1. Ivan has the following utility function U(x,y) = In(x) + y where x represents food and y represents other goods. Ivan has £10 to spend on these two goods. Suppose that the initial price of x (Px) is £1 per unit, and that of y (Py) is £1 per unit. (i) What is the Marginal Rate of Substitution at the point X = 10, Y = 10? What is Ivan's optimal bundle? Note that MUx = 1/x and MUy=1. (ii) Explain the method above for finding out Ivan's optimal consumption bundle. To do that, consider what happens when the consumption choice changes.

1. Ivan has the following utility function U(x,y) = In(x) + y where x represents food and y represents other goods. Ivan has £10 to spend on these two goods. Suppose that the initial price of x (Px) is £1 per unit, and that of y (Py) is £1 per unit. (i) What is the Marginal Rate of Substitution at the point X = 10, Y = 10? What is Ivan's optimal bundle? Note that MUx = 1/x and MUy=1. (ii) Explain the method above for finding out Ivan's optimal consumption bundle. To do that, consider what happens when the consumption choice changes.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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2. Sam's is interested in two goods, X and Y. His indirect utility function is U* = M px-0.7 py0.7-1. ( same as U* = M /(px0.7 py1-0.7 ) ) where M is Sam's income, and px and py denote respectively the price of good X and the price of good Y. Sam's market demand function for good X is X*=0.7M/px . Find the absolute value of the change in Sam's consumers surplus if the price of good X rises from 1 to 8 dollars due to a per-unit tax imposed by the government, assuming his income is M=533 and price of good Y is equal to 4.
Sarge's utility function is U(X1,X2)= X1*X2. If his marginal rate of substitution (MRS) is 3 and he is currently consuming 36 units of good 2, how many units of good 1 is he consuming? [A] Please put your answers in numerical values with no comma or decimal places.
3. The utility that Elena receives by consuming food F and clothing C is given by U(F, C) = FC + F. Food costs £1 per unit, and clothing costs £2 per unit. Elena's income is £22. MUF = C+1 and MUc = F. (i) Define the term Marginal Rate of Substitution (MRS) (ii) Find the utility maximizing values of C and F for the numerical values given above (Hint: You can assume interior solution). (iii) Now suppose that price of C and Elena's income remain unchanged at £2 per unit and £22, respectively, while the price of F varies. Find the equation of the demand for F as a function of the unit price of F (PF).
c Serpil's utility function is U(B,C)= B · C , where B = veggie burgers per week and C = packs of cigarettes per week. a) What is her marginal rate of substitution if veggie burgers are on the vertical axis and cigarettes are on the horizontal axis? b) Serpil's income is $120, the price of veggie burger is $2, and that of a pack of cigarettes is S1. How many burgers and how many packs of cigarette does Serpil consume to maximize her utility? Illustrate your answers in a graph.
Monica consumes only goods A and B. Suppose that her marginal utility from consuming good A is equal to 1/A, and her marginal utility from consuming good B is 1/B. Assume the price of A is $0.50, the price of B is $4.00, and Monica's income is $120.00. Assume A is on the x axis. At a bundle, A=1, B=2, Monica's MRS is ___________. At this bundle, Monica should a) buy more A and less B b) buy more B and less A Monica should optimally buy ________ units of good A and _______ units of good B.
Suppose an individual is currently spending all of their income on a bundle of books and pizza, but they are not sure whether the bundle maximizes their utility. Assume the individual has a strictly diminishing marginal rate of substitution over these two goods. At their current bundle of books and pizza, the individual's marginal utility from consuming books is 6 utils and their marginal utility from consuming pizza is 3 utils. If the current price of a book is $12 and the price of a pizza is $7, which of the following statements must be true: A. The individual can increase their utility by consuming more books and less pizza B. The individual is maximizing their utility C. The individual can increase their utility by consuming more pizza and fewer books
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
5. Jonas purchases only two goods, starfruit (S) and kiwi (K). He has an income of $60 and can buy starfruit at $2 per pound and kiwi at $3 per pound. His utility function is U(S,K)=3S+4K. That is, his (constant) marginal utility for starfruit is 3 and his marginal utility for kiwi is 4. What bundle of starfruit and kiwi should he purchase to maximize his utility? Why?
A KU student maximizes his sporting utility by playing Golf (G) and Tennis (T). His function is given as: U(G,T) = G + T Graphically characterize the student’s indifference curve. What is the Marginal Rate of Substitution between Golf and Tennis What is the behaviour of the Marginal Rate of Substitution for these type of goods.
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4. Use the following information to calculate Wren's optimal bundle and his resulting utility: IC:U(x,y) = x0.5, 0.5 Px = 1, Py = 4, m = 48