Question

In Tuftsville, everyone lives along Main Street, which is 10 miles long. There are 1,000 people uniformly spread up and down Main Street, and every day they each buy a fruit smoothie from one of the two stores located at either end of Main Street. Customers ride their motor scooters to and from the store using $0.50 worth of gas per mile. Customers buy their smoothies from the store offering the lowest price, which is the store’s price plus the customer’s travel expenses getting to and from the store.

Ben owns the store at the West end of Main Street and Will owns the store at the East end of Main Street.

1. (a) If Ben charges p1 and Will charges p2, what is the location of the customer who is indifferent between going to Ben’s or to Will’s store? How many customers go to Will’s store and how many go to Ben’s store? What are the demand functions that Ben and Will face?

2. (b) Assume that the marginal cost of a smoothie is constant and equal to $1 for both Ben and Will. In addition, each of them pays Tuftsville $250 per day for the right to sell smoothies. Find the equilibrium prices, quantities sold, and profits net of the $250 license fee.

From now, assume that Ben sets his price first and then Will sets his price p2. After the prices are posted consumers get on their scooters and buy from the store with the lowest price including travel expenses.

(c) What is the location of the customer who is indifferent between going to Ben’s or to Will’s store?

(d) How many customers go to Will’s store and how many go to Ben’s store? What are Ben and Will’s prices and profits? Compare with your answer in part (b). Does Ben have a first-mover advantage or disadvantage?

Answer 1

Chegg policy requires first 4 parts to be answered. Each question here asks multiple questions in single part. Answering as many as possible in the given time. Please post the rest separately.

Since the total cost (price+gas) should be same for a customer who is indifferent, it means that if the customer is situated at x distance from Ben,

p1+.5x=p2+(10-x)*.5

p1+.5x=p2+5-.5x

i. Distance of indifferent customer for Ben=x=p2+5-p1

ii. Customers going to ben's store=100*x (since per mile there are 100 customers)= 100(p2-p1)+500

iii. Customers going to Will's store=1000-Ben's customers= 1000-100(p2-p1)-500=500-100(p2-p1)

iv. The above 2 are the demand functions only as they show the quantity each store will be able to sell depending upon its own price and price of the other seller.

Total cost per day for the sellers is= 1*number of smoothies sold+250.

They will each sell where MC=MR. MC is 1 only.

Revenue=Price*Quantity.

For ben

=p1*100(p2-p1)+500p1

=100p1p2-100p1²+500p1

Differentiating to get MR

=100p2-200p1+500. This is for Ben.

So, MR=MC, hence

100p2-200p1+500=1

For Will

Revenue= 500p2-100p2²+100p1p2

MR=500-200p2+100p1

Hence

500-200p2+100p1=1

Solving for p1 and p2, we get

v. Price that Ben will set= p1=4.99.

vi. Price that Will will set, p2=4.99

quantities sold at these prices

vii. For ben=

100(4.99-4.99)+500=500

viii. For will

500-100(4.99-4.99)=500

ix. Profits=Revenue-Cost

=4.99*500-1*500-250

=1745

Profit for both will be 1745