14. Steve Rogers consumes shiny metal shields, denoted as good s, and blue face masks, denoted as good f. The price of shields is ps = 2 and the price of blue face masks is pf = 2. Steve has an income of m= 100 and preferences over shields and face masks given by the Cobb-Douglas utility function u(s, ƒ) = så ƒ½. (a) Write down Steve's budget line and solve for his optimal bundle of shields and face masks (s*, f*). Show your solution graphically by placing shields on the horizontal axis and face masks on the vertical axis. Label Steve's optimal bundle as bundle "A" and be sure to label all intercepts of the budget line. (b) A fancy new store called Avengers Market opens up down the street and offers to sell shields to Steve for a lower price of ps = 0.5. Solve for Steve's new optimal bundle at these prices. Label it as bundle “C” and label all intercepts associated with the new budget line. (c) The owner of Avengers Market, Bruce Banner, is an intelligent person. Now that Steve has enjoyed the lower price, Bruce tells Steve that Steve must pay a membership fee in order to continue shopping at Avengers Market and have access to the lower price for shields. Find the maximum fee that Steve is willing to pay to Bruce by calculating Steve's compensating variation for the price change of shields from på = 2 to pg = 0.5. Using the definition of compensating variation, explain why the compensating variation measures the maximum amount Steve is willing to pay to continue shopping at Avengers Market. (d)
14. Steve Rogers consumes shiny metal shields, denoted as good s, and blue face masks, denoted as good f. The price of shields is ps = 2 and the price of blue face masks is pf = 2. Steve has an income of m= 100 and preferences over shields and face masks given by the Cobb-Douglas utility function u(s, ƒ) = så ƒ½. (a) Write down Steve's budget line and solve for his optimal bundle of shields and face masks (s*, f*). Show your solution graphically by placing shields on the horizontal axis and face masks on the vertical axis. Label Steve's optimal bundle as bundle "A" and be sure to label all intercepts of the budget line. (b) A fancy new store called Avengers Market opens up down the street and offers to sell shields to Steve for a lower price of ps = 0.5. Solve for Steve's new optimal bundle at these prices. Label it as bundle “C” and label all intercepts associated with the new budget line. (c) The owner of Avengers Market, Bruce Banner, is an intelligent person. Now that Steve has enjoyed the lower price, Bruce tells Steve that Steve must pay a membership fee in order to continue shopping at Avengers Market and have access to the lower price for shields. Find the maximum fee that Steve is willing to pay to Bruce by calculating Steve's compensating variation for the price change of shields from på = 2 to pg = 0.5. Using the definition of compensating variation, explain why the compensating variation measures the maximum amount Steve is willing to pay to continue shopping at Avengers Market. (d)
Chapter17: Capital And Time
Section: Chapter Questions
Problem 17.13P
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Transcribed Image Text:14. Steve Rogers consumes shiny metal shields, denoted as good s, and blue face masks, denoted
as good f. The price of shields is p. = 2 and the price of blue face masks is pf = 2. Steve has
an income of m = 100 and preferences over shields and face masks given by the Cobb-Douglas
utility function u(s, ƒ) = s₹ ƒ½.
(a) Write down Steve's budget line and solve for his optimal bundle of shields and face
masks (s*, f*). Show your solution graphically by placing shields on the horizontal axis
and face masks on the vertical axis. Label Steve's optimal bundle as bundle "A" and be
sure to label all intercepts of the budget line.
(b)
A fancy new store called Avengers Market opens up down the street and offers to
sell shields to Steve for a lower price of ps = 0.5. Solve for Steve's new optimal bundle
at these prices. Label it as bundle "C" and label all intercepts associated with the new
budget line.
(d)
The owner of Avengers Market, Bruce Banner, is an intelligent person. Now that
Steve has enjoyed the lower price, Bruce tells Steve that Steve must pay a membership
fee in order to continue shopping at Avengers Market and have access to the lower price
for shields. Find the maximum fee that Steve is willing to pay to Bruce by calculating
Steve's compensating variation for the price change of shields from på = 2 to ps = 0.5.
Using the definition of compensating variation, explain why the compensating
variation measures the maximum amount Steve is willing to pay to continue shopping
at Avengers Market.
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