Find the Marginal Utility of X; the Marginal Utility of Y; the ratio MUx / MUy for each of the following:
a. U(x,y) = 15x.2y.3
b. U(x,y)=.5xy
c. U(x,y)=6x.4y.5
d. U(x,y)=3x.5y.8



Find the Marginal Utility of X; the Marginal Utility of Y; the ratio MUx / MUy...
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 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) = 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?
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?
Rachel’s utility funtion U = x ∗ y, where MUx = y and MUy = x. The price of x is 2 and the price of y is unknown and equal to the variable py. Rachel’s budget constraint is 40 = 2 ∗ x + py ∗ y. When Rachel maximizes utility subject to her budget constraint, she purchases 5 units of y. What must be the price of y and the amount of x consumed? (Hint: solve for how...
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....
Suppose that a consumer’s utility function is U=xy with MUx=y and MUy=x. Suppose the consumer‘s income is $480. For this question you may need to use the following approximations: sqrt(2) is approximately 1.4, sqrt(3) is approx. 1.7 and sqrt(5) is approx 2.2. a) Initially, the price of y is $4 and the price of x is $6. What is the consumer’s optimal bundle? b) What is the consumer's initial utility? Now suppose that price of x increases to $8 and...
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...