2. Ping receives a weekly allowance to purchase soda (x) and juice (y) at school. His preferencesover these two goods can be represented by the utility function U(x,y) =0.5x+ 5lny where xrepresents the number of cans of soda and y represents the number of juice boxes.a) Given his preferences find his Marshallian demand functions for soda (x) and juice (y).b) Suppose that the price of a can of soda is $1.5 and that Ping has $30 to spend on soda andjuice. Write Ping's demand curve for juice (y). Illustrate his demand curve.c) Suppose that the price of a box of juice is $1 (the price of soda and income remain $1.5 and$30, resp.). Use your demand functions to find his best bundle. In an indifference curvediagram illustrate his best bundle at these prices.For the remainder of the question assume that Ping's allowance (income) rises to $36 per week andthe prices of the two goods are unchanged at Px= $1.5 and Py= $1.d) Use your demand functions to find his new best bundle.e) Illustrate the new budget line and the new best bundle that you found above in your diagramfor part (c). Be sure to indicate the slopes of both budget lines.f) What is the income elasticity of soda (as a function of prices and income)?

Given Utility function U=0.5X+5logY where X=Soda Y=Juice Budget constraint M=Px.X+Py.Y

Answered: 2. Ping receives a weekly allowance to…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Questions 1. Will's utility from vacations (91) and meals (92) is given by the function U(V, M) = 91 x 92. Last year, the price of vacations was $200 and the price of meals was $50. This year, the price of meals rose to $75, while the price of vacations remained the same. Both years, Will had an income of $1500. (a) What is the compensating variation for the price change in meals? (b) What is the equivalent variation for the price change in meals?
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Q1. Jason has preferences defined over novels (good x) and DVDs (good y) described by the utility function U(x,y)= x2y2. He has income of $120; novels cost $5 each, while DVDs are priced at $15 each. a) Calculate Jason's optimal consumption bundle, AND his maximized utility level Suppose the price of novels increases to $7.5, while the price of DVDs and income are unchanged. b) In the same diagram, draw his old and new budget constraint; AND calculate his nep optimal bundle. c) Calculate the Total Effect (TE), Substitution Effect (SE) and Income Effect (E) of novels associated with the price increase of novels; AND SHOW them in your initial diagram. (Hint: keep 2 decimals if need)
Rick consumes 2 goods, Chicken McNuggets (M) with Szechuan sauce (S). His utility function is U(M, S) = M2/3 S1/3 and his income is m. The price of Chicken McNuggets is p, and the price of Szechuan sauce is 1. On the same graph, show the income and substitution effects of the increase in p from 1 to 2 on Rick’s consumption of Chicken McNuggets. Are Chicken McNuggets a normal or inferior good for Rick? Explain your answer.
Suppose Carlos has to choose between purchasing jewelry and water. Which of the following is the utility-maximizing rule that Carlos should follow while choosing the optimal quantities of these two goods? (Note: In the answer options that follow, MU stands for "marginal utility.") O (MU of Water) x (Price of Water) = (MU of Jewelry) x (Price of Jewelry) O MU of Water = MU of Jewelry MU of Jewelry %3D Price of Water MU of Water Price of Jewelry MU of Jewelry Price of Jewelry MU of Water %3D Price of Water Since water costs little and jewelry is expensive, it must follow that when people choose their optimal quantities of water and jewelry to purchase, the marginal utility they receive from the last piece of jewelry they buy is than the marginal utility they receive from the last gallon of water they buy.
Suppose an individual is currently spending all of their income on a bundle of books and pizza, but they are not sure whether the bundle maximizes their utility. Assume the individual has a strictly diminishing marginal rate of substitution over these two goods. At their current bundle of books and pizza, the individual's marginal utility from consuming books is 6 utils and their marginal utility from consuming pizza is 3 utils. If the current price of a book is $12 and the price of a pizza is $7, which of the following statements must be true: A. The individual can increase their utility by consuming more books and less pizza B. The individual is maximizing their utility C. The individual can increase their utility by consuming more pizza and fewer books
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6. Consider a consumer with the utility function u(x,, x2) = In(x,) + x2 and the budget constraint p, x1 + P2X2 = m. Derive the consumer's demand functions for x, and x2.
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1) Max chooses to purchase movie tickets and restaurant meals every week with his $100. If the price of a movie ticket is $20 and the price of a restaurant meal is $25, then the slope of his budget constraint will be, a) 1/5 b) -1/5 c) 4/5 d) -4/5 2) Marginal rate of substitution(MRS) is the rate at which consumer is willing to trade one good for another. It must be true that: a) MRS is the slope of an indifference curve in reference to a particular bundle of goods. b) MRS is not the same along an indifference curve that is of usual shape. c) MRS is same along an indifference curve that is of usual shape. d) Both a) and b).

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