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2. Find the maximum of the following utility functions with respect to X = x2 (120-40...
1. Consider the following utility functions (a) For each of these utility functions: i. Find the...
1. Consider the following utility functions (a) For each of these utility functions: i. Find the marginal utility of each good. Are the preferences mono- tone? ii. Find the marginal rate of substitution (MRS) iii. Define an indifference curve. Show that each indifference curve (for some positive level of utility) is decreasing and convex. (b) For the utility function u2(x1, x2), can you find another utility function that represents the same preferences? Find the relevant monotone trans formation f(u) (c)...
What are the marginal utilities of x1 and x2 given the following utility functions, then find...
What are the marginal utilities of x1 and x2 given the following utility functions, then find the MRS: U(x1, x2) = 4 x1 + 8 x2 U(x1, x2) = (x1 + 2)(x2 + 1) Example. To find the marginal utility for x1, think about how a 1 unit increase in x1, keeping all else constant, will change the amount of utility U. Once you have the marginal utilities for both, you can calculate the MRS.
1. (20 points) Mac has utility over x; and x2 given by u(x1, x2) = min...
1. (20 points) Mac has utility over x; and x2 given by u(x1, x2) = min . If P. = $1. P. = $1. and I = $100. find the value of xı* (Hint: This is Leontief utility, the kind with right-angled indifference curves) 2. (10 points) If P, = $4, P2 = $2, and I = $20, and my utility is given by u(x1, x2) = 4x1 + 3x2, find x* (Note: I'm asking for optimal consumption of Good...
6.] For the following utility functions, find consumer demand as a function of prices and income...
6.] For the following utility functions, find consumer demand as a function of prices and income for both goods [i.e. find x (p v.p2,m) and x2(p,p,m)]. You can assume that preferences are smooth and convex and that you are at an interior optimum. (For extra practice, you can try finding the consumer demand for the utility functions above.) A. u(x,, B. u(xi, x) = 1089 + xi
Suppose a consumer has a utility function U(x1, x2) = Inxi + x2. The consumer takes...
Suppose a consumer has a utility function U(x1, x2) = Inxi + x2. The consumer takes prices (p1 and p2) and income (I) as given. > 1. What is special about P2 1) Find the demand functions for and x2 assuming these demand functions? Are both goods normal? Are these tastes homothetic? 2) Now find the demand functions for x1 and x2 assuming-<1. You probably P2 assumed the opposite above, so now will you find something different. Explain 3) Graph...
Suppose a consumer has a utility function U (x1,x2) = Inxi + x2. The consumer takes...
Suppose a consumer has a utility function U (x1,x2) = Inxi + x2. The consumer takes prices (p1 and p2) and income (I) as given 1) Find the demand functions for x1 and x2 assuming -> 1. What is special about Р2 these demand functions? Are both goods normal? Are these tastes homothetic? <1. You probably P2 2) Now find the demand functions for x1 and x2 assuming assumed the opposite above, so now will you find something different. Explain....
Lorelai's choice behavior can be represented by the utility function u(x1, 2) 0.9n(x)0.1x2. The prices of...
Lorelai's choice behavior can be represented by the utility function u(x1, 2) 0.9n(x)0.1x2. The prices of both xi and x2 are $5 and she has an income of $40. 1. What preference does this utility function represent? (Hint: the utility is function is not linear, but at least linear in good x2) 2. Drawinwg indifference curves: you can copy down the graph on your paper using econgraphs. Set the preferences and parameters accordingly as given in the question. Click on...
Lorelai's choice behavior can be represented by the utility function 11(xi, X2) = 0.91n(xi) + 0.1x2...
Lorelai's choice behavior can be represented by the utility function 11(xi, X2) = 0.91n(xi) + 0.1x2 The prices of both x and x2 are $5 and she has an income of $40. 1. What preference does this utility function represent? (Hint: the utility is function is not linear, but at least linear in good x2.) 2. Drawinwg indifference curves: you can copy down the graph on your paper using econgraphs. Set the preferences and parameters accordingly as given in the...
For the following utility functions, a. Find the marginal rate of substitution. b. Derive the equation...
For the following utility functions, a. Find the marginal rate of substitution. b. Derive the equation for the indifference curve where utility is equal to a value of 100. c. Plot the indifference curve where utility is equal to a value of 100. (1) u(x1, x2) = x1x2; (2) u(x1, x2) = x1x2 + 10x2; (3) u(x1, x2) = x12 + x2
1. Consider the utility function: u(x1,x2) = x1 + x2. Find the corresponding Hicksian demand function....
1. Consider the utility function: u(x1,x2) = x1 + x2. Find the corresponding Hicksian demand function. 2. For each of the three utility functions below, find the substitution effect, the income effect, and the total effect that result when prices change from p =(2, 1) to p' = (2,4). Assume the consumer has income I = 20. (a) Before doing any calculation, make an educated guess about the relative magnitude of the three substitution effects and the three income effects...
1. Consider the following utility functions (a) For each of these utility functions: i. Find the marginal utility of each good. Are the preferences mono- tone? ii. Find the marginal rate of substitution (MRS) iii. Define an indifference curve. Show that each indifference curve (for some positive level of utility) is decreasing and convex. (b) For the utility function u2(x1, x2), can you find another utility function that represents the same preferences? Find the relevant monotone trans formation f(u) (c)...
1. (20 points) Mac has utility over x; and x2 given by u(x1, x2) = min . If P. = $1. P. = $1. and I = $100. find the value of xı* (Hint: This is Leontief utility, the kind with right-angled indifference curves) 2. (10 points) If P, = $4, P2 = $2, and I = $20, and my utility is given by u(x1, x2) = 4x1 + 3x2, find x* (Note: I'm asking for optimal consumption of Good...
6.] For the following utility functions, find consumer demand as a function of prices and income for both goods [i.e. find x (p v.p2,m) and x2(p,p,m)]. You can assume that preferences are smooth and convex and that you are at an interior optimum. (For extra practice, you can try finding the consumer demand for the utility functions above.) A. u(x,, B. u(xi, x) = 1089 + xi
Suppose a consumer has a utility function U(x1, x2) = Inxi + x2. The consumer takes prices (p1 and p2) and income (I) as given. > 1. What is special about P2 1) Find the demand functions for and x2 assuming these demand functions? Are both goods normal? Are these tastes homothetic? 2) Now find the demand functions for x1 and x2 assuming-<1. You probably P2 assumed the opposite above, so now will you find something different. Explain 3) Graph...
Suppose a consumer has a utility function U (x1,x2) = Inxi + x2. The consumer takes prices (p1 and p2) and income (I) as given 1) Find the demand functions for x1 and x2 assuming -> 1. What is special about Р2 these demand functions? Are both goods normal? Are these tastes homothetic? <1. You probably P2 2) Now find the demand functions for x1 and x2 assuming assumed the opposite above, so now will you find something different. Explain....
Lorelai's choice behavior can be represented by the utility function u(x1, 2) 0.9n(x)0.1x2. The prices of both xi and x2 are $5 and she has an income of $40. 1. What preference does this utility function represent? (Hint: the utility is function is not linear, but at least linear in good x2) 2. Drawinwg indifference curves: you can copy down the graph on your paper using econgraphs. Set the preferences and parameters accordingly as given in the question. Click on...
Lorelai's choice behavior can be represented by the utility function 11(xi, X2) = 0.91n(xi) + 0.1x2 The prices of both x and x2 are $5 and she has an income of $40. 1. What preference does this utility function represent? (Hint: the utility is function is not linear, but at least linear in good x2.) 2. Drawinwg indifference curves: you can copy down the graph on your paper using econgraphs. Set the preferences and parameters accordingly as given in the...
1. Consider the utility function: u(x1,x2) = x1 + x2. Find the corresponding Hicksian demand function. 2. For each of the three utility functions below, find the substitution effect, the income effect, and the total effect that result when prices change from p =(2, 1) to p' = (2,4). Assume the consumer has income I = 20. (a) Before doing any calculation, make an educated guess about the relative magnitude of the three substitution effects and the three income effects...
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