Fabian With a utility function of U-2XY, Fabian's MU, = 2Y and his MUy = 2X , where MU is marginal utility. Write an equation for Fabian's marginal rate of substitution (MRS). Suppose Fabian's income is $120 and Px - $6 and Py-$2, where Px is the price of X and Py is the price Y. Write an equation for Fabian's budget constraint. Vrite the equation that equates the slope of Fabian's budget constraint to the slope of Fabian's indiffere urve: Fabian is spending all of his income, how much X and how much Y will he choose? Use the equation ou wrote in part's b and e to answer this question. hat will Fabian's utility be with this combination of X and Y?
Fabian With a utility function of U-2XY, Fabian's MU, = 2Y and his MUy = 2X , where MU is marginal utility. Write an equation for Fabian's marginal rate of substitution (MRS). Suppose Fabian's income is $120 and Px - $6 and Py-$2, where Px is the price of X and Py is the price Y. Write an equation for Fabian's budget constraint. Vrite the equation that equates the slope of Fabian's budget constraint to the slope of Fabian's indiffere urve: Fabian is spending all of his income, how much X and how much Y will he choose? Use the equation ou wrote in part's b and e to answer this question. hat will Fabian's utility be with this combination of X and Y?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:8. Fabian consumes X and Y and the following utility function represents his utility: U = 2XY
a. With a utility function of U = 2XY, Fabian's MU, = 2Y and his MU, = 2x ,where MU is marginal
utility. Write an equation for Fabian's marginal rate of substitution (MRS).
b. Suppose Fabian's income is $120 and Px = S6 and Py-$2, where Px is the price of X and Py is the price of
Y. Write an equation for Fabian's budget constraint.
c. Write the equation that equates the slope of Fabian's budget constraint to the slope of Fabian's indifference
curve:
d. If Fabian is spending all of his income, how much X and how much Y will he choose? Use the equations
you wrote in part's b and c to answer this question.
e. What will Fabian's utility be with this combination of X and Y?
f. Now suppose the price of X increases to P.=10.
Write the equation that equates the slope of Fabian's budget constraint to the slope of Fabian's
indifference curve.
How will this change the optimal combination of X and Y?
What is Fabian's utility with this new combination of X and Y? Is it higher or lower than when
Px=6?
g. List two points on Fabian's demand schedule:
P
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