For each of the following utility functions: Calculate MUx, MUy, MRSx,y; determine whether or not the property of “more is better” is satisfied for both
goods; determine whether or not the marginal utility of x
diminishes,
remains constant, or increases as the consumer buys more x;
determine whether or not the marginal rate of substitution
diminishes, remains constant, or increases as the consumer
substitutes x for y along an indifference curve; and sketch the
graph of a typical indifference curve.
(a) U(x,y)=(xy)^1/2
I really need help with the indifference curve part of the question!
U = (xy)1/2 = x1/2y1/2
y1/2 = U / (x1/2)
Squaring,
y = (U2) / x [Equation of indifference curve]
Utility remains constant along an indifference curve (IC) while x and y varies along it. So, for purpose of drawing the IC, let us (hypothetically) assume that U = 10. Then,
y = 100 / x
We may develop following data table:
x | y |
1 | 100 |
5 | 20 |
10 | 10 |
20 | 5 |
25 | 4 |
50 | 2 |
100 | 1 |
Graph of IC:
This is the generalized shape of IC for given utility function, which you can draw without any specific U and x-y values.
For each of the following utility functions: Calculate MUx, MUy, MRSx,y; determine whether or not the...
Calculate MUx, MUy, MRSx,y; determine whether or not the property of “more is better” is satisfied for both goods; determine whether or not the marginal utility of x diminishes, remains constant, or increases as the consumer buys more x; determine whether or not the marginal rate of substitution diminishes, remains constant, or increases as the consumer substitutes x for y along an indifference curve; and sketch the graph of a typical indifference curve. U(x,y)=xy+x
Consider the utility function U(x,y) = 3x+y, with MUx=3 and MUy=1 a) Is the assumption that more is better satisfied for both goods b) Does the marginal utility of x diminish, remain constant, or increase as the consumer buys more x? Explain. c)What is MRS x,y? d) Is MRS x,y diminishing, constant, or increasing as the consumer substitutes x for y along an indifference curve? e) On a graph with x on the horizontal axis and y on the vertical...
Consider the utility function U(x,y) = 3x+y, with MUx=3 and MUy=1 a) Is the assumption that more is better satisfied for both goods b) Does the marginal utility of x diminish, remain constant, or increase as the consumer buys more x? Explain. c)What is MRS x,y? d) Is MRS x,y diminishing, constant, or increasing as the consumer substitutes x for y along an indifference curve? e) On a graph with x on the horizontal axis and y on the vertical...
U (x, y) = 3x3 + 6y3 a)Calculate MUx and MUy. b) Do the consumer’s preferences exhibit a diminishing marginal utility for each good? c) Calculate MRSx,y. d) Do the consumer’s preferences exhibit a diminishing marginal rate of substitution of x?
Consider the utility function U(x,y) = 3x+y, with MUx=3 and MUy=1 e) On a graph with x on the horizontal axis and y on the vertical axis, draw a typical indifference curve (it is not exactly to scale, but it needs to reflect accurately whether there is a diminishing MRS x,y). Also, indicate on your graph whether the indifference curve will intersect either or both exes. label the curve U1. f) on the same graph draw a second indifference curve...
U (x, y) = 3x3/4 + 3y a)Calculate MUx and MUy. b) Do the consumer’s preferences exhibit a diminishing marginal utility for each good? c) Calculate MRSx,y. d) Do the consumer’s preferences exhibit a diminishing marginal rate of substitution of x?
U (x, y) = 4x11/6 y1/6 . a)Calculate MUx and MUy. b) Do the consumer’s preferences exhibit a diminishing marginal utility for each good? c) Calculate MRSx,y. d) Do the consumer’s preferences exhibit a diminishing marginal rate of substitution of x?
U (x, y) = 5x1/3 y2/3 a)Calculate MUx and MUy. b) Do the consumer’s preferences exhibit a diminishing marginal utility for each good? c) Calculate MRSx,y. d) Do the consumer’s preferences exhibit a diminishing marginal rate of substitution of x?
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.
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...