Joe Bob from Workout Problem 4.12 has a cousin Don who consumes goods 1 and2. Don thinks that 3 units of good 1 is always a perfect substitute for 2 units of good2. Which of the following utility functions is the only one that would not representDon's preferences?O Ux1, x2) = min{2x1, 3x2).O Uxq, x2) = 20x1+ 30x2 - 10,000.%3DO Ux1, x2) = 2x1 + 3x2 + 1000.%3DO Ux, x2) = 4x, + 12x, x2 + 9x²2.More than one of the above does not represent Don's preferences.

We know that utility function of perfect substitute is the form of straight line equation…

Answered: Joe Bob from Workout Problem 4.12 has a…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Given the utility function U (x1, x2) = x³x2.7 select all that are true. a) 30% of the budget is spent on good 1. ○b) V (p, I) = 30.370.7 I 10 P1P2 c) If P2 = 2 and I = 60, then $18 is spent on good 21. d) If P1 = 9, P2 = 2, and I = 60 then the consumer enjoys 1.81 utils of utility. e) Half the budget is spent on good 1 and the other half is spent on 2.
Andrea has a budget of £21 to spend on toothbrushes and tooth paste. He does not receive any utility from owning a toothbrush, but for the consumption of every tube of tooth paste he gains a utility of 2 utils – but only if he owns a tooth brush. Without a tooth brush, Andrea gains no utility from consuming tooth paste. In addition, after consuming 10 tubes of tooth paste, a toothbrush needs to be replaced, i.e., Andrea needs to buy a new one. The current price of tooth brushes on the market is £5 and the current price for tooth paste is £1 per tube. Assume that Andrea aims to maximise consumer surplus. wwwwwww a) In a graph, draw total utility as a function of number of toothpaste tubes, assuming that Andrea buys 1 tooth brush. b) How many tubes will Andrea buy if he wants to maximise consumer surplus, assuming that Andrea can buy any amount of tooth brushes? What is Andrea's total consumer surplus? c) How many tubes will he buy if the current price is £0.50 per tube? d) Find Andrea's…
Problem 2 Suppose that John's preferences over meat (M) and vegetables (V) are represented by the following utility function U(M,V) = a ln(M) + (1 − a) ln(V) where 0 < a < 1. ¹No claim of realism is made for the numbers in this example. 1 (a) Write down the Lagrangian for John's optimization problem. (Recall that John max- imizes utility given an income, I, and prices på and på for the goods.) (b) Solve for John's optimal consumption bundle (M*, V*) (as a function of income and prices) using the Lagrangian method. = (c) Suppose a = . Suppose also that John has income I = 1 and pv 2. What is the value of John's optimal happens if John's income doubles to I = 400? 200 and faces prices p consumption bundle? What =
Andrea has a budget of £21 to spend on toothbrushes and tooth paste. He does not receive any utility from owning a toothbrush, but for the consumption of every tube of tooth paste he gains a utility of 2 utils – but only if he owns a tooth brush. Without a tooth brush, Andrea gains no utility from consuming tooth paste. In addition, after consuming 10 tubes of tooth paste, a toothbrush needs to be replaced, i.e., Andrea needs to buy a new one. The current price of tooth brushes on the market is £5 and the current price for tooth paste is £1 per tube. Assume that Andrea aims to maximise consumer surplus. a) In a graph, draw total utility as a function of number of toothpaste tubes, assuming that Andrea buys 1 tooth brush. b) How many tubes will Andrea buy if he wants to maximise consumer surplus, assuming that Andrea can buy any amount of tooth brushes? What is Andrea's total consumer surplus? c) How many tubes will he buy if the current price is £0.50 per tube? e d) Find Andrea's…
Alexi has a budget of $21 to spend on toaster and breads. He does not directly gain any utility from owining a toaster but for every slice of toasted bread he consumes he gain 2 units of utility, that is if he owns a toaster. Without the toaster, he gain 0 units of utility from consuming plain bread. Suppose the toaster has inferior quality and will break after toasting only 10 slices, then Alexi needs to buy a new one. The current market price for cheap toaster is $5 and the price for a single slice of bread is $1. Assume that Alexi aims to maximize consumer surplus. Find Alexi's income-consumption curve for slices of bread for incomes between $0 and $21, assuming a price of $1 per slice.
The price of good "a" is $5 and the price of good "b" is $15. If the marginal utility of good "a" is 20 then the marginal utility of good "b" must be ________ to have an optimum combination of goods purchased. 80 20 60 4

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