3. State whether the following statements are true, false, or uncertain. Briefly explainyour reasoning:(a) If a household is behaving optimally and is at an interior solution, then themarginal utility per unit of each good must be equal.(b) If houschold A has a utility function uA(ZA1; ZA2) = TA2 and household Bhas a utility function ug(TB1, I2) = 2 In(r1) + In(a2), then the householdswill choose different consumption bundles.(c) A household with strictly convex preferences may consume only one of twogoods.

(a) True, because according to rule of optimum consumption and interior solution, the maximum…

Answered: 3. State whether the following…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Reese thinks peanut butter and chocolate are great when separate, but when they combine they are even more epic. In other words, Reese likes to eat either peanut butter or chocolate, but when he eats them together, he gets additional satisfaction from the combination. His preference over peanut butter (x) and chocolate (y) is represented by the utility function: u(x, y) = xy + x + y Which of the following is NOT true about Reese’s preference? (a) The MRS decreases when x increases.(b) The preferences are homothetic.(c) The marginal utility of y is higher when x = 10 than when x = 5.(d) For any a > 0, Reese prefers the bundle (x =a/2 , y = a/2 ) over either the bundle (x = a, y = 0) or (x = 0, y = a).
2) Which of the following utility functions represent the same preferences? Explain. a) U (x₁, x₂) = X₁ X₂ b) W (x₁, x₂) = 5lnx₁ +5lnx₂ c) V (x₁, x₂) = x₁¹/3x₂ ¹/3 - 0.8 d) Z(x₁, x₂) = 0.5x₁ + 0.5x₂
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.…
2. Suppose there are n identical consumers, each with a utility function u(x, y): = ax = x²+y. Each consumer has different disposable income w. The price of good x is p dollars, and the price of composite good y is equal to 1 dollar. Assume a > 0 and b > 0. (Hint: Question 1) (a) Calculate the marginal utility of good x and good y. Then, calculate the marginal rate of substitution between good x and good y. (b) Calculate the individual demand of consumer 1 for good x. (c) Calculate the aggregate demand for good x. (d) Draw a graph showing the market demand curve for good x. (e) Discuss whether an increase in disposable income for each consumer lead to an increase in the consumption of good x? This increase in disposable income can result from various factors, such as a decrease in taxes, government stipends, or other forms of income support. (f) Discuss the effect on demand for good x if there is an increase in the price of good x. This increase in the price of good x can result from…
Only typed solution
Problem 1 (25pts) Benjamin spends his time either watching movies (x1) (he uses "on demand" option, cable TV) or listening to songs MP3 downloaded from the Internet (x2). His preferences are described by - U(x1, x2) = ln(x1) + In(x2) - a) Derive Benjamin's demand for movies and MP3 files as a function of prices p1, p2 and his income m. (do not use Cobb Douglas formula but rather derive demand using "two secrets of happiness"). b) Fix the price of MP3 at p2 = 1, and income on m = 10. Find the price offer curve (give an exact formula x2 = f(x1)) and plot it in the commodity space. Find the demand curve x1 = f(p1) and plot it in the graph (with p₁ on vertical axis and x1 on horizontal axis). == c) Is x1 an ordinary good or a Giffen good? Explain. d) Now fix p₁ = 1 and p2 = 1. In the commodity space, plot the income offer curve. In addition, in two separate graphs, plot Engel curves for both movies and MP3 files. Argue that the two commodities are normal (not inferior). e) For the demand…
Find the optimal bundle using the following utility functions and budget constraints. 1. U(x,y)=lnx+yand2x+y=10 2. U(x,y)=3x+2yand3x+2y=24 3. U(a,z)=3a+2zand3a+6z=24 4. U(a,z)=a2z2 and4a+2z=485. U(x,z)=a2z3 and3a+2z=36
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.
Please refer to the following information to answer the question (in bold) below: You enjoy consuming apples (A) and oranges (O). Suppose that your utility function over both goods is given by . Your marginal utility function for apples is Your marginal utility function for oranges is O You utility increases due to the price change U (A, 0) = AO³ You utility decreases due to the price change MUA = 0³ . Currently, the price of apples is $10/peck, the price of oranges is $5/pound, and your income is $160. Assume that apples are your horizontal axis good and oranges are your vertical axis good. Let's say the price of oranges rises to $10/pound of oranges. Comparing the utility you receive from your old consumer equilibrium bundle to your new consumer equilibrium bundle, how does the increase in the price of oranges impact your level of satisfaction as a consumer? MUO = 340² ЗАО2 You utility is unaffected by the price change You utility could either rise or fall due to the price change

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