Question

For the utility function U(X,Y) = XY^3, find the marginal rate of substitution and discuss how MRS XY changes as the consumer substitutes X for Y along an indifference curve.

Answer #1

and

If consumer consumes more of X and less of Y along a downward sloping indifference curve, then the absolute value of MRS keeps on decreasing. This is also known as law of diminishing marginal utility. The below schedule shows the same -

X |
Y |
MRS = Y/3*X |

5 | 58.48 | 3.90 |

6 | 55.03 | 3.06 |

7 | 52.28 | 2.49 |

8 | 50.00 | 2.08 |

9 | 48.07 | 1.78 |

Consider a consumer whose preferences over the goods are
represented by the utility function U(x,y) = xy^2. Recall that for
this function the marginal utilities are given by MUx(x, y) = y^2
and MUy(x, y) = 2xy.
(a) What are the formulas for the indifference curves
corresponding to utility levels of u ̄ = 1, u ̄ = 4, and u ̄ = 9?
Draw these three indifference curves in one graph.
(b) What is the marginal rate of substitution...

Find
Marginal Utility for x and determine if it is diminishing
Marginal utility for y and determine if its diminishing
Marginal rate of Substitution of x for y (MRS xy) and determine
if its diminishing
U(x,y)=2x^(2/3)y^(1/3)
U(x,y)=x^3+4y^(1/4)

Suppose a consumer has the utility function U (x, y) = xy + x +
y. Recall that for this function the marginal utilities are given
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(a) What is the marginal rate of substitution MRSxy?
(b)If the prices for the goods are px =$2 and py =$4,and if the
income of the consumer is M = $18, then what is the consumer’s
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(c) What if instead the prices are...

Jen’s utility function is U (X, Y ) = (X + 2)(Y + 1), where X is
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a. Write an equation for Jen’s indifference curve that goes
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b. Suppose that the price of each good is 1 and that Jen has an
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Consider the utility function U(x, y) =
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(y0.6/x0.6) and MUy = 0.6
(x0.4/y0.4).
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goods?
b) Does the marginal utility of x diminish, remain constant, or
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c) What is MRSx, y?
d) Is MRSx, y diminishing, constant, or increasing as the consumer
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e) On a graph with x on...

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(c) Suppose that the market for good X is composed of 3000
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(d) Use calculus to show that the market demand function
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1. Consider the following information:
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y) = xy.
Maria’s utility function is U(x, y)
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Nancy’s utility function is U(x,y) =
-xy.
Chawki’s utility function is U(x,y) = xy -
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Marwan’s utility function is U(x,y)= x(y +
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Bob’s preferences are described by the following utility
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