1. A consumer with the utility function U(x₁,x₂) = xx faces prices p₁ = 4, P2 = 5 and has an income of $200. For this consumer, holding prices fixed: a. Derive an expression for the Engel Curve for x₂. b. Plot this Engel curve. c. Holding p₁ and m fixed, plot this consumer's demand curve for x₂.
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- 1. A consumer with the utility function U(x₁,x₂) = xx faces prices p₁ = 4, P2 = 5 and has an income of $200. For this consumer, holding prices fixed: a. Derive an expression for the Engel Curve for x₂. b. Plot this Engel curve. c. Holding p₁ and m fixed, plot this consumer's demand curve for x₂.4. 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.2. Donald derives utility from only two goods, carrots (X) and donuts (Y). His utility function is as follows: U(X, Y) = XY. Donald has an income (M) of S120 and the price of carrots (Px) and donuts (PY) are both $1. a) Find the marginal utility that Donald receives from carrots (MUx) and from donuts(MUY) )
- 1. 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 px 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 p 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). = 15,2. Sally consumes two goods, X and Y. Her utility function is given by the expression U = 3XY². The current market price for X is £10, while the market price for Y is £5. Sally's current in come is £500. (a) Sketch a set of two indifference curves for Sally in her consumption of X and Y. (b) Write the expression for Sally's budget constraint. Graph the budget constraint and determine its slope. (c) Determine the X,Y combination which maximises Sally's utility, given her budget constraint. (d) Calculate the impact on Sally's optimum market basket of an increase in the price of X to $15. What will happen to her utility as a result of the price increase?2. Sally consumes two goods, X and Y. Her utility function is given by the expression U = 3XY². The current market price for X is £10, while the market price for Y is £5. Sally's current income is £500. (a) Sketch a set of two indifference curves for Sally in her consumption of X and Y. (b) Write the expression for Sally's budget constraint. Graph the budget constraint and determine its slope. (c) Determine the X, Y combination which maximises Sally's utility, given her budget constraint. (d) Calculate the impact on Sally's optimum market basket of an increase in the price of X to $15. What will happen to her utility as a result of the price increase?
- Considering the following Diagram of consumer equilibrium, answer the following questions. If consumer has $100 to spend on X and Y at Budget line DE, what are the prices of X and Y products. What combination of X & Y maximizes the consumer’s total utility at Budget line DE? Why a consumer has moved to point B on Budget line DE1 from Point A of Budget line DE? Derive the demand curve of X product. What is relationship between X and Y productsI need help with my homework assignment that i dont undertsand. Suppose a consumer has a utility function given by U(X,Y) = MIN(X, 2Y). The consumer has $90 to spend (M = $90). The Price of good Y is PY = $1. Using a graph, sketch the consumer’s demand curve for Good X. Make sure to identify three points on the demand curve. Make sure your graph is neat, accurate, and scaled properly.1. The consumer has the utility function u(x1, x2)= x1 0.5x2 1/2 with a price level of x1 is $2 and the price of good x2 is $2, and he has income by 100. Then, the price of item 1 drops to $1, then how much compensating and equivalent variations?
- 5. Julio who consumes two goods Food (F) and clothing (C) has a utility function given by U(F,C)= sqrt(F)C. The price of food is $3 and the price of clothing is $5 and Julio's weekly budget for food and clothing is $100. a. What is Julio's MRSFe (marginal rate of substiution of food for clothing) when utility is maximized? Explain. b. If Julio is at point where MRSFC= 1, where is that point relative to the utility maximzing bundle (show this in a diagram)? c. Can Julio change his bundle so as to increase his satisfaction and if so in what way? Explain fully 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 consumer has the following utility function: Ulx, y) = xy -y, *21 where x and y represents the quantities consumed of goods X and Y. y 20 What will be the substitution and income effects for X and Yassuming that the consumer attempts to maintain the same level of utility achieved before price of Y increased (that is, when price of Y was $1)? SEx= +0.5 IEx = -0.5 SE, = -0.25 IE- = -0.25 SEx= +0.293 IE = -0.293 SEy = -0.414 IE, = +0.414 SEr= +0.25 IE SE, = -0.75 IE, = -0.75 = -0.25 SEx= +0.414 IEx = -0.414 SEy = -0.293 IE, = -0.207 Income = $3 Px= $1, Py= $22. Consider a consumer who purchases two goods, x and y. The consumer’s utility function is U(x, y) = xy. Assume initially that the consumer’s income is $160, the price of x is Px= $8, and the price of y is Py= $1.a) Find the utility maximizing bundle of x and y.b) Find the total utility at the utility maximizing bundle.c) Now assume the price of x decreases to $4. Re-compute the values from part a) at the new price.
