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- Depict utility function on a number line: U(x)=(x-6)^2 Indifference set around x-3 Lower contour set of x=5What are some key points about the utility-maximization modelUtility Maximization A consumer faces income constraints and has CES preferences of the following form: U(x, y) =x y Find the consumer’s demand for x as a function of prices and income
- Donald likes fishing (X1) and hanging out in his hammock (X2). His utility function for these two activities is u(x1, x2) = 3X12X24. (A) Calculate MU1, the marginal utility of fishing. (B) Calculate MU2, the marginal utility of hanging out in his hammock. (C) Calculate MRS, the rate at which he is willing to substitute hanging out in his hammock for fishing. (D)Last week, Donald fished 2 hours a day, and hung out in his hammock 4 hours a day. Using your formula for MRS from (c) find his MRS last week. (E) This week, Donald is fishing eight hours a day, and hanging out in his ham mock two hours a day. Calculate his MRS this week. Has his MRS increased or decreased? Explain why? (F) Is Donald happier or sadder this week compared to last week? Explain.Explain the derivation of the demand curve of a consumer using the indifference curve theory.A utility maximizing consumer with preferences u(x, y) - x2y1/2 allocates 60 dollars towards the purchase of goods x and y. Prices are py - 0.5 and px – 1. With the purchase of a discount card prices are py - 0.5 and px - 0.25. Calculate the maximum fee the consumer should pay to purchase this card. Provide an Indifference Curve and Budget Line Diagram to illustrate and quantify the Substitution Effect (a to b) and Income Effect (b to c) of this price change. Quantify all intercepts and intersections.
- Distinguish between cardinal and ordinal utilityDefine A consumer prefers a higher indifference curve to a lower one.Greg has the following utility function: u = x0.47x953. He has an income of $52.00, and he faces these prices: (p₁. p₂) = (1.00, 3.00). Suppose that the price of x, increases by $1.00. Calculate the equivalent variation for this price change.
- A consumer utility function is U=(x1,x2) Where X1 is the quantity of good 1 that is bought, X2 is the quantity of good 2 that is bought. The price of good 1 is $10 and the price for good 2 is $2. If the consumer's income is $100 what will the consumer's optimal utility level be? b. Using Lagrange multilplier method. optimise the utility function x0.25 y0.25 subject to the budget constraint 24=x/10+ysuppose a consumer consumes two goods x and y with utility function u=x^0.5+y^1.5, does the utility funciton exhibit diminishing marginal utility for (i) x (ii)y?For each of the following utility functions draw the indifference curve that passes through (1,1). Label at least three points on each curve and indicate the direction of increased preference: a) u(x1, x2 ) = 3x1 b) u(x1, x2 ) = x1 + 2x2 c) u(x1, x2 ) = x1+ logx2 d) u(x1, x2 ) = min (2x1, x2) e) u(x1, х2) %3D max (1, x2)