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1. Consider the following utility functions (a) For each of these utility functions: i. Find the...
For each of these utility functions, b. Compute the MRS. c. Do these tastes have...
For each of these utility functions,
b. Compute the MRS.
c. Do these tastes have diminishing marginal rates of
substitution? Are they convex?
d. Construct an indifference curve for each of these functions
for utility numbers U1 = 10 , U2 = 100 , U3 = 200 .
e. Do these utility functions represent different preference
orderings?
1. Consider the following utility functions: (i) U(x,y)- 6xy, (ii) U(x,y)=(1/5)xy, MU,--y and MU,--x ii) U(x,y)-(2xy)M 8xy2 and MUy -8x2y MU,-6y and...
4. consider the following utility functions a) for each of these utility function what is the equation of an indifferenc...
4. consider the following utility functions
a) for each of these utility function what is the equation of an
indifference curve ?
c) for each utility function show weather the function exhibits
the diminishing rate of substitution property
d) do the above utility function represent the same preference
ordering? why or why not?
c) Suppose the price of beer doubles, but the price of pizza and Tom's income stay the same. How much beer is Tom consuming as a percentage...
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 2. For each of the following utility functions: (i) u1(x1,T2) = 2x2. (a) Graph the...
Question 2. For each of the following utility functions: (i) u1(x1,T2) = 2x2. (a) Graph the indifference curves for utility levels u -1 and u 2 (b) Find the marginal rate of substitution function MRS. (c) For u and us, graph the locus of points for which the MRS of good 2 for good 1 is equal to 1, and the locus of points for which the MRS is equal to 2.
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...
Indifference curves and utility: Consider the utility function ? (?1, ?2) = 6?1^1/2 + ?2 that...
Indifference curves and utility: Consider the utility function ? (?1, ?2) = 6?1^1/2 + ?2 that describes Moe’spreferences. For the following, think of q1 as the variable you would graph on the horizontal axis. a. Derive an expression for his marginal utility (U1) from a small increase in q1 holding q2 fixed. Also, find U2. b. What is Moe’s marginal rate of substitution (MRS)? Give a brief (2 sentences maximum) intuitive description of what MRS represents. c. Given your answer...
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
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)...
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.
5. Consider the utility function U(x, y) = 2/x + y. 1) Is the assumption that...
5. Consider the utility function U(x, y) = 2/x + y. 1) Is the assumption that "more is better” satisfied for both goods? 2) What is MRS, for this utility function? 3) Is the marginal rate of substitution diminishing, constant, or increasing in x as the consumer substitutes x for y along an indifference curve? 4) Will the indifference curve corresponding to this utility function be convex to the origin, concave to the origin, or straight lines? Explain.
For each of these utility functions,
b. Compute the MRS.
c. Do these tastes have diminishing marginal rates of
substitution? Are they convex?
d. Construct an indifference curve for each of these functions
for utility numbers U1 = 10 , U2 = 100 , U3 = 200 .
e. Do these utility functions represent different preference
orderings?
1. Consider the following utility functions: (i) U(x,y)- 6xy, (ii) U(x,y)=(1/5)xy, MU,--y and MU,--x ii) U(x,y)-(2xy)M 8xy2 and MUy -8x2y MU,-6y and...
4. consider the following utility functions
a) for each of these utility function what is the equation of an
indifference curve ?
c) for each utility function show weather the function exhibits
the diminishing rate of substitution property
d) do the above utility function represent the same preference
ordering? why or why not?
c) Suppose the price of beer doubles, but the price of pizza and Tom's income stay the same. How much beer is Tom consuming as a percentage...
Question 2. For each of the following utility functions: (i) u1(x1,T2) = 2x2. (a) Graph the indifference curves for utility levels u -1 and u 2 (b) Find the marginal rate of substitution function MRS. (c) For u and us, graph the locus of points for which the MRS of good 2 for good 1 is equal to 1, and the locus of points for which the MRS is equal to 2.
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
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)...
5. Consider the utility function U(x, y) = 2/x + y. 1) Is the assumption that "more is better” satisfied for both goods? 2) What is MRS, for this utility function? 3) Is the marginal rate of substitution diminishing, constant, or increasing in x as the consumer substitutes x for y along an indifference curve? 4) Will the indifference curve corresponding to this utility function be convex to the origin, concave to the origin, or straight lines? Explain.
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