Suppose Lan's utility function is U₁(x,y) =x₁y₁¹⁰ and Dan's utility function is Up(x,y) =xD³yD³, where x; and y; denote respectively the amount of good X and of good Y consumed by person i, i=L, D. A total of 44 of each good is available and it is to be divided efficiently between Lan and Dan. How many units of good Y should Lan get if we give Dan 14 units of good Y such that the allocation is efficient?

Suppose Lan's utility function is U₁(x,y) =x₁y₁¹⁰ and Dan's utility function is Up(x,y) =xD³yD³, where x; and y; denote respectively the amount of good X and of good Y consumed by person i, i=L, D. A total of 44 of each good is available and it is to be divided efficiently between Lan and Dan. How many units of good Y should Lan get if we give Dan 14 units of good Y such that the allocation is efficient?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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…
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Please provide full derivation, and 5. Casper consumes cocoa and cheese. Cocoa is sold in an unusual way. There is only one supplier, and the more cocoa you buy from him, the higher the price you have to pay per unit. In fact y units of cocoa will cost Casper y2 dollars. Cheese is sold in the usual way at a price of 2 dollars per unit. Casper's income is 20 dollars and his utility function is U(x, y)=x+2y, where x is his consumption of cheese and y is his consumption of cocoa. a. Sketch Casper's budget set and shade it in. b Sketch some of his indifference curves and label the point that he chooses. c. Calculate the amount of cheese and the amount of cocoa that Casper demands at these prices and this income.
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…
1.2 Ann and Bob each own 10 bottles of beer and, altogether, they own 20 bags of peanuts. There are no other people and no other goods in the economy, and no production of either good is possible. Using a to denote bottles of beer and y to denote bags of peanuts, Ann's and Bob's preferences are described by the following utility functions: UA (XA, YA) = TAYA and UB (XB, YB) = 2xB+ YB. In each of the following cases, determine the market equilibrium price ratio and allocation and depict the equilibrium in an Edgeworth box diagram. (a) Bob owns 20 bags of peanuts and Ann owns no peanuts. (b) Bob owns 15 bags of peanuts and Ann owns 5 bags. (c) Ann owns 20 bags of peanuts and Bob owns no peanuts.
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5) A consumer of two goods, good 1 and good 2, has a utility function u (X1, X2) = x1 0,6. X2 0,4, where x denotes units of good 1 and X2 units of good 2. The price of good 1 is 5 euros And the price of good 2 is 3 euros per unit and the consumer’s income is 150 euros. Suppose that only the price of good 1 changes and that the new price is p, ‘ = 2. Then the demand function of good 1 that is derived from the utility function is Choose one: A) X1= 0.6m/p1 B) X1= 6m/p1 C) X1= 4m/p1 D) X1= 0.4m/p1 E) Not defined
A, B, C