10) Suppose that the utility function of an individual can be described as U(X,Y) = 4X + 2Y. For this utility function the MRS A) is always X*Y B) is always constant C) is always X/Y D) is always X+Y E) is always X-Y.
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10) Suppose that the utility function of an individual can be described as U(X,Y) = 4X +
2Y. For this utility function the MRS
A) is always X*Y
B) is always constant
C) is always X/Y
D) is always X+Y
E) is always X-Y.
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- If the utility function of an individual takes the form: U = U ( x 1, x2) = (x1 + 2) 2 (x2 + 3) 3 Where U is total utility, and x1 and x2 are the quantities of two commoditiies consumed: (a) Find the marginal-utility function of each of the two commodities (b) Find the value of the marginal utility of the first commodity when 3 units of each commodity are consumed.Kate’s utility function includes coffee (c) and sugar (s). She only consumes coffee and sugar together, and she only consumes in the ratio of one unit (cup) of coffee with two units (spoons) of sugar. Her utility function is What is her marginal utility of sugar if she has 4 cups of coffee and 6 spoons of sugar? Remember that unit are infinitely divisible (you can have parts of units). (a) 0 (b) 1 (c) ½ (d) 2Charlie's utility function is (1-a) U(xa, XB) = Ax“xr-) where A > 0 and a > 0
- For each of the following utility functions get the marginal utility of consumption of each of the goods. 1/2 1/2 (a) u(a,b) = a b (b) u(x, y) = x³/4y1/4 (c) u(a, b) = n(a) + In(x) (d) u(x, y) = ln(x) + ln(y) (e) u(a, b) = 2xa +Xb3) Oğuz has the utility function U(x1,X2) = x:*x2². (X: nuts, X2: berries). %3D a) If Oğuz has 25 units of nuts and 17 units of berries, the price of nuts is 2 and the price of berries is 1 liras, what would be the optimal consumption of Oğuz? b) Assume the prices change, so that nuts cost 1 and berries cost 3 liras. What is the new demand? In this change, What is the pure substitution effect? What is the income effect? c) In the change calculated in part (b), what is the pure substitution effect? d) In the change calculated in part (b), what is the income effect? In the change calculated in part (b), what is the endowment effect?Let u(x) be a utility function that represents the preferences of a household. We say that the function v(x) is a monotonic transformation of u if f(·) is a strictly increasing function and v(x) = f(u(x)). (a) Show that if v(x) is a monotonic transformation of u, it represents the same preferences. (b) Can you explain why taking a monotonic transformation of a utility function does not change the marginal rate of substitution? (c) What kind of preferences are represented by a utility function of the form U(x1,x2) = ? What about the function U(x1,x2) = 13x1+13x2?
- 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.Ice cream and cakes are perfect substitutes for a child, and 2 units of ice cream is always worth 3 units of cakes (however many ice creams or cakes she might have, she would be willing to give up 2 ice creams to get 3 more cakes to keep the same utility level) . (a) Write down a utility function u(x,y) that represents the child's preferences, where x is the number of ice creams and y is the number of cakes she has. (b) If the prices are px= 8 and py =5, and she has $140 to spend on the two goods this summer, what is her optimal bundle? (c) If the price of ice creams decreases slightly, down to px = 7, what happens to her optimal bundle in this case? Did it change "slightly" compared to (b)?1. A consumer has the utility function U(x,y) = 2x y' where x and y represent the quantity consumed of goods X and Y. a) Find the consumer's marginal rate of substitution of X for Y. For parts (b) and (c) assume that the consumer has $100 to spend on goods X and Y which have fixed prices of px=1 and py=3. Use the Lagrangian method to solve the consumer's optimization problem: b) What are the first order conditions of the Lagrangian. Assume the solution to the consumer's optimization problem is c) interior. Solve for the consumer's optimal consumption bundle for any prices and income.
- Anna has an income of 1000 euros and utility function U(x,y)=x²y³. The prices of the two goods are P₁=5 and Py-20. a) Define the budget constraint and represent it graphically. (1 Marginal utility and marginal rate of substitution Suppose an individual who derives utility u(x, y) from consuming a units of good X and y units of good Y. For each of the following utility functions, derive the marginal utility of good X, the marginal utility of good Y, and the marginal rate of substitution between X and Y. (A) u(x, y) = x+by¹/3 (B) u(x, y) = (xy) (C) u(x, y) = ax + xy + by² (D) u(x, y) = n(ax + y) 1 (E) u(x, y) = (x² + √y²) = 2ASAP 1. Consider a consumer with utility u(x1,x2) = .5lnx1 + .5lnx2 (b) Now, consider an equivalent representation of the above utility functionx51 x52 Does this utility function have the "increasing difference property"? Howabout the "strict increasing difference" property?
