6. Anthony spends his income on fishing lures (L ) and guitar picks (G ). Lures are priced at $2,while a package of guitar picks costs $1. Assume that Anthony has $30 to spend and hisutility function can be represented as U(L,G) = L 0.5 GO5.a. Given the utility function in this problem, use calculus to derive the marginal utilities offishing lures and guitar picks.b. Using the tangency condition, what is the MRSL,G?c. What is the optimal number of lures and guitar picks for Anthony to purchase?d. At the optimal bundle, how much utility does Anthony have?e. If the price of guitar picks doubles to $2, how much income must Anthony have tomaintain the same level of utility?f. Suppose that the prices of lures and guitar picks are $2 and $1 (as they were before theprice change) and that Anthony still has only $30 to spend. Use a Lagrangian to solve hisconstrained utility maximization problem and confirm that the answer is the same asthat to part (c).g. Now suppose that the prices of lures and guitar picks are $2 and $2 (as they were afterthe price change). Assuming Anthony wants to maintain the same level of utility as hedid before the price change with the lowest possible expenditure, write a statement ofAnthony's constrained optimization problem. Use a Lagrangian to solve Anthony'sexpenditure-minimization problem and confirm that the answer is the same as that topart (e).h. Again suppose that the prices of lures and guitar picks are $2 and $2 (as they were afterthe price change). This time, however, assume that Anthony still has only $30 to spend.Use a Lagrangian to solve his constrained utility-maximization problem.codar

Given utility function:- U(L, G) = L0.5 G0.5 PL = 2, PG = 1, Budget(B) = 30

Answered: Anthony spends his income on fishing…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Rhea is determining how many gallons of milk (M) and loaves of bread (B) to purchase. Use the information in italics to answer the bolded question below: Rhea's marginal utility function for milk: MUN • Rhea's marginal utility function for bread: M = 0.5M-2 MUB = 0.5MB-1/2 • Rhea has $60 to spend on bread and milk. • The price of milk (Pm) is $3/gallon of milk. • The price of bread (Pb) is $1/loaf of bread. • For the sake of computation, assume that bread is the horizontal axis good (i.e., good X) and milk is the vertical axis good (i.e., good Y). When you set up the optimal budget decision rule for Rhea's consumer problem, which of the following statements best describes how much she will buy of both goods at her consumer equilibrium? O For each gallon of milk, Rhea will buy 1/3 loaf of bread. O For each gallon of milk, Rhea will buy 3 loaves of bread. For each gallon of milk, Rhea will buy 1 loaf of bread. O For each gallon of milk, Rhea will buy 6 loaves of bread.
2. Ping receives a weekly allowance to purchase soda (x) and juice (y) at school. His preferences over these two goods can be represented by the utility function U(x,y) =0.5x+ 5lny where x represents 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 and juice. 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 curve diagram illustrate his best bundle at these prices. For the remainder of the question assume that Ping's allowance (income) rises to $36 per week and the 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)…
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.
Rick consumes 2 goods, Chicken McNuggets (M) with Szechuan sauce (S). His utility function is U(M, S) = M2/3S1/3 and his income is m. The price of Chicken McNuggets is p, and the price of Szechuan sauce is 1. g. On the same graph, show the (hypothetical) budget constraint that is tangent to the indifference curve from part (e) but parallel to the budget constraint in part (f). h. 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. i. Find the equation representing the (hypothetical) budget constraint drawn in part (g). Hint: you know this budget constraint has the same prices as in part (f), so you need to find the income level m that makes the budget constraint just tangent to the indifference curve passing through Rick’s chosen consumption bundle in part (e).
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
Sally consumes two goods, X and Y. Her utility function is given by the expression U = 2XY3. The current market price for X is $20, while the market price for Y is $10. Sally's current income is $500. a. Write the equation for Sally's budget constraint. What is the slope of her budget line? b. Determine the X,Y combination which maximizes Sally's utility, given her budget constraint.
1. In a simple but delicious world, Joey eats only sandwiches, s, and jam, j. He has a Cobb-Douglas utility function U(j, s) = Nj1-asª, where 0 0. The price of jam is pj, the price of sandwiches is Ps, and Joey has a monthly budget Y to spend on lunch. a. Explain why you can safely use a simpler Cobb-Douglas utility function, V(j, s), to represent Joey's preferences, which is the same as U(j, s) except for replacing N with 1. b. Transform V(j,s) by taking natural logs and bringing down exponents. Explain why it is useful to do this for a Cobb-Douglas utility function, but not for a quasi-linear utility function. Use In(V(j, s)) and the substitution method to derive the formulas for Joey's optimal amount of jam, j*, and sandwiches, s*, to buy and consume per month. Simplify your answers so that you arrive at the С. (1-a)Y aY formulas j* = and s* Ps d. What fraction of his income does Joey spend on jam, and what fraction on sandwiches?
Define the Marginal Rate of Substitution between two goods (X and Y).If a consumer’s preferences are given by U(X,Y) = X1/4Y 3/4, compute the consumer’s marginalrate of substitution as a function of X and Y. Calculate the MRS if the consumer has chosen toconsumer 12 units of X and 30 units of Y.
Rick consumes 2 goods, Chicken McNuggets (M) with Szechuan sauce (S). His utility function is U(M, S) = M2/3S1/3 and his income is m. The price of Chicken McNuggets is p, and the price of Szechuan sauce is 1. d. Use the equation from part (c) and the budget constraint from part (a) to find Rick’s demand for each of the two goods. e. Suppose m=100 and p=1. How much of each good does Rick consume? Draw a graph showing Rick’s budget constraint and indifference curve passing through his chosen consumption bundle. f. Suppose m=100 and p=2. How much of each good does Rick consume? On the same graph from part (e), show Rick’s budget constraint and indifference curve passing through his new chosen consumption bundle.
A student has a lunch utility function U(S, P) 8S + 3P, where S is number of salads per month and P is number of pizzas per month. The price of a salad is $5, the price of a pizza is 8, and his monthly income for lunch is $80. a) Derive the equation representing the consumer's demand for Salad. Represent the demand for Salad graphically. b) The price of Salad goes up to $25 and the price of Pizza does not change. Compute and represent graphically the new equilibrium of the student. What can you tell about the substitution effect on Salad and pizza
Alice receives an allowance of 500 dollars that she spends on buying snacks (S) and tea (T). The price of each snack is 10 dollars and the price of each tea is 5 dollars. Her utility is given by: U (S, T) = 2S³/4 +T3/4 (a) Find her marginal rate of substitution (MRS) between S and T. (b) Write Alice's budget constraint. (c) Find Alice's optimal consumption and the optimal A. (d) What is her new consumption if the price of tea becomes 10 dollars? Note: numeric solutions for questions (c) and (d) are not integers.
Given Barbara's estimated Cobb-Douglas utility function, 0.8. 0.2 U(q1, 92) = q, q2 for CDs, q1, and DVDS, q2, derive her Engel curve for movie DVDS. Illustrate in a figure. Let p be the price of DVDS, $1.00 be the price of CDs, and Y be income. Barbara's Engel curve for movie DVDS is Y=- (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a subscript can be created with the character.) 24 étv MacBook Air 80 DII DD F2 F3 F4 F5 F6 F7 F8 F9 へ @ 23 2$ & * 2 3 6. 8. 9. W E Y U S F G H J C V M B N

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