1. Rachel eats eggs and toast for breakfast and insists on having 3 pieces of toast for every two eggs she eats. a. Write down Rachel's utility function for eggs and toast. Derive her demand functions for eggs and toast. b. Predict what will happen to her consumption of eggs and toast if an income tax cut increases her income by 5%, ceteris paribus. Justify your prediction.

1. Rachel eats eggs and toast for breakfast and insists on having 3 pieces of toast for every two eggs she eats. a. Write down Rachel's utility function for eggs and toast. Derive her demand functions for eggs and toast. b. Predict what will happen to her consumption of eggs and toast if an income tax cut increases her income by 5%, ceteris paribus. Justify your prediction.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.1P

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A consumer has utility u(x,y) = x^4 y^2 where x is this year’s consumption, and y is next year’s consumption. She makes 600 dollars income this year and 720 dollars income the next year. There is also a bank where she can borrow money at the interest rate r=%50 and lend money (to the bank) at the interest rate r=%20 (of course, she will decide to borrow or lend this year and pay off her debt or receive her savings the next year). a. Should she borrow money from or lend to the bank this year? How much b. If her utility were u(x,y) = xy2 instead, re-solving (a), would she borrow money or lend? How much? c. If her utility were u(x,y) = x^c y^2, what should “c” be so that she ends up neither borrowing nor lending?
I NEED HELP WITH PART B! (a) A consumer has utility u(x,y,z) = ln(x) + 2ln(y) + 3ln(z) over the three goods, x,y and z and pz=1. Optimally she consumes 30 units of z. What is her income? How much money does she spend on x? (HINT: MUx = 1/x, MUy= 2/y, MUz = 3/z and remeber the "equivalent bang for the buck" condition). (b) Forget about (a). Suppose you have t= 29 hours in total to spend on 3 projects X,Y and Z to make some money. If you spend x hours on project X, you make 2 sqrt(x) dollars; If you spend y hours on project Y, you make 3 sqrt(y) dollars; If you spend z hours on project Z, you make 4sqrt(z) dollars; Writing down your "utility function" u(x,y,z) and the constraint, solve the utility maximization problem; what is the optimal amount of time to spend on x? on y? on z?
(a) A consumer has utility u(x,y,z) = ln(x) + 2ln(y) + 3ln(z) over the three goods, x,y and z and pz=1. Optimally she consumes 30 units of z. What is her income? How much money does she spend on x? (HINT: MUx = 1/x, MUy= 2/y, MUz = 3/z and remeber the "equivalent bang for the buck" condition). (b) Forget about (a). Suppose you have t= 29 hours in total to spend on 3 projects X,Y and Z to make some money. If you spend x hours on project X, you make 2 sqrt(x) dollars; If you spend y hours on project Y, you make 3 sqrt(y) dollars; If you spend z hours on project Z, you make 4sqrt(z) dollars; Writing down your "utility function" u(x,y,z) and the constraint, solve the utility maximization problem; what is the optimal amount of time to spend on x? on y? on z?
Eren’s two main hobbies are taking vacations overseas (V) and eating expensive meals (M). His utility function is given as: U(V,M) = V^2MLast year, the average price of taking a vacation overseas was US$200 and the average price of an expensive meal is $50. However, due to supply problems in Onions, the average price of an expensive meal rose to $75. The average price of a vacation did not change. His income, which is $1500, did not change. Suppose that the Department of Welfare wants to know how much should be given to Eren to offset his change un utility due to the price increase of an expensive meal. Calculate the compensative variation (CV).
Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Calculate the change in consumer surplus from consuming the expensivemeals considering the price change (Hint: you need to compare his optimalconsumption bundle before and after the price change to get the change in CS).
H2. when Saturday comes, what is the utility of doing your roommate’s request on Saturday under quasi-hyperbolic discounting (round your final answer to two decimal places)?
Only typed answer and don't use chat gpt and don't answer in table 2. Charlie consumes apples (A) and bananas (B). His utility function is . The price of apples is $1, the price of bananas is $2, and Charlie’s income is $40. The price of bananas suddenly falls to $1. (a) Before the price change, how many apples and bananas did Charlie consume? (b) After the price change, how many apples and bananas did Charlie consume? (c) If after the price change, Charlie’s income had changed so that he could only attain his original level of utility, how many apples and bananas would he have consumed? (d) What are the magnitudes of the price, substitution, and income effects for the consumption of bananas?
3) Joshua is a utility maximizer and likes ice cream. He likes vanilla ice cream, but wouldhappily switch to chocolate ice cream if offered 1 scoop of chocolate ice cream for everyscoop of vanilla ice cream he has to give up. He has $5 of income to spend on ice cream.If vanilla ice cream costs $1 per scoop and chocolate ice cream costs $2.5 per scoop,Joshua will consume ______ scoops of chocolate and ______ scoops of vanilla ice creamper day.A) 0; 5B) 5; 0C) 2; 0D) 0; 2E) None of the above.
Suppose Gregg consumer chocolate candy bars and oranges. He is given four candy bars and three oranges. He can buy or sell a candy bar for $2 each. Similarly, he can buy or sell an oranges for $1. If he has no source of income, draw the budget contraint and write the equation. What is the most he can spend, Y pon these goods?
Felice lives and works for two periods. In the first period, she earns 520 coconuts and in the second period, she earns 570 coconuts. In each period, she pays 20 coconuts in taxes.a. Suppose that Felice can save or borrow from a bank at the same interest rate of 10%. Suppose also that she likes to consume today 240 coconuts. Draw herbudget constraint including both intercepts, her endowment point including its coordinates, and use an indifference curve to show her optimal consumption point and its coordinates.b. Suppose that the government cuts taxes by 10 coconuts. What will the government have to do to taxes in the future period to meet its lifetime budget constraint?c. What is the effect of the government’s action on Felice’s lifetime wealth, budget constraint and endowment point? Show and explain.d. What is the effect of the tax cut on her current consumption and welfare? Does the Ricardian equivalence hold? Explain!e. Now suppose that the economy enters a recession, and some…
Suppose you are given the following information for a particular individualconsuming two goods, a and b: Pa = $5, Pb = $6, MUa = 100, MUb = 200, and income (m) = $200.a) Sketch the budget set. What is the slope of the Budget Line? What are maximal possibleconsumptions of a and b?b) What is the MRSab for the two goods?c) Is this person maximizing her utility? How can you tell?d) Should she consume more of good a or of b? Explain.e) Why can’t you tell what her optimal bundle is? Explain.
Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Calculate for the equivalent variation (EV) for the price change.