Answered: 3. Natasha's preferences are… | bartleby

Microeconomics A Contemporary Intro

Microeconomics A Contemporary Intro

10th Edition

ISBN:9781285635101

Author:MCEACHERN

Publisher:MCEACHERN

Chapter6: Consumer Choice And Demand

Section: Chapter Questions

Problem 13PAE

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3. Natasha's preferences are represented by the utility function U(QA,QB) = 2QAQB,
where QA stands for the number of apples and QB stands for the number of bananas.
Her income is $30. An apple costs $1 and a banana costs $P.
%3D
(a) Describe her optimal affordable consumption bundle, varying the price of a ba-
nana from $1 to $10.

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4. Minnie enjoys dessert by eating chocolate cake (C) and apple pie (P) according to the utility function U = Min [C, P]. In any given week, Minnie %3D spends £20 to purchase these two products. Assume that Minnie is a utility maximiser and has to pay 50p for a unit of apple pie and £2 for a unit of chocolate cake. (i) Consider the bundle C = 20 and P = 5. Is this the utility maximizing choice subject to Minnie's budget?. %3! (ii) Suppose that Minnie chooses the exact bundle that maximizes her utility. How would the utility maximizing choice of C be affected if price of P went up? (iii) Explain under which conditions the tangency condition does not work. Given that the tangency condition does not work, discuss how we can find out the optimal consumption bundle for a consumer.
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.
2. Tom spends all his $100 weekly income on two goods, apples and bananas. His utility function is given by U (A, B) = AB, where A and B stand for the quantity of apples and bananas consumed by Tom. If PA = $4 and PB= $10, how many apples and bananas will he consume? Make sure you write out the utility maximization problem explicitly, including the decision variable(s). What if his utility function is given by U (A, B) = A0.5B 0.5?
Which one is answer?
Jessica has an income of $216 and she is buying apple cider and books. Apple cider is $8 per unit and books are $24 each. The following table shows her marginal utility per dollar spent. Which of the bundles will maximize her total utility? Enter the letter of the bundle only. Bundle Q(A) MU/$(A) Q(B) MU/$(B) 9. 6.13 5.13 B. 3. 8. 5.38 5.21 6. 7 4.63 5.29 6. 3.88 5.38 12 3.13 5.46 4. 2.38 5.54 G. 18 1.63 5.63 H. 21 0.88 5.71 24 0.13 5.79 27 0. Answer 15
please give answer step by step
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.
Assume that you have a budget of Taka 4000 that can spend on two goods like: coke and burger. Suppose coke costs Taka 100 per unit and burger costs 400 per unit. Suppose also that your utility function is given by the equation U(B, C) = 20BC. Write your budget equation. What combination of coke and burger should you buy to maximize utility?
5. Tony’s preferences for apples (qa) and pies (qi) are captured by the utility functionU(qa, qi) = min(2qa, 3qi). Tony has an income of $120.(a) Find the right mix of apples and pies that would change the utility of Tony.(b) Find Tony’s optimal consumption bundle when the price of an apple is $2 and theprice of a pie is $2.(c) Find Tony’s optimal consumption bundle when the price of an apple is $2 and theprice of a pie is $3.
Question 3. Suppose that Janice only cares about tea (T) and coffee (C). Her utility function is U = 2T + 4C. The price of T is $1.50, and the price of C is $2.50. Janice has a budget of $15 for tea or coffee during the week. (a) Write down the consumers maximization problem. (b) What are the consumption quantities of T and C that will maximize Janice's utility?
EXERCISE 7 Aisha is considering how to allocate the next 6 hours of her free time. She could choose between leisure (L) and helping her neighbour with the house chores. If she decides to help her neighbour, she is going to get paid at £25 per hour, which she can then spend on her favourite pizza (P). Suppose the price of pizza is £12.50. Aisha's preferences for leisure and pizza are given by the following utility function: U(L, P) = 3L + P. (MU₁ = 3, MUp = 1). a) Write down Aisha's budget equation and draw the corresponding budget line. Clearly label the axes and calculate the coordinates of the points of intersection of the budget line with each axis. b) Calculate Aisha's marginal rate of substitution between leisure and pizza. Explain the concept of MRS and interpret the figure obtained. c) Find Aisha's optimal consumption bundle, both algebraically and graphically. Explain your reasoning. d) Would Aisha's optimal choice change if she could get a discount on her pizza purchases so…
4. Tim wants to maximise his utility given his utility function of U (A, B) = A² B¹. He faces the following prices and income: PA = 25; PB = 20; M = 250. However, a change in the price of good A to PA 22 will change his optimal bundle. If he is only interested in being able to consume his original bundle of goods, how much income would he need after the price change? = (a) Tim would require £54 less income (b) Tim would require £18.33 more income (c) Tim would require £10 less income (d) Tim would require £16.66 more income (e) Tim would require £16.66 less income

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