2. Vibha consumes three goods X, (shirts), X, (food in pounds), and X, (shelter in squarefeet).Vibha's utility function is given by:U (X,, X, X,) = 5ln Xt 3ln X + 2ln X,where In (x) or log. (x) is the natural logarithm.Vibha's weekly income is $100.Let the price of X, = P, = $10, the price of X, = P, = $2, and the price of X, = P; = $4.What is the equation for Vibha's budget constraint?а.b.|How many shirts, pounds of food, and square feet of shelter, will Vibha consume,as a rational consumer?

Rational consumer always consumes bundle of goods which provides him maximum utility. when law of…

Answered: 2. Vibha consumes three goods X,…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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6. Consider a consumer with the utility function u(x,, x2) = In(x,) + x2 and the budget constraint p, x1 + P2X2 = m. Derive the consumer's demand functions for x, and x2.
= x 2 y. This Consider a consumer with the utility function U (x, y) = Vxy 글3글2-iy and MU, Vx = x? They have 1 function gives MU Va a budget of $60, and pr 1 and Py 2. Find optimal consumption of x and y.
6. A consumer has an expenditure function given by E = Ū(P+). When the consumer has an income of 100, it can reach a maximum utility of 20. The price of x increases by 3 and the consumer's income increases by 25. Are they better off or worse off than before the changes? Explain how you know. Full solution please
EXERCISE 5 Loise spends £20 on tea (T) and coffee (C). Her preferences for these goods can be described by the following utility function: ( , ). Suppose that one cup of tea costs £1.60 while one cup of Loise’s favourite coffee costs £4.00. Find Loise’s optimal consumption bundle. Provide both algebraic and graphical solution. Explain your reasoning. Discuss how Loise’s optimal consumption choice would change when her disposable budget changes. If the price of tea increases to £2.00 per cup, how should the price of coffee change so that Loise can be as well off as before this change in prices? Discuss the implications of the price change from c) on Loise’s optimal choice. In your discussion, include the analysis of the substitution and income effects as well as Loise’s demand for tea and/or coffee.
Suppose we are able to model the total utility function for the consumption of two goods, good x and good z. The utility function is structured as U(x, z) = 3x2 + z2 - 2xz. The consumer is faced with the prices of goods x and z. The price for each unit of good x and z is $1 each. The consumer has an income $1 (in thousands). How many units of each good should the consumer consume so as to maximize his/her utility?
Question 7 A consumer has a utility function 100-(x₁-4)4 -(x2-3)4 and a budget constraint of 9x1+3x2 <200. How much of good 2 do they consume?
4. John has a utility for the quantity of sandwiches, Xs, and quantity of burgers, Xp, that he consumes, represented by the following equation: U(X,X) = XX His income is Y = $24. The price of a sandwich changes from X, = $1 to X, = $4 while the price of a burger remains at X, = $6. Solve for the compensating variation and equivalent variation associated with this price increase.
Define the Marginal Rate of Substitution between two goods (X and Y).If a consumer’s preferences are given by U(X,Y) = X1/4Y 3/4, compute the consumer’s marginalrate of substitution as a function of X and Y. Calculate the MRS if the consumer has chosen toconsumer 12 units of X and 30 units of Y.
The utility function of a consumer is u = √x + 2y. (a) Calculate how much MRS of that consumer when x = 4. (b) If the consumer currently consumes 4 units of goods x and the price ratio of Px / Py = 1/4, then the consumer should increase or decrease the consumption of goods x?
A student has a lunch utility function U(S, P) 8S + 3P, where S is number of salads per month and P is number of pizzas per month. The price of a salad is $5, the price of a pizza is 8, and his monthly income for lunch is $80. a) Derive the equation representing the consumer's demand for Salad. Represent the demand for Salad graphically. b) The price of Salad goes up to $25 and the price of Pizza does not change. Compute and represent graphically the new equilibrium of the student. What can you tell about the substitution effect on Salad and pizza
3. You have an income of $24 per week and the only two goods you consume are apples (x1) and orange juice (x2). The price per apple is $4 and the price of a bottle of orange juice is $3. Suppose that your weekly optimal consumption bundle is 4 bottles of orange juice and 3 apples . a. Illustrate this in a graph using indifference curves and budget lines. Be sure to fully label the graph. b. Write down the conditions for utility maximization and relate this to the graph that you drew. c. Now suppose that the price of apples falls to $2, and I take enough money away from you such that you are just as well off as you were before, will you buy more of fewer bottles of orange juice? Explain why or why not in words and with a graph. (Hint: think about income and substitution effects
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.

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