Suppose that there are two goods (X and Y). The price of X is $2 per unit, and the price of Y IS S1 per unit. There are two consumers (A and B). The utility functions for the consumers are UA (X,Y) = X0.5 yo.5 UB (X,Y) = X 0.8 y.2 Consumer A has an income of $100, and Consumer B has an income of $300. a. Use a Lagrangian to solve the constrained utility-maximization problem for Consumer A. b. Use a Lagrangian to solve the constrained utility-maximization problem for Consumer B. C. Calculate the marginal rate of substitution of Y for X (X is increasing and Y is decreasing; MRSXY) for consumer A at his or her optimal consumption bundles. d. Calculate the marginal rate of substitution of Y for X for consumer B at his or her optimal consumption bundles. e. Suppose that there is another consumer (let's call her C). You don't know anything about her utility function or her income. All you know is that she consumes both goods. What do you know about C's marginal rate of substitution at her optimal consumption bundle? Why?
Suppose that there are two goods (X and Y). The price of X is $2 per unit, and the price of Y IS S1 per unit. There are two consumers (A and B). The utility functions for the consumers are UA (X,Y) = X0.5 yo.5 UB (X,Y) = X 0.8 y.2 Consumer A has an income of $100, and Consumer B has an income of $300. a. Use a Lagrangian to solve the constrained utility-maximization problem for Consumer A. b. Use a Lagrangian to solve the constrained utility-maximization problem for Consumer B. C. Calculate the marginal rate of substitution of Y for X (X is increasing and Y is decreasing; MRSXY) for consumer A at his or her optimal consumption bundles. d. Calculate the marginal rate of substitution of Y for X for consumer B at his or her optimal consumption bundles. e. Suppose that there is another consumer (let's call her C). You don't know anything about her utility function or her income. All you know is that she consumes both goods. What do you know about C's marginal rate of substitution at her optimal consumption bundle? Why?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
![Suppose that there are two goods (X and Y). The price of X is $2 per unit, and the price of Y
IS SI per unit. There are two consumers (A and B). The utility functions for the consumers
are
U A(X,Y) = X0.5 yo.5
UB (X,Y) = X 0.8 yo.2
%3D
Consumer A has an income of $100, and Consumer B has an income of $300.
a. Use a Lagrangian to solve the constrained utility-maximization problem for Consumer A.
b. Use a Lagrangian to solve the constrained utility-maximization problem for Consumer B.
C. Calculate the marginal rate of substitution of Y for X (X is increasing and Y is decreasing;
MRSXY) for consumer A at his or her optimal consumption bundles.
d. Calculate the marginal rate of substitution of Y for X for consumer B at his or her optimal
consumption bundles.
e. Suppose that there is another consumer (let's call her C). You don't know anything
about her utility function or her income. All you know is that she consumes both goods.
What do you know about C's marginal rate of substitution at her optimal consumption
bundle? Why?
С.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F237376bc-3885-4a48-a3e3-6ce53540f723%2F26fbd84c-d473-4899-99e1-59ffac9d3197%2Fy2r08d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose that there are two goods (X and Y). The price of X is $2 per unit, and the price of Y
IS SI per unit. There are two consumers (A and B). The utility functions for the consumers
are
U A(X,Y) = X0.5 yo.5
UB (X,Y) = X 0.8 yo.2
%3D
Consumer A has an income of $100, and Consumer B has an income of $300.
a. Use a Lagrangian to solve the constrained utility-maximization problem for Consumer A.
b. Use a Lagrangian to solve the constrained utility-maximization problem for Consumer B.
C. Calculate the marginal rate of substitution of Y for X (X is increasing and Y is decreasing;
MRSXY) for consumer A at his or her optimal consumption bundles.
d. Calculate the marginal rate of substitution of Y for X for consumer B at his or her optimal
consumption bundles.
e. Suppose that there is another consumer (let's call her C). You don't know anything
about her utility function or her income. All you know is that she consumes both goods.
What do you know about C's marginal rate of substitution at her optimal consumption
bundle? Why?
С.
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