.d. For <1, what is the effect of increasing the self-control parameter ẞ upon theconsumption c,? Explain your finding.

Step 1: To find the optimal level of consumption from the perspective of date 𝑡, we need to…

Answered: 3.4 Let c represent calories (or…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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1.2) Suppose that a consumer’s utility function is U=10 ln⁡x+20 ln⁡y. A) Find the marginal utility of x, MU_x, and the marginal utility of y, MU_y.B) Suppose that the consumer has R3600 to spend on x and y, while p_x=200 and p_y=400. C) Use the Lagrange multiplier (LM) method to find the levels of x and y that will maximise the consumer’s utility, subject to her budget constraint. D) Find and interpret the value of the Lagrange multiplier. Show that MRCS=p_x/p_y at the utility maximising levels of x and y.
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
If the utility function (U) between food (F) and clothing (C) can be represented as U = F*C, then which combination of food and clothing will a rational consumer choose? a. (F, C) = (9, 25) O b. (F, C) = (25, 4) O c. (F, C) = (4, 16) d. (F, C) = (4, 25)
Problem 2.3 Let the consumer's preferences over consumption bundles (x1, x2) be represented by the utility function u(x1,X2) = /x1 +1·(x2+1). Which of the following statements is correct? (a) The utility function v,(x1,x,) = In(x, + 1) + 3 ln(x, + 1) also represents the consumer's preferences. (b) The utility function v,(x1,x2) = In(x1 + 1) + In(x2 + 1)² also represents the consumer's preferences. (c) None of the statements is correct.
Anthony seeks to maximize the following utility function u(x, y) = x'/3y2/3 subject to the budget constraint Pæa + PyY = I 1 where pr, Py, x, y, I > 0. a) Find Anthony's utility-maximizing bundle (x*, y*) as a function of pæ, Py, and I. b) Show that y* is decreasing in py and increasing in I (hint: use partial derivatives). c) What share of Anthony's income is spent on x? What share is spent on y? In other words, calculate Pa and Pu. Are these shares a function of prices? Pyy* Note: The above utility function is Cobb-Douglas, and all Cobb-Douglas functions have these share formulas for any values for the exponents. d) What is the impact of a change in pr on Anthony's utility?
Suppose the function for the utility from good c is denoted as U(c)=2c2. Which of the following expressions indicates the marginal utility of c? 1/c2 1/square root of c All of the above are correct.
A consumer with $120 income and the utility function u(x,y) = (x^2)y where x is food and y clothing can go for shopping in one of the two stores A or B, where the prices for food and clothing are respectively pAx = 1, PAy = 80 and PBx = 8, PBy = 1. (a) If she can visit only one of the stores, which one would she go and what would be her optimal bundle there? Could she afford this very bundle at the other store? (HINT: How happy would she be if she chooses to go to store A for shopping? To store B? Which one is higher and what bundle would she buy there?) (b) If she can freely visit both stores (so that she buys each good from the store where it is sold cheaper), what would be her optimal bundle? What would she buy from each store? (c) How much money would she be willing to give up (out of her $120 budget) for the ability to visit both stores as in (b) rather than being restricted to shopping in only one store (the one she chooses in (a)? (HINT: suppose she pays $A for this privilege.…
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Part A . Consider an economy with the following features. • There are 100 identical consumers that derive utility from consuming three different goods: software, computers, and good m. • Each consumer decision utility function is given by U (c, 8) = 4c¹/48¹/4+m, where e denotes the amount of computers that she consumes, s denotes the amount of software that she consumes, and m denotes the amount of good m that she consumes. cand s must be non-negative, but m can take any real value. • Computers are produced by 20 identical competitive firms with a total cost function given by 10c². • Software is produced by 40 identical competitive firms with a total cost function given by 20s². . QUESTION 1: What are the equilibrium prices for software and comput- ers in equilibrium? Part B • Suppose that there is a positive technology shock in the software industry so that that the new cost function of the software firms becomes 10s². Let C and S denote, respectively, the aggregate level of…
Please use Kuhn Tucker 5. A consumer's utility function is: u(x) = x1+ /®2 (c) Verify the properties of the indirect utility function. (d) Calculate the expenditure function and verify its properties.

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