3. Consider the following utility function: U = 5 x1 + 2 x2 Also consider the following bundles: A=(6, 6) B=(8, 4) C=(4,11) D=(7, 9) E=(9, 3) If x1=20, how much of x2 does the consumer has to consume to obtain a utility level of 150? 50 300 170 25
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3. Consider the following utility function: U = 5 x1 + 2 x2 Also consider the following bundles: A=(6, 6) B=(8, 4) C=(4,11) D=(7, 9) E=(9, 3) If x1=20, how much of x2 does the consumer has to consume to obtain a utility level of 150?
50
300
170
25
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- 1. Pindyck and Rubinfeld (2018) Chapter 4 Appendix, Exercise #5 Jae has the following utility function: U(X,Y)= 20X+ 80Y – X² – 2Y?, where X is consumption of CDs, with a price of $1, and Y is consumption of movie videos, with a rental price of $2. Jae plans to spend $41 on both forms of entertainment. Determine the number of CDs and video rentals that will maximize Jae's utility. а.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…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.
- 5. What kind of preferences are represented by a utility function of the form u(x1, x2) = x1 + V*2? Is the utility function v(x1, x2) = xỉ + 2x1Vx2+x2 a monotonic transformation of u(x1, x2)? 6. Consider the utility function u(x1, x2) = Vx1x2. What kind of pref- erences does it represent? Is the function v(1, x2) transformation of u(x1, x2)? Is the function w(x1, x2) = xỉx, a monotonic transformation of u(x1, x2)? = x²x2 a monotonicQ6) Utility Ratio and Consumption Maximization A consumer downloads 3 movies and 4 apps per week. Suppose the price is $2 per movie and $2 per app, and the marginal utility for this consumption level is 6 for a movie and 8 for an app. Instructions: Round your responses to one decimal place. a. Calculate, show the formula, marginal utility per dollar. ..Per movie ......Per app b. Is this optimal consumption? c. If not, how should they change their consumption to maximize?Anatoly's marginal utility for DVDS (D) is MU X and his marginal utility for Xbox games (X) is MUx D. Anatoly's income is $120, the price of a DVD is $20.00, and the price of an Xbox game is $10.00. How many DVDS and Xbox games does Anatoly consume to maximize his satisfaction? Anatoly consumesDVDs andXbox games. (Enter your responses using integers.)
- 14. Consider the following utility function: U(x, y) = xy+x with MUx = y+1 and MUy = x.As the consumer buys more x, the marginal utility of x:(a) Diminishes(b) Remains constant(c) IncreasesQUESTION 12 The relationship between the marginal utility that George gets from eating a bag of cookies and the number of bags he eats per month is as follows: Bags of Cookies Marginal Utility 1 2 3 4 5 6 20 16 12 8 4 0 George receives 2 units of utility from the last dollar spent on each of the other goods he consumes. If cookies cost $4 per bag, how many bags of cookies will he consume per month if he maximizes utility?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.
- A consumer buys Bread (B) and Milk (M) each week at price of 20 and 16 respectively. Suppose that the consumer's current consumption of Bread and Milk is giving him MUBread = 80 and MUMilk = 70. Is the consumer buying the utility-maximizing combination of bread and milk? If not, how should he reallocate his expenditures between the two goods to maximize utility? Draw diagram and explain.3. Suppose Mary enjoys Pepsi and Coke according to the functionU(P;C) = 4C + 5P. What does her utility function say about her MRS of Coke for Pepsi? What do her indi§erence curves look like? What type of goods are Pepsi and Coke for Mary? If Pepsi and Coke each cost $1 and Mary has $20 to spend on these products, how many units of each product should she buy in order to maximize her utility? Show this utility maximiz- ing combination combination of Pepsi and Coke on the graph. how would her consumption and utility maximizing bundle of Coke and Pepsi change if the price of Coke decreases to 50 cents. 4. Vera is an impoverished graduate student who has only $100 a month to spend on food. She has read in a government publication that she can assure an adequate diet by eating only peanut butter and carrots in the Öxed ratio of 2 pounds of peanut butter to 1 pound of carrots, so she decides to limit her diet to that regime. a) If peanut butter costs $4 per pound and carrots cost $2 per…3) Suppose Joe's utility for lobster (L) and soda (S) can be represented as U =10.5 50.5 MUL=0.5 L -0.5 s0.5, MUs=0,5 L0.5 s-0.S. Joe walks into a restaurant with $72. Lobsters cost $18 each and sodas cost $2 each. How much lobster and soda will Joe consume if he intends to spend all his money? (There are no tax and no tips.)