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  Problem 2: Price Hikes, Heavy Thumbs (5 points each)

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Problem 2: Price Hikes, Heavy Thumbs (5 points each). Adam is a gro-

cer. He sells apples, a very common fruit, and chirimoyas, a very unusual fruit.

Adam's customers are all identical and their preferences can be represented by

the utility function:

r I 2

U(ryay = —> (hp — 2) ty,

2a

 

where the quantity « denotes consumption of chirimovas in pounds and y ce-

notes cCoustuuption of “all other fruits”. Please let p, denote the price of chiri-

moyas in dollars per pound and p, denote the price of “all other fruits” in dollars

per pound. You may assume that every customer has m dollars to spend. The

quantity 6, denotes the customers’ “chirimoya bliss point”. Note that there is

no “apple bliss point” so customers will always spend their entire budget. You

may also assume that customers will always purchase some positive quantity of

chirimoyas and of “all other fruits”.

 

1. (5 points) Set. up and solve the consumer's utility maximization prob-

lem. Suppose that. Adam has listed the price of chirimoyas at p? dollars

per pound. How many pounds of chirimoyas does the customer want to

purchase at that price?

 

2. (5 points) Suppose that. unbeknownst to the customer, Adam charges a

price of pf dollars per pound of chirimoyas for each pound the customer

wanted to purchase originally, Llow much harm does this decision cause

his customers?

 

3. (5 points) Suppose, now, that Adam decides to use his thumb to weigh

down the scale. That is, he charges the price p? per pound of chirimoyas

(for every pound the customer purchases), but instead of giving the cus-

tomer 2° pounds of chirimoyas, he gives them:

 

zg<x°

pounds. How much harm does this decision cause his customers?

 

4. (5 points) Assume that 6, = 10, p, = 1, and a = 1. Please provide a

graphical analysis of the different. “tricks” that Adam uses. Please graph

the customer’s Marshallian demand function for chirimoyas and label the

harm caused to the consumer, the revenue collected by Adam. aud all

relevant prices and quantities. You may use separate graphs if you wish,

but make sure they are clearly labeled.

 

5. (5 points) Suggest a rule that wonld allow you to compare, in a meaningful

way, the harm caused by Adam to his customers if he uses the different

“tricks” discussed in the previous parts of this problem. You do not need

to carry out any computations. A short auswer im words that clearly

explains your thinking will suffice.

 

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