2. A consumer has utility function и(х, у) — x+y for two goods, where x > 0 denotes the amount of X consumed and y>0 the amount of Y consumed. Each unit of X costs p dollars, each unit of Y costs q dollars, and the consumer has a budget for X and Y of M dollars. Use the Lagrange multipliers method to find the quantities x of X and y of Y the consumer will consume in order to maximize his utility subject to the budget constraint. M Show that x' +y' Hence find the optimal value, ^',of the Lagrange multiplier, simplify your expression as much as possible.

2. A consumer has utility function и(х, у) — x+y for two goods, where x > 0 denotes the amount of X consumed and y>0 the amount of Y consumed. Each unit of X costs p dollars, each unit of Y costs q dollars, and the consumer has a budget for X and Y of M dollars. Use the Lagrange multipliers method to find the quantities x of X and y of Y the consumer will consume in order to maximize his utility subject to the budget constraint. M Show that x' +y' Hence find the optimal value, ^',of the Lagrange multiplier, simplify your expression as much as possible.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.7P

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7. A consumer has preferences for coffee and pancakes that are complete, continuous, transitive, monotonic, and convex. At her current consumption bundle on the budget line, you could take away a maximum of 2 cups of coffee if you give her 5 extra pancakes without changing her utility. The price of a cup of coffee is $4, and the price of a pancake is $1. Assume you graph pancakes on the X-axis and coffee on the Y-axis. At the current consumption bundle, the bang per buck is higher for pancakes than coffee, and the consumer’s indifference curve is flatter than her budget line. a. True b. False Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
a. Suppose Fiona’s income is $100 per week, which she allocates between chocolates and books. Chocolates cost $2 each. Books cost $10 each if she purchases between 1 and 5 books. If she purchases more than 5 books in a week, the price falls to $5 for the 6th book and all subsequent books. Draw the budget constraint. Is it possible that Fiona might have more than one utility-maximizing solution? b. Confirm that if a consumer’s utility function is described by U = 2X + Y, and prices are px = 2 and py = 1, there is no unique utility maximizing solution regardless of income level. What does this tell you about X and Y as commodities? (Hint: draw a graph showing a budget constraint and indifference curve using the information provided.)
Mr Banda faces the following utility function from consuming nshima [X] and Rice [Y] U = 3XY 1 3 Mr Banda’s budget allocation for nshima and rice is K240. The price of nshima is K60 per Kg while that of Rice is K20 per Kg. A. How much nshima and rice should Mr. Banda consume to maximize his utility and What is the total utility at the optimum? b. What is the Lagrange multiplier? c. What will be the increase in utility when the budget allocation is increased to K241?
The utility derived by a consumer from the consumption of two commodities is given by the function U (A, B) = 0.5In (A) + 0.5 In (B) where A are the number of units of the first commodity consumed and B are the number of units of the second commodity consumed each month. A unit of the first commodity costs $8 and a unit of the second commodity costs $ 4 using the Lagrange multiplier method determine the optimal quantity of each of the commodities consumed each month given that consumer has $32 to spend on both commodities each month
Devon's utility function can be written as ?1^0.50?2^0.50, where ?1 is the quantity of hamburgers consumed and x2 is the quantity of milk shakes. His income is $2,400.00. 1) Hamburgers cost $8.00 each and the price of one milk shake is $4.00. If he is maximizing his utility, how much will Devon spend on hamburgers? $ 2)The price of hamburgers decreases to $7.37 each. Now, how much will Devon spend on hamburgers if he is maximizing his utility? $
Assume that you have a budget of Taka 4000 that can spend on two goods like: coke and burger. Suppose coke costs Taka 100 per unit and burger costs 400 per unit. Suppose also that your utility function is given by the equation U(B, C) = 20BC. Write your budget equation. What combination of coke and burger should you buy to maximize utility?
Question 2 David spends his budget on chocolate and chip. His utility function is given by ?(?1,?2)= 2?1?2, where ?1 is the number of chocolates he consumers per week, and ?2 is the number of chips he buys per week. A chocolate costs 10 SEK, and a chip costs 20 SEK. David’s weekly budge for consuming on these two goods is 120 SEK. (1) What is David’s budge line? Draw the budget line on a graph with chocolate amounts on the horizontal axis and chip amounts on the vertical axis. Write explicitly at which points budget line crosses the axis. (2) What is David’s marginal utilities for the two goods, respectively? What is his marginal rate of substitution between the two goods? (3) What is David’s optimal choice? Calculate the numerical answer for the optimal bundle. Also draw an indifference curve for David on the same graph as question(1) and show the optimal bundle.
Megan is a college student who consumes food and transportation. Last year, she consumed 90 meals and purchased 100 gallons of gasoline per month. Suppose that last year the price of a meal was $5 and the price of a gallon of gasoline was $2.23. However, this year, the price of a meal is $6 and the price of a gallon of gasoline is $3.92. As a result, Megan consumes 100 meals and 80 gallons of gasoline. For this example, assume Megan's utility this year is the same as her utility last year (and that her preferences have not changed). Calculate a Laspeyres cost-of-living index for Megan using 100 as the base for last year. In particular, the Laspeyres index for this year is nothing. (Enter your response rounded to two decimal places.)
Suppose Karpov also enjoys eating nuts and berries. His utility function is u(c1,c2)=min{c1+2c2,2c1+c2}u(c1,c2)=min{c1+2c2,2c1+c2} where c1c1 is nuts and c2c2 is berries. However, Karpov faces different prices to Magnus. The prices he faces for nuts and berries are 3 and 2 respectively. Given his income of 10, how many units of nuts and berries does he consume? At what prices will Karpov only consume nuts and no berries? And, at what prices will he only consume berries and no nuts? Find all price and income combinations where Karpov will choose to consume equal quantities of berries and nuts.
PLEASE HELP ME ANSWER IT AS FAST AS YOU CAN Dalal consumes only two goods for lunch and dinner: risotto (R) and lamb machboos (M). Dalal’s utility function isgiven by U(R,M) = R + 4M. Suppose that a risotto dish costs 3 KD and that a dish of lamb machboos costs 6 KD.Dalal has 300 KD a month to spend on her lunch and dinner meals. a. How many risotto and lamb machboos dishes will Dalal buy each month if she maximizes utility?Dalal’s brother, Jassem, wants to make her happier and is considering two options: giving her a 60 KD gift card that can only be spent on risotto from one of the Italian restaurants or giving her some cash money.If Jassem chooses to give Dalal the 60 KD risotto gift card:b. How many risotto meals can Dalal add to her optimal basket? c. What utility level will Dalal get given her income and the risotto gift card?Suppose that Jassem instead chooses the second option and promises Dalal to raise her income to the level thatensures making her as happy as the first…
1. Mary has $100 to spend on goods X and Y. The price of Y is pY = $2.50. Mary has wellbehaved preferences and two of her indifference curves are shown on the above graph along with sometangent points. **This is a graphical problem. You may visually estimate (eyeball) any quantities you need.You may need to locate additional tangencies. a) Suppose the price of X is $1.25. On the graph above, label Mary’s budget line as (BLA) and label Mary’soptimal consumption bundle as bundle A. b) Now suppose the price of X rises to $5. On the graph above, label Mary’s budget line as (BLB) and labelMary’s optimal consumption bundle as bundle B. c) Next find the Hicks Compensated Bundle. To do this, put your ruler on budget line BLB and move yourruler in a parallel fashion until it just touches the indifference curve through bundle A. Label this tangencyas bundle C and draw the line tangent line, along with appropriate || parallel marks, and label this line asthe compensated budget line BLC. Please…
Suppose that Lynn enjoys sugar in her coffee. She has very particular preferences, and she must have exactly three spoonfuls of sugar for each cup of coffee. Let C be the number of cups of coffee, and S be the number of spoonfuls of sugar. Also, let PC be the price of a cup of coffee. Suppose Lynn has $12 to spend on Coffee and Sugar. Also, the price of Sugar is $.20 per spoonful. Graph Lynn’s Price consumption curve for prices, PC = $.60, PC = $.90, and PC = $1.80. Please put the number of cups of coffee (C) on the horizontal axis, and the number of spoonfuls of Sugar (S) on the vertical axis. Be sure to graph each budget constraint associated with each price of Coffee, identify Lynn’s optimal bundle on each budget constraint, and make sure your graph is labeled carefully and accurately.