1. Constrained Consumer Choice: Mitzie loves green tea and cappuccinos, where G and C denote cups of green tea and cappuccinos that Mitzie consumes. Mitzie has a modest weekly budget, Y=$42, from providing care to her beloved Uncle Morty. The price of a cup of green tea (PG) is $1 and the price of a cup of cappuccino (Pc) is $3. Mitzie has preferences that can be described by the quasilinear utility function: U(G, C) = 2G + C. Use this information to answer the following questions. a. Set up Mitzie's constrained utility maximization problem. Be sure to identify what she is maximizing and what is her constraint. b. Suppose that G is on the x-axis and C is on the Y-axis. What is Mitzie's marginal rate of substitution (MRS) and her marginal rate of transformation (MRT)? Illustrate (without precisely computing) in a graph with a budget constraint and indifference curve the choice of G and C that maximizes Mitzie's utility. c. Following up on part b., calculate numerical values for Mitzie's optimal consumption of G and C using the budget constraint and the fact that at the optimal bundle MRS = MRT. d. Now let's grind out the solution to Mitzie's optimal choice of G and C using the substitution method. Using her budget constraint, write an equatic for the cups of cappuccinos Mitzie buys in terms of her cups of green tea. Given this write Mitzie's utility purely as a function of the cups of green tea she chooses to consume and do this symbolically. e. Using your set-up from part (d), find the cups of green tea and cappuccinos Mitzie will chose to purchase. First do this symbolically and then plug in numbers for income for prices. f. How much utility does Mitzie get from consuming her utility maximizing bundle of goods?
1. Constrained Consumer Choice: Mitzie loves green tea and cappuccinos, where G and C denote cups of green tea and cappuccinos that Mitzie consumes. Mitzie has a modest weekly budget, Y=$42, from providing care to her beloved Uncle Morty. The price of a cup of green tea (PG) is $1 and the price of a cup of cappuccino (Pc) is $3. Mitzie has preferences that can be described by the quasilinear utility function: U(G, C) = 2G + C. Use this information to answer the following questions. a. Set up Mitzie's constrained utility maximization problem. Be sure to identify what she is maximizing and what is her constraint. b. Suppose that G is on the x-axis and C is on the Y-axis. What is Mitzie's marginal rate of substitution (MRS) and her marginal rate of transformation (MRT)? Illustrate (without precisely computing) in a graph with a budget constraint and indifference curve the choice of G and C that maximizes Mitzie's utility. c. Following up on part b., calculate numerical values for Mitzie's optimal consumption of G and C using the budget constraint and the fact that at the optimal bundle MRS = MRT. d. Now let's grind out the solution to Mitzie's optimal choice of G and C using the substitution method. Using her budget constraint, write an equatic for the cups of cappuccinos Mitzie buys in terms of her cups of green tea. Given this write Mitzie's utility purely as a function of the cups of green tea she chooses to consume and do this symbolically. e. Using your set-up from part (d), find the cups of green tea and cappuccinos Mitzie will chose to purchase. First do this symbolically and then plug in numbers for income for prices. f. How much utility does Mitzie get from consuming her utility maximizing bundle of goods?
Chapter10: Consumer Choice Theory
Section: Chapter Questions
Problem 8P
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Transcribed Image Text:1. Constrained Consumer Choice: Mitzie loves green tea and cappuccinos, where G and C denote cups of green
tea and cappuccinos that Mitzie consumes. Mitzie has a modest weekly budget, Y=$42, from providing care to
her beloved Uncle Morty. The price of a cup of green tea (PG) is $1 and the price of a cup of cappuccino (Pc) is
$3. Mitzie has preferences that can be described by the quasilinear utility function: U(G, C) = 2Gz + C. Use
this information to answer the following questions.
a. Set up Mitzie's constrained utility maximization problem. Be sure to identify what she is maximizing and
what is her constraint.
b.
Suppose that G is on the x-axis and C is on the Y-axis. What is Mitzie's marginal rate of substitution
(MRS) and her marginal rate of transformation (MRT)? Illustrate (without precisely computing) in a
graph with a budget constraint and indifference curve the choice of G and C that maximizes Mitzie's
utility.
c.
Following up on part b., calculate numerical values for Mitzie's optimal consumption of G and C using
the budget constraint and the fact that at the optimal bundle MRS = MRT.
d.
Now let's grind out the solution to Mitzie's optimal choice of G and C using the substitution method.
Using her budget constraint, write an equation for the cups of cappuccinos Mitzie buys in terms of her
cups of green tea. Given this write Mitzie's utility purely as a function of the cups of green tea she
chooses to consume and do this symbolically.
e.
Using your set-up from part (d), find the cups of green tea and cappuccinos Mitzie will chose to
purchase. First do this symbolically and then plug in numbers for income for prices.
f.
How much utility does Mitzie get from consuming her utility maximizing bundle of goods?
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