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4. [25 POINTS]Use separate graphs to draw indifference curves for each of the following utility functions: (a) 6 POINTS...
.Use separate graphs to sketch two indifference curves for people with each of the following utility...
.Use separate graphs to sketch two indifference curves for people with each of the following utility functions: U(x, y) = x + 2y. U(x, y) = min{x,2y}. What type of preferences are represented by a utility function of the form U(x, y) = square root of x+y? What about the utility function V(x,y) = 13x+13y? Consider the utility function u(x,y) = ?^2 ?^3. What kind of preferences does it represent? Is the function v(x,y) = ?^4 ?^5 a monotonic transformation...
For each of the following utility functions, draw an indifference map with 3 in curves. Be...
For each of the following utility functions, draw an indifference map with 3 in curves. Be sure to label your axes, and label your curves as IC1, IC2, and ICs, where difference 1 U2 U (X,Y)=3X+5Y U3. (5 points each) a. U(X, Y) U(X, Y) -X2 + ln(Y) min(3X,5Y) c. d.
For each of the following utility functions, draw an indifference map with 3 indifference curves. Be...
For each of the following utility functions, draw an indifference map with 3 indifference curves. Be sure to label your axes, and label your curves as IC1, IC2, and IC3, where U1 < U2 < U3. (5 points each) a. ?(?, ?) = 3? + 5? b. ?(?, ?) = ? 2 + ? 2 c. ?(?, ?) = −? 2 + ln(?) d. ?(?, ?) = min(3?, 5?)
For each of the following functions, i) pick three utility levels and draw the precise indifference...
For each of the following functions, i) pick three utility levels and draw the precise indifference curves that are associated with the levels of your choice, ii) label the utility level of the lines--you cannot just draw random lines and assign arbitrary utility levels, and iii) give the name of preferences they represent (hint: see figures in textbook chapter 3) 2. u(x,2) -min(xi,x2) 5. u(xi, x2) -xjx2
For each of the following functions, i) pick three utility levels and draw the precise indifference...
For each of the following functions, i) pick three utility levels and draw the precise indifference curves that are associated with the levels of your choice, ii) label the utility level of the lines -- you cannot just draw random lines and assign arbitrary utility levels, and iii) give the name of preferences they represent (hint: see figures in textbook chapter 3). 1. u(x1, 12) = I1 + 2.12 2. u(21, 22) = min(21, 22) 3. u(x1,22) = 21 4....
4. Graph a typical indifference curve for the following utility functions and determine whether they have...
4. Graph a typical indifference curve for the following utility functions and determine whether they have convex indfference curves. a. U = 3x + y. b. U = (x2 + y2) c. U = (x2 - y2) 2 d. U = x3 y3 e. U = logx + logy.
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)...
III. Graphs (10 points each, 20 points) 1. Draw indifference curves that reflect the following preferences....
III. Graphs (10 points each, 20 points) 1. Draw indifference curves that reflect the following preferences. a. Tony thinks a cup of coffee and a cup of tea provide the same utility: b. Mary loves potatoes and hates rice. Suppose the industry for Vitamin C is a constant-cost industry (ie the production cost will not change with the number of firms in the industry) and the market for Vitamin C is perfectly competitive, illustrate what happens to the market both...
For each of the following 5 utility functions assume that α>0 and β>0 U^A (x_1,x_2...
For each of the following 5 utility functions assume that α>0 and β>0 U^A (x_1,x_2 )=x_1^α x_2^β U^B (x_1,x_2 )=αx_1+βx_2 U^C (x_1,x_2 )=αx_1+βlnx_2 U^D (x_1,x_2 )=(α/β)lnx_1+lnx_2 U^E (x_1,x_2 )= -αlnx_1-βlnx_2 Calculate the MRS for each utility function Which utility function represent a preference with linear indifference curves? Which of these utility functions represent the same underlying tastes? Which of these utility functions does not satisfy the monotonicity assumption? Which of these utility functions represent...
8. Problems 3.8 k1/6 Suppose indifference curves for a utility function U are given by z...
8. Problems 3.8 k1/6 Suppose indifference curves for a utility function U are given by z --kısx-usy-As. The utility function U k associated with these indifference curves is Suppose indifference curves for a utility function U are given by y 0.51/x2 - 4 (x2-k) -0.5x The utility function U k associated with these indifference curves is Suppose indifference curves for a utility function U are given by z-- 2x The utility function U k associated with these indifference curves is
For each of the following utility functions, draw an indifference map with 3 in curves. Be sure to label your axes, and label your curves as IC1, IC2, and ICs, where difference 1 U2 U (X,Y)=3X+5Y U3. (5 points each) a. U(X, Y) U(X, Y) -X2 + ln(Y) min(3X,5Y) c. d.
For each of the following functions, i) pick three utility levels and draw the precise indifference curves that are associated with the levels of your choice, ii) label the utility level of the lines--you cannot just draw random lines and assign arbitrary utility levels, and iii) give the name of preferences they represent (hint: see figures in textbook chapter 3) 2. u(x,2) -min(xi,x2) 5. u(xi, x2) -xjx2
For each of the following functions, i) pick three utility levels and draw the precise indifference curves that are associated with the levels of your choice, ii) label the utility level of the lines -- you cannot just draw random lines and assign arbitrary utility levels, and iii) give the name of preferences they represent (hint: see figures in textbook chapter 3). 1. u(x1, 12) = I1 + 2.12 2. u(21, 22) = min(21, 22) 3. u(x1,22) = 21 4....
4. Graph a typical indifference curve for the following utility functions and determine whether they have convex indfference curves. a. U = 3x + y. b. U = (x2 + y2) c. U = (x2 - y2) 2 d. U = x3 y3 e. U = logx + logy.
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)...
III. Graphs (10 points each, 20 points) 1. Draw indifference curves that reflect the following preferences. a. Tony thinks a cup of coffee and a cup of tea provide the same utility: b. Mary loves potatoes and hates rice. Suppose the industry for Vitamin C is a constant-cost industry (ie the production cost will not change with the number of firms in the industry) and the market for Vitamin C is perfectly competitive, illustrate what happens to the market both...
8. Problems 3.8 k1/6 Suppose indifference curves for a utility function U are given by z --kısx-usy-As. The utility function U k associated with these indifference curves is Suppose indifference curves for a utility function U are given by y 0.51/x2 - 4 (x2-k) -0.5x The utility function U k associated with these indifference curves is Suppose indifference curves for a utility function U are given by z-- 2x The utility function U k associated with these indifference curves is
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