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Given the following two utility functions (the superscripts on the utility functions merely...
PLEASE WRITE NEATLY. Given: U(x2)min(3x, ,6x2) P = 4, P-5, 1-20 a) Graph two indifference curves...
PLEASE WRITE NEATLY.
Given: U(x2)min(3x, ,6x2) P = 4, P-5, 1-20 a) Graph two indifference curves for this utility function. b) Write the function for the budget constraint and graph it c) What are the utility maximizing amounts of x, and x, given the budget constraint? d) Would your answer change if the utility function were U(x1,x2)-min(x,,2%)? Why or why not?
PLEASE WRITE NEATLY SO I CAN UNDERSTAND AND DIFFERENTIATE THE VARIOUS SYMBOLS AND VARIABLES. Given: U(x,,x,)-3x...
PLEASE WRITE NEATLY SO I CAN UNDERSTAND AND DIFFERENTIATE THE
VARIOUS SYMBOLS AND VARIABLES.
Given: U(x,,x,)-3x 6x2 P 4, P5,1 20 a) Write the function for the indifference curve and graph it. b) Write the function for the budget constraint and graph it c) What are the utility maximizing amounts of xand x2 given the budget constraint:? d) Do the utility maximizing amounts of x and x2 change if P increases to 5 while P stays constant at 5? Why...
question #5 (b) Suggest two distinct utility functions that represent such preterences. (Hint: Think about monotonic...
question #5
(b) Suggest two distinct utility functions that represent such preterences. (Hint: Think about monotonic transformations.) (c) Find MRS analytically. How does MRS depend on the values of (1, 72). Intuitively explain why (d) She spends her total income of $100 paying pi $2 for each Red Delicious and p2 $1 for each Gala. Find her optimal demand and show it on the graph. (e) Describe Kate's optimal choice(s) when p $1. Consumer Demand 5. For each of the...
Show Working please 3. Calculate the MRS for EACH of the following utility functions. (Remember MRS...
Show Working please
3. Calculate the MRS for EACH of the following utility functions. (Remember MRS is always negative with a downward sloping indifference curve) a. U (x1,x2) = 3x1 + 4x2 b. U (x1,x2) = 3x1x3 c. U (x1, x2) = 4x - 4x2 d. U (x1, x2) = 16x{ x e. U(x,y) = 2 Vx+2,77 f. U(x,y) = 3x2 /y g. U(x,y) = 16x4y3 4. Explain the following in words making reference to the indifference curve. a. (3,3)...
Do the following utility functions represent the same preferences? Please provide your reasoning (a) u(X1; XY)...
Do the following utility functions represent the same
preferences? Please provide your reasoning
(a) u(X1; XY) = X1 X2, V(X; X2) = 3(x] X2)2 +6 (b) u(x]; X») = X1X2, V(X]; X2) =-3(x1x2)2 +6 (c) u(x1,x2)=X]X2,v(x1,x2)=lnx1 +lnx2 (d) u(x]; X) = X1 X2, V(X1; X2) = x1 + x2
Given two utility functions U(x, y) = x2/3 y4/5 and U(x, y) = x2 + y,...
Given two utility functions U(x, y) = x2/3 y4/5 and U(x, y) = x2 + y, with Px = 2, Py = 1, budget is 10 unit, show the consumer choice respectively.
.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...
Question 1 For the following utility functions (3 pts each for a, b, and c): •...
Question 1 For the following utility functions (3 pts each for a, b, and c): • Find the marginal utility of each good at the point (5, 5) and at the point (5, 15) • Determine whether the marginal utility decreases as consumption of each good increases (i.e., does the utility function exhibit diminishing marginal utility in each good?) • Find the marginal rate of substitution at the point (5, 5) and at the point (5, 15) • Discuss how...
2. Janice consumes two goods, X and Y. Janice has a utility function given by the...
2. Janice consumes two goods, X and Y. Janice has a utility function given by the expression: U = 4x0.5y 0.5 The current prices of X and Y are $25 and $50, respectively. Janice currently has an income of $750 per time period (Put X on the horizontal axis and Y on the vertical axis). a) Is the assumption that "more is better” satisfied for both goods? b) Calculate MRSxy. Determine if it is diminishing for this utility function. c)...
1. (a) Write the following two functions in terms of , and say where they are...
1. (a) Write the following two functions in terms of , and say where they are holomorphic: i. x2 + y2 - y - 2+ ix ii. (x + 7txt) +i(y-2) (b) Show that the function f(x) = eri-y (cos(2«ry)+isin(2xy)) is entire, and find its deriva- tive. Write it in terms of .
PLEASE WRITE NEATLY.
Given: U(x2)min(3x, ,6x2) P = 4, P-5, 1-20 a) Graph two indifference curves for this utility function. b) Write the function for the budget constraint and graph it c) What are the utility maximizing amounts of x, and x, given the budget constraint? d) Would your answer change if the utility function were U(x1,x2)-min(x,,2%)? Why or why not?
PLEASE WRITE NEATLY SO I CAN UNDERSTAND AND DIFFERENTIATE THE
VARIOUS SYMBOLS AND VARIABLES.
Given: U(x,,x,)-3x 6x2 P 4, P5,1 20 a) Write the function for the indifference curve and graph it. b) Write the function for the budget constraint and graph it c) What are the utility maximizing amounts of xand x2 given the budget constraint:? d) Do the utility maximizing amounts of x and x2 change if P increases to 5 while P stays constant at 5? Why...
question #5
(b) Suggest two distinct utility functions that represent such preterences. (Hint: Think about monotonic transformations.) (c) Find MRS analytically. How does MRS depend on the values of (1, 72). Intuitively explain why (d) She spends her total income of $100 paying pi $2 for each Red Delicious and p2 $1 for each Gala. Find her optimal demand and show it on the graph. (e) Describe Kate's optimal choice(s) when p $1. Consumer Demand 5. For each of the...
Show Working please
3. Calculate the MRS for EACH of the following utility functions. (Remember MRS is always negative with a downward sloping indifference curve) a. U (x1,x2) = 3x1 + 4x2 b. U (x1,x2) = 3x1x3 c. U (x1, x2) = 4x - 4x2 d. U (x1, x2) = 16x{ x e. U(x,y) = 2 Vx+2,77 f. U(x,y) = 3x2 /y g. U(x,y) = 16x4y3 4. Explain the following in words making reference to the indifference curve. a. (3,3)...
Do the following utility functions represent the same
preferences? Please provide your reasoning
(a) u(X1; XY) = X1 X2, V(X; X2) = 3(x] X2)2 +6 (b) u(x]; X») = X1X2, V(X]; X2) =-3(x1x2)2 +6 (c) u(x1,x2)=X]X2,v(x1,x2)=lnx1 +lnx2 (d) u(x]; X) = X1 X2, V(X1; X2) = x1 + x2
2. Janice consumes two goods, X and Y. Janice has a utility function given by the expression: U = 4x0.5y 0.5 The current prices of X and Y are $25 and $50, respectively. Janice currently has an income of $750 per time period (Put X on the horizontal axis and Y on the vertical axis). a) Is the assumption that "more is better” satisfied for both goods? b) Calculate MRSxy. Determine if it is diminishing for this utility function. c)...
1. (a) Write the following two functions in terms of , and say where they are holomorphic: i. x2 + y2 - y - 2+ ix ii. (x + 7txt) +i(y-2) (b) Show that the function f(x) = eri-y (cos(2«ry)+isin(2xy)) is entire, and find its deriva- tive. Write it in terms of .
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