Happy Goluki likes tea (good 1) and cookies (good 2). Her preferences are represented by the utility function U(q₁,92) = (q₁)⁰.5+(q₂)0.5, where q₁ is the number of cups of tea and q2 is the number of cookies. Goluki is given I = $180, which she is allowed to spend as she wishes on tea and cookies. a) Calculate Goluki's optimal bundle if the price of tea is p₁=$1 and the price of cookies is p2=$2. Call this bundle A and show it on a graph (put tea on the horizontal axis). b) Suppose that the price of tea increases to $5 (I know, I can't believe it either, but Melbourne does have some very fancy tea places) and the price of cookies stays the same. Calculate Goluki's new optimal bundle of tea and cookies (call it bundle B). Show it on a graph from part a). c) If at new prices (pnew, $5 and p₂=$2) Goluki has just enough income to achieve the same

Happy Goluki likes tea (good 1) and cookies (good 2). Her preferences are represented by the utility function U(q₁,92) = (q₁)⁰.5+(q₂)0.5, where q₁ is the number of cups of tea and q2 is the number of cookies. Goluki is given I = $180, which she is allowed to spend as she wishes on tea and cookies. a) Calculate Goluki's optimal bundle if the price of tea is p₁=$1 and the price of cookies is p2=$2. Call this bundle A and show it on a graph (put tea on the horizontal axis). b) Suppose that the price of tea increases to $5 (I know, I can't believe it either, but Melbourne does have some very fancy tea places) and the price of cookies stays the same. Calculate Goluki's new optimal bundle of tea and cookies (call it bundle B). Show it on a graph from part a). c) If at new prices (pnew, $5 and p₂=$2) Goluki has just enough income to achieve the same

Economics (MindTap Course List)

13th Edition

ISBN:9781337617383

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter20: Consumer Choice: Maximizing Utility And Behavioral Economics

Section: Chapter Questions

Problem 5WNG

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If Ginna spends her entire budget, she could buy a chosen set of groceries and also buy 10 notebooks. If she spends only half of her budget, she could only buy a set of groceries and could not afford any notebooks. Suppose Ginna's budget is £150. Her preferences for groceries (G) and notebooks (N) can be described by the following utility function: U (G, N) = 30G + 2N (MUG = 30, MUN = 2). a) Find Ginna's optimal consumption bundle. Provide both algebraic and graphical solution. Explain your reasoning. b) Discuss how the price of a notebook should change for Ginna to change her optimal consumption choice. c) If the price of a notebook increases by 50%, how should the price of the groceries drop so that Ginna can be as well off as before this change in prices? d) Discuss the implications of the price change from c) on Ginna's optimal choice. In your discussion, include the analysis of the substitution and income effects as well as Ginna's demand for groceries and/or notebooks.
Every month, a family of three spends $2,000 on food (F) and other items (O). The family’s preferences are represented by the utility function U(F,O) = F1/5O4/5. The unit price of food and the unit price of other items are both $1.a) Find this family’s monthly food expenditure. The family could join a consumers’ club. At the club, food costs 20% less than in other stores (i.e., at the food club PF = $0.8). b) Suppose the club did NOT charge a membership fee: how much money would the family spend on food? How much food would the family buy? c) Would the family be willing to pay more than $80 to join the consumers’ club? Clearly justify your answer.
Every month, a family of three spends $2,000 on food (F) and other items (O). The family’s preferences are represented by the utility function U(F,O) = F1/5O4/5. The unit price of food and the unit price of other items are both $1. Find this family’s monthly food expenditure.The family could join a consumers’ club. At the club, food costs 20% less than in other stores (i.e., at the food club PF = $0.8)
Joyce consumes x1 and x2 together in fixed proportions. She always consumes 1 unit of x2 for 2 units of x1. What is the utility function that describes her preference?
Linda loves buying shoes and going out to dance. Her utility function for pairs of shoes, S, and the number of times she goes dancing per month, T, is U(S + T) = 2ST, so Mus = 2T and Mut = 2S. It costs Linda $50 to buy a new pair of shoes or to spend an evening out dancing. Assume that she has $500 to spend on shoes and dancing What is the equation for her budget line? Draw it (with T on the vertical axis), and label the slope and intercepts. What is Linda’s marginal rate of substitution? Explain. Use math to solve for her optimal bundle. Show how to determine this bundle in a diagram using indifference curves and a budget line
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Krissy spends all her income on holiday lights (L) and fishing bait (B). Lights are priced at $2, while a pack of bait costs $1. Assume that Krissy has $30 to spend and her utility function can be represented as: U(L,B) = L²B² with: MU=2LB² and MU=2L²B (Assume B is on the y-axis when graphing). How much utility does Krissy obtain from the optimal bundle? Note: enter number(s) only and convert any fraction to a decimal.
Kate’s utility function includes coffee (c) and sugar (s). She only consumes coffee and sugar together, and she only consumes in the ratio of one unit (cup) of coffee with two units (spoons) of sugar. Her utility function is What is her marginal utility of sugar if she has 4 cups of coffee and 6 spoons of sugar? Remember that unit are infinitely divisible (you can have parts of units). (a) 0 (b) 1 (c) ½ (d) 2
Jackie has a budget of $36 per month to spend on snacks. She can spend this budget on bags of potato chips (C) and Hershey chocolate bars (H). Potato chips cost $4 per bag, while Hershey bars cost $1 per bar. The utility that Jackie receives from consuming potato chips and Hershey bars is represented by the following utility function: U=3C2 H. Given that Jackie seeks to maximize her utility, find the number of potato chip bags and Hershey chocolate bars that Jackie will purchase each month.
Question 2 David spends his budget on chocolate and chip. His utility function is given by ?(?1,?2)= 2?1?2, where ?1 is the number of chocolates he consumers per week, and ?2 is the number of chips he buys per week. A chocolate costs 10 SEK, and a chip costs 20 SEK. David’s weekly budge for consuming on these two goods is 120 SEK. (1) What is David’s budge line? Draw the budget line on a graph with chocolate amounts on the horizontal axis and chip amounts on the vertical axis. Write explicitly at which points budget line crosses the axis. (2) What is David’s marginal utilities for the two goods, respectively? What is his marginal rate of substitution between the two goods? (3) What is David’s optimal choice? Calculate the numerical answer for the optimal bundle. Also draw an indifference curve for David on the same graph as question(1) and show the optimal bundle.
Julio loves gardening. His favourite plants are tulips and hydrangeas. His utility function is ' u(t,h)= t +100h -h^2 where t is the number of tulipsin his garden and h is the number of hydrangeas in his garden. suppose he has a 500 square feet for his garden. each tulip takes up 1 square foot of space and each hydrangeas takes up 4 square feet. he gets both plants for free.If he wanted to maximize his utility, how many tulips should he plant, what about hydrangeas? b) if his yard was only 144 square feet, how many tulips would he plant? How many hydrangeas? C) In order to plant both tulips and hydrangeas, how big does his garden need to be. carfeully explain.
You have $3,000 to spend on entertainment this year (lucky you!). The price of a day trip (T) is $40 and the price of a pizza and a movie (M) is $20. Suppose that your utility function is U(TM) T1/3M2/3. a. What combination of T and M will you choose? b. Suppose that the price of day trips rises to $50. How will this change your decision?