Question 2: Write an equation for the MRS for the following utility functions and find two...
Question 2: Write an equation for the MRS for the following utility functions and find two bundles where the consumer is indifferent (i.e. lie on the same indifference curve). (a) U(A, P) = A 1 2 P 1 2 (b) U(A, P) = 2A + 3P (c) U(A, P) = min{2A, P} (d) U(A, P) = 2A 2 + 3P
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Question 2: Write an equation for the MRS for the following
utility functions and find two...
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)...
Problem Show that each of the follwing utility functions has a diminishing MRS but that they...
Problem Show that each of the follwing utility functions has a diminishing MRS but that they exhibit constant, increasing, and decreasing marginal utility, respectively. a) UE,y) = ry b) U(I,y) = rºy c) U(x,y) = ln I + Iny W Pyoblem A consumer is willing to trade 3 units of for 1 unit of y when she has 6 units of rand 5 units y. She is also willing to trade in 6 units of for 2 units of y...
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...
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
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...
Let basket A be (x, y) = (4, 3). For each of the following utility functions...
Let basket A be (x, y) = (4, 3). For each of the following utility functions (a-d), answer the following questions (iiv): i) Determine the utility at basket A ii) Write out the equation for the indifference curve that basket A lies on. (simplify to y equals some function of x) iii) Find 3 other points that lie on the same indifference curve as A. iv) Calculate the MRSx,y at basket A and give an economic interpretation of what the...
1. Clara's utility function is U(X,Y)= (x + 2)(Y +1). a) Write an equation for Clara's...
1. Clara's utility function is U(X,Y)= (x + 2)(Y +1). a) Write an equation for Clara's indifference curve that goes through the point(X,Y)-(2,8). b) Suppose that the price of each good is one and that Clara has an income of 11. Write an equation that describes her budget constraint. c) Find an equation the describes Clara's MRS for any given commodity bundle (X,Y). d) Use the equations in parts b) and e) to solve for Clara's optimal bundle Hint use...
4. Consider the utility function U(x,y) -Iny (a) Find the marginal rate of substitution, MRS of...
4. Consider the utility function U(x,y) -Iny (a) Find the marginal rate of substitution, MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of x and y. How do you interpret these functions? How might a consumer choose between z and y as she tries to increase utility by, for example, consuming more when their income increases?
2. Show that each of the following utility functions has a diminishing MRS. Do they exhibit...
2. Show that each of the following utility functions has a diminishing MRS. Do they exhibit constant, increasing, or decreasing marginal utility? Is the shape of the marginal utility function an indicator of the convexity of indifference curve? a. (2) U(X,Y) = XY b. (2) U(X,Y) = x2y2 c. (2) U(X,Y) = In X + In Y
2. For each of the three utility functions below, answer these questions: Does the marginal utility...
2. For each of the three utility functions below, answer these questions: Does the marginal utility of good x diminish, remain constant, or increase as the consumer buys more x, holding good y constant? Justify. Does the MRS of x for y diminish, remain constant, or increase as the consumer substitutes good y for more of good x to the right along an indifference curve? Justify. . . a. U(x, y)xyb, where 0 < a < 1 and b> 0...
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)...
Problem Show that each of the follwing utility functions has a diminishing MRS but that they exhibit constant, increasing, and decreasing marginal utility, respectively. a) UE,y) = ry b) U(I,y) = rºy c) U(x,y) = ln I + Iny W Pyoblem A consumer is willing to trade 3 units of for 1 unit of y when she has 6 units of rand 5 units y. She is also willing to trade in 6 units of for 2 units of y...
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...
1. Clara's utility function is U(X,Y)= (x + 2)(Y +1). a) Write an equation for Clara's indifference curve that goes through the point(X,Y)-(2,8). b) Suppose that the price of each good is one and that Clara has an income of 11. Write an equation that describes her budget constraint. c) Find an equation the describes Clara's MRS for any given commodity bundle (X,Y). d) Use the equations in parts b) and e) to solve for Clara's optimal bundle Hint use...
4. Consider the utility function U(x,y) -Iny (a) Find the marginal rate of substitution, MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of x and y. How do you interpret these functions? How might a consumer choose between z and y as she tries to increase utility by, for example, consuming more when their income increases?
2. Show that each of the following utility functions has a diminishing MRS. Do they exhibit constant, increasing, or decreasing marginal utility? Is the shape of the marginal utility function an indicator of the convexity of indifference curve? a. (2) U(X,Y) = XY b. (2) U(X,Y) = x2y2 c. (2) U(X,Y) = In X + In Y
2. For each of the three utility functions below, answer these questions: Does the marginal utility of good x diminish, remain constant, or increase as the consumer buys more x, holding good y constant? Justify. Does the MRS of x for y diminish, remain constant, or increase as the consumer substitutes good y for more of good x to the right along an indifference curve? Justify. . . a. U(x, y)xyb, where 0 < a < 1 and b> 0...
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