not use ai please Bonus Question (Optional w/ Extra Points)Consider a simple utility function of the form: U(x, y) = xªy¹-a.=a) Solve the expenditure minimization problem and use your solution to show that theexpenditure function for this person is E(px, Py, u) K¹uppy, where K is someparameter in terms of a, and u is the threshold utility level in the expenditure mini-mization problem.b) Compute the Hicksian demand function for good x.

Part (a) Expenditure Minimization Problem Part (b) Hicksian Demand for Good xThe Hicksian demand…

Answered: Bonus Question (Optional w/ Extra…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.13P

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Question: How We Can Check Convexity And Monotonicity Of The Utility Function. How we can check convexity and monotonicity of the utility function.
Mariah consumes music downloads (M) and concert tickets (C). Her utility function is giveh by U = 0.5M? + 2C². a. Using calculus, what is the marginal utility of music downloads? b. Using calculus, what is the marginal utility of concert tickets? Write the equation for the MRSMC (i.e., the MRS of C for M; M is increasing, C is С. decreasing). d. Would the bundles of (M = 4 and C = 1) and (M = 2 and C = 2) be on the same %3D %3D %3D %3D indifference curve? How would you know? e. Calculate the MRSMC when M = 4 and C =1 and when M = 2 and C = 2. Explain why the %3D %3D values of MRSMC differ across these two bundles. f. Based on your answers above, are Mariah's indifference curves convex? Explain using the values calculated. er this
he Calculus of Utility Maximization and Expenditure Minimization -End of Appendix Problem uppose that there are two goods, X and Y. The price of X is $2 per unit, and the price of Y is $1 per unit. There are two onsumers, A and B. The utility functions for the consumers are UA(X,Y)= X05.05 UB(X,Y)= X0.8y0.2 Consumer A has an income of $100, and Consumer B has an income of $300. Using Lagrangians, solve for the optimal bundles of goods X and Y for both consumers A and B. a. The optimal bundle for consumer A is X = 25 and Y* = 50 - b. The optimal bundle for consumer B is X = 120 and Y* = 60
Would you expect total utility to rise or fall with additional consumption of a good? Why?
Law of equi marginal utility is an important law of cardinal utility analysis. Explain this law with the help of its assumptions. Furthermore, there is a relationship between total and marginal utilities where they both pass through different stages when the consumer continues his or her consumption regularly. Elaborate.
Q50 Marginal utility analysis predicts a downward-sloping demand curve for good X because... a. As PX rises, the consumer increases purchases of X such that MUX/PX is equal to MU/P for all other products. b. As PX falls, the ratio MUX/PX becomes smaller, causing the consumer to purchase more of good X. c. As PX falls, the consumer increases purchases of X until MUX/PX is equal to MU/P for all other products. d. Utility-maximising consumers equate the marginal utility received for each product consumed. e. All demand curves are downward sloping, regardless of the behaviour of consumers.
Exercise Suppose the utility function of a person consuming two commodities X and Ywith income Birr 600 is given by U = 2 X 06Y 04 If the per unit price of X is Birr 20 and per unit price of Y is Birr 40 a) What is the utility maximizing level of consumption of X & Y ? b) Find the MRSyy at the optimum ?
A consumer’s weekly income is $5000, the price of a cell phone is $1250, and the price of a watch is $500. What quantity of cell phones and watches will maximize the consumer’s utility if they spend their entire weekly income on cell phones and watches? Explain your answer using marginal analysis. 1A. Suppose that this consumer’s income elasticity for watches is 5.4. what does this indicate about watches? If the cross-elasticity calculates to 0.8 what does this indicate about the relationship between watches and cell phones? 2 Determine and explain the Profit Maximization output of a perfectly competitive firm
Please no written by hand and no emage Consider a consumer that consumes 2 teaspoons of sugar with each cup of coffee. For each cup of coffee with sugar the consumer gains 10 utils.a) Write down the utility function that gives the total utility if the consumer consumes S teaspoons of sugar and C cups of coffee. The consumer has assigned £7 per week to be spent on drinking coffee with sugar. The current price of coffee is £0.50 per cup and each spoon of sugar costs £0.10. b) Calculate the optimal weekly consumption bundle for this consumer.c) Does the consumer view C and S as complements or substitutes?
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.
Illustrate and explain how consumer equilibrium is achieved using the indifference curve?Discuss how the demand elasticity of a product changes? Give examples.
Donald likes fishing (X1) and hanging out in his hammock (X2). His utility function for these two activities is u(x1, x2) = 3X12X24. (A) Calculate MU1, the marginal utility of fishing. (B) Calculate MU2, the marginal utility of hanging out in his hammock. (C) Calculate MRS, the rate at which he is willing to substitute hanging out in his hammock for fishing. (D)Last week, Donald fished 2 hours a day, and hung out in his hammock 4 hours a day. Using your formula for MRS from (c) find his MRS last week. (E) This week, Donald is fishing eight hours a day, and hanging out in his ham mock two hours a day. Calculate his MRS this week. Has his MRS increased or decreased? Explain why? (F) Is Donald happier or sadder this week compared to last week? Explain.

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