1.Imagine that Cupertino is a town comprised of just one street that is 1 mile l
ID: 1250363 • Letter: 1
Question
1.Imagine that Cupertino is a town comprised of just one street that is 1 mile long. There are 10,000 students (consumers) evenly spaced along the road. Suppose that Josh’s is the only coffee business in town, and that (for now) it has only one branch. That branch is located in the middle of town, and sells a cup of coffee for $1. Students are all coffee drinkers who choose between buying once cup of coffee and zero every day. They each value a cup of coffee identically at $1.50. However, it is costly to travel to and from Josh’s. Travel costs are equal to $1/mile, so total travel costs are equal to $x, where x is the distance traveled in miles.a) What are the travel costs of a student located at the end of the road? What would that student be willing to pay for a cup of coffee?
b) At a price of $1, how many students will buy a cup of coffee?
c) What is the highest price that Josh’s could charge if it wanted to sell a cup of coffee to every student?
d) If Josh’s could open two stores (starting from scratch), where would they optimally be located along the street? (Remember, they have the same owners, and are jointly profit maximizing.) At these locations, what is the maximum price they could charge if they wanted to sell to every student?
e) Draw the Hotelling diagram that represents this problem. Clearly mark the areas that represent consumer surplus, travel costs, and profit (assume MC=0).
Explanation / Answer
a.
The road goes half a mile each way from Josh's that means that at most a customer will have to travel half a mile.
As travel costs are $1/mi that means the most a customer will have to pay is 50 cents. So if a customer came from the end of the road the coffee would cost the same as its benefit; so the customer would be indifferent.
b.
At a price of $1, 9998 will buy coffee and the 2 people at the ends of the road again will be indifferent
c.
The coffee shop could charge $1.00 - epsilon (infinitely small amount) to get the last two people at the ends of the street to buy the coffee. Since money is discrete we can say 99 cents.
d.
While it is very tempting to just divide up the street into thirds, the problem would be that the middle would be double covered, or if you are doing 1/6 and 5/6 the ends would be double covered. The Optimal place to put the stores where there is no double coverage is at 1/4 and 3/4. Which each store covering 1/4 in either direction. 1/4 mi * $1/mi = 25 cents.
e.
as i cannot draw you a picture I can tell you how to do so
everyone is getting their coffee for 1$ but gets a 1.50 benefit. so for every 1/100 of a mile you go away from the store, consumer surplus is reduced by one penny. You have 1 mi / 100 = 0.01. There are 100 different penny brackets / 10,000 people. So there are 100 people per penny bracket. Therefore for every 1/100 of a mile you go away from the store, total consumer surplus is decreased by a dollar, and total travel costs increaes by a dollar (gas use is continous while the payment for gas is discrete)
If MC = 0 then there will be a flat supply curve, and MR = $1 because that is the price for coffee.
I really hope I helped you out. Take it easy
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