Question 3 (Demand). Carlos really likes pizza. His utility function for Little Caesar's (xi) and Woodstock's (x.) isgiven by:U(xi, x2) = x;+2x2The price of x,is $10 and Carlos spends $50 on pizza.a) Graph the demand curve for x1, with pi (the price of x) on the y-axis and x, on the x-axis. (Hint: Therewill be a range of prices where the demand for x, will be 0). Explain you graph.Page 2

The consumer's demand theory would result in the indifference curve analysis with the budget line.…

Answered: Question 3 (Demand). Carlos really…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Suppose a consumer's utility function is U(x₁,x₂)=x₁x₂. The price of Good 1 is 1, the price of Good 2 is 2, and his income is 40. 1st Question 3 On a graph, use blue ink to draw the consumer's budget line. (Use a ruler and try to make this line accurate.) Plot a few points on the indifference curve that gives him a utility of 150 and sketch this curve with red ink. Now plot a few points on the indifference curve that gives him a utility of 300 and sketch this curve with black ink or pencil.
Please help awnsering the following question. Thank you
U(x, y) = xayb A consumer maximises utility subject to a budget constraint M = Pxx+Pyy Where px is the price of good x, py is the price of good y and M is the budget available. a. Derive an expression for the marginal utility of x. Under what condition is the marginal utility diminishing. b. Derive an expression for the marginal utility of y. Under what condition is the marginal utility diminishing.
Suppose that the price of good X is $6 and the price of good Y is $2. You have $144 to spend and your preferences over X and Y are defined as: U(x,y) = x2/3y1/3 Calculate the marginal utility of X Calculate the Marginal Utility of Y What is the optimal Choice of X and Y given the PX = $6, PY = $2 and I = $144 If Income is increased to $150 calculate how the optimal choice of X and Y change
21. A consumer has a utility function defined over two goods X and Y. Let the quantity of Good X be x ≥ 0 and the quantity of Good Y be y ≥ 0. The utility function is given below: u(x, y) = xy + 2y. Assume that the consumer has income m and that prices are på and py. (a) Explain whether the preferences underlying this utility function satisfy completeness and transitivity. (b) Explain whether the preferences underlying this utility function satisfy monotonicity and convexity. (c) Find the consumer's Marshallian demands for Good X and Good Y at prices px > 0 and Py > 0. (d) Show that goods X and Y are normal goods and explain whether either good is a substitute for the other. (e) Assume that px 10, Py = 5 and m = 100. Suppose that px increases to px = 15, how much of the change in demand for Good X is via the substitution effect and how much is via the income effect? Note: You may assume an interior solution (i.e. x > 0 and y> 0). =
QUESTION 4 Linguini and Colette consume only éclair (x,) and profiterole (x2). Linguini has utility function UA = x4x4 and Colette has utility function UB = 2xfx. Linguini is endowed with 10 éclair (x,) and 3 profiterole (x), while Colette is endowed with 20 éclair (x,) and 9 profiterole (x2). (a) Draw an Edgeworth box with x, on the horizontal axis and x, on the vertical axis. Position Linguini on the bottom left corner and Colette on the top right comer. Indicate the total number of units of x, and x2. Label the endowment allocation. (b) Derive the equation of the contract curve, ie., find x(x). In your graph in (a), draw the contract curve.
1. Jan has the following utility function for broccoli: U(B) = 54B - 0.5B³ a) What is Jan's marginal utility function?
Suppose Al is currently consuming five movies and two concerts per month. If his utility function is given by U = 15MC, where Mrepresents the number of movies seen and C represents the number of concerts attended, Al's total utility is equal to: 75 15 150 10 30
Consider a consumer whose utility function is (screenshot) Assume the consumer has income $120 and initially faces the prices px=$1 and py=$1. How much x and y would they buy? Draw the budget constraint and the demands.
A consumer has a budget set aside for entertainment during the year, and they spend the budget on concerts and plays. The consumer has a strong preference for attending concerts over plays: the two activities are substitutes, but not very strong substitutes. Sketch the indifference curves for this consumer on a graph, with concert tickets on the vertical axis and play tickets on the horizontal axis. Briefly explain why the consumer might ultimately choose to purchase a large number of play tickets, even though they have a strong preference for concerts. Include a budget line on your graph to illustrate this case.
2. Suppose John's utility function is UX,Y) = 4/XY , where X is consumption of beer and Y is consumption of pizza. For this utility function, ( Calculus Kahuna say: MUx = 2\Y/X and MUy = 2\X/Y ) a) Find three different bundles: (X,Y) = (2, 4½), (2, 3), (4, 24) and find the utility they provide John. Plot the three bundles and connect them with an indifference curve. J-L. IIII -+-+- - -4-L 7-T-T-r הרד - דר -LJ-J-L- 1-L -LJ-J-I ---
2. Vibha consumes three goods X, (shirts), X, (food in pounds), and X, (shelter in square feet). 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?

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