Johanna has / =$181 to spend on goods x1 and x2. Her utility function is given byU (a1, 22) = 2 min{ax1, bx,} where a =3 andb =5. Good x1 costs p1 =$10 per unit, and good x2 costs p2 =$9 per unit.How much of good x, does Johanna consume?Enter a numerical value below. You may round to the second decimal if necessary. (Partial quantities areallowed.)

Answered: Image /qna-images/answer/03d7e048-8a0a-445c-9d7b-0a7ca5a879f6.jpg

Johanna has / =$181 to spend on goods x1 and x2. Her utility function is given by U (21, 22) = 2 min{ax,, ba2} where a =3 and b-5. Good x costs p1 =$10 per unit, and good x2 costs p2 =$9 per unit. How much of good x1 does Johanna consume? Enter a numerical value below. You may round to the second decimal if necessary. (Partial quantiti allowed.)

Johanna has / =$181 to spend on goods x1 and x2. Her utility function is given by U (21, 22) = 2 min{ax,, ba2} where a =3 and b-5. Good x costs p1 =$10 per unit, and good x2 costs p2 =$9 per unit. How much of good x1 does Johanna consume? Enter a numerical value below. You may round to the second decimal if necessary. (Partial quantiti allowed.)

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 6QP

See similar textbooks

Similar questions

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?
Joe Bob from Workout Problem 4.12 has a cousin Don who consumes goods 1 and 2. Don thinks that 3 units of good 1 is always a perfect substitute for 2 units of good 2. Which of the following utility functions is the only one that would not represent Don's preferences? O Ux1, x2) = min{2x1, 3x2). O Uxq, x2) = 20x1+ 30x2 - 10,000. %3D O Ux1, x2) = 2x1 + 3x2 + 1000. %3D O Ux, x2) = 4x, + 12x, x2 + 9x²2. More than one of the above does not represent Don's preferences.
10
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.
Donna and Jim are two consumers purchasing strawberries and chocolate. Jim’s utility function is ?(?,?) = ?? and Donna’s utility function is ?(?,?) = ?2? where x is strawberries and y is chocolate. Jim’s marginal utility functions are MUx=y and MUy=x while Donna’s are MUx=2xy and MUy=x2. Jim’s income is $100, andDonna’s income is $150. What is the optimal bundle for Donna if the price of strawberries is $2 and the price of chocolate is $4?
1 Consider a consumer who consumes only two goods, 21 and z2. His utility function is u (21, 22) = In z1 + 2. where In represents the natural logarithm. 1.a Derive the consumer's MRS of good 1 for good 2 using calculus to calculate his marginal utility from z and his marginal utility from z2. 1.b If the price of z1 is $2 per unit and the price of z2 is $4 per unit, and the consumer's income is $100, What is the equation of this consumer's budget line? 1.c What are the optimal consumption choices, z and z5, for this consumer? Show your work.
A consumer with the following utility function U = xy? faces two constraints. The first is the normal budget constraint where he has GH¢150 and the price of x and y are both GH¢1. Also, the consumer has been issued 200 ration coupons by the government which he must use whenever he buys either x or y. It takes 2 coupons to buy an x and 1 coupon to buy a y (for example: to buy 3 units of x it would require GH¢3 or 6 coupons) (i) Write down the Lagrangian for this problem. (ii) Applying the steps of Kuhn-Tucker, find the optimal x and y. Identify which constraints, if any, are binding.
A consumer has a budget of $3000 in a given period, and wishes to buy two goods, X and Y, so as to maximise his utility. The price of good X is $5 and the price of good Y is $2, and his MRS is given by the formula 2Y/X. How many units of good X will he buy in that period?
Suppose the total utility function for the consumer who is consuming two goods, good x and good z is U(x, z) = ln(2x) + 2lnz. The consumer’s income is $16 and is faced with the prices of each unit of good x and good z. The price per unit of good x is $4 and the price per unit of good z is $1. How many units of good x and good z should the consumer consume so as to maximize his/her utility? Also, what will be the total utility earned from the consumption of that many units of good x and good z?
A consumer can consume two goods, A and B, and has the utility function U-15A1/281/2, The consumer's budget is $900, the price of good A is $15 per unit and the price of good B is $45 per unit. (Assume A is the horizontal axis good and B is the vertical axis good. Both goods are infinitely divisible, but round numerical answers to 2 decimal places as necessary) What is the consumer's marginal rate of substitution? What is the consumer's marginal rate of transformation? What is the formula for the consumer's budget constraint? What is the consumer's utility-maximizing bundle given the utility function and budget constraint? A B H
Suppose that the price of good X is $6 and the price of good Y is $2. You have $144 to spend and your preferences over X and Y are defined as: U(x,y) = x2/3y1/3 Calculate the marginal utility of X Calculate the Marginal Utility of Y What is the optimal Choice of X and Y given the PX = $6, PY = $2 and I = $144 If Income is increased to $150 calculate how the optimal choice of X and Y change
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