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

See similar textbooks

Similar questions

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).
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?
Can you assist me with answering all parts of this question?
Peter's preferences over two goods, x and y, are represented by the utility function u(x, y) = y + 2x. a) Peter is currently consuming bundle A = (2,4) with 2 units of good x and 4 units of good y. Calculate his current level of utility from consuming this bundle. b) Write the expression the indifference curve representing Peter's current level of utility (i.e., the one you found in part (a). Next draw this indifference curve. c) By looking at the indifference curve you drew in part (b), answer the following questions: Does Peter like good x? Good y? Explain. What can you say about the marginal rate of substitution of good x for y, MRSxy? Is it positive? Negative? Constant? Increasing? Decreasing? Interpret/explain your answer in terms of the tradeoffs Peter is willing to make between goods to keep the same utility level. d) On the same graph you drew in part (b), draw the indifference curve for a utility level of 10. Plot and label in the graph bundles B = (1,2), C = (1,6), and D =…
Gino derives utility from only two goods, carrots (Qc) and donuts (Qd). His utility function is as follows:U(Qc,Qd) = (Qc)(Qd)The marginal utility that Donald receives from carrots (MUc) and donuts (MUd) are given as follows:MUc = Qd MUd = QcGino has an income (I) of £120 and the price of carrots (Pc) and donuts (Pd) are both £1. - suppose a lump sum tax of the same dollar amount, of a 1 pound tax per unit on donuts, is levied on Gino. what is Gino's utility maximising market basket? - why would Gino prefer a per unit tax over the lump sum tax, or vice versa, or why is he indifferent between the two taxes.
Question #1: Solving for Income and Substitution Effects Fernando loves to garden and purchases garden gnomes (G) and garden hoes (H). Fernando has the following utility function, U(G,H) = G4 H3/4. Suppose that Fernando has an income of $830 and the initial price of a garden gnome (PG) is equal to $15 and the price of a garden hoe (PH) is equal to $10. (a) Use the Lagrangian Method to solve for the optimal basket of goods. (b) Calculate the utility that Fernando receives if he consumes the optimal basket. (c) Suppose that the price of garden gnomes rises to $25 per unit. Use the Lagrangian Method to solve for the new optimal basket of goods. Find the total effect of the price change on the consumption of each good. (d) Find the substitution effect of the increase in the price of garden gnomes on the consumption of each good. (e) Find the income effect of the decrease in the price of garden gnomes on the consumption of each good. Are the goods normal or inferior? Briefly explain your…
1. Joe Bob has a utility function given by u(x1, x2) = x + x² + 2x1x2. (a) Compute Joe Bob's marginal rate of substitution. (b) Joe Bob's cousin, Al, has a utility function given by v (1, 2) = x₁ + x2. Compute Al's marginal rate of substitution. (c) Do u (x1, x2) and v(x1,x2) represent the same preferences?
Andy purchases only two goods, apples (a) and kumquats (k). He has an income of $1,000 and can buy apples at $10 per pound and kumquats at $10 per pounc utility function is U(a, k) = 4a + 3k. What is his marginal utility for apples and his marginal utility for kumquats? Andy's marginal utility for apples (MU) is MU, = and his marginal utility for kumquats (MU) is MU, = (Enter your responses as whole numbers.) What bundle of apples and kumquats should he purchase to maximize his utility? Andy should consume apples and kumquats. (Enter your responses as whole numbers.) React tv MacBook Air 80 DI DD F1 F2 F3 F5 F6 F7 F8 F9 F10 @ #3 $ % & 1 2 4 7 8. 9 Q W E Y { A S F G H. J C V M ption command command option .. .. V B