6. (iii)

a)Imagine there are two ice cream vendors on a linear beach of 10 yards long.

We assume that:

Consumers are evenly distributed along the beach, located at the end points and spaced 3 feet apart.

Production costs are zero. Both vendors sell ice cream for $2.00

Consumers walk to the closest vendor to buy ice cream. The cost to consumers of travel to the vendor is 1 cents per yard (money equivalent of consumer's time).

Note that one-yard equals to 3 feet.

Given:

The only equilibrium location for both vendors is to be in the middle, they get the maximum profit and market share in that location.

If each customer walks to the ice cream vendor nearest to him, we then we can put one vendor a quarter of the way along the boardwalk and one vendor three-quarters of the way along the boardwalk.

The consumer halfway along the boardwalk will be indifferent between the two ice-cream vendors; each has a market share of one-half of the customers.

However, if you move a little to the right, you will steal some of the other vendors customers and you won't lose any of yours.

Both vendors have an incentive to move towards the middle in order to maximize market share and profits. Both vendors will reason the same way

Assumption:

Each vendor tries to get the maximum number of customers.

Question:

Each ice cream vendor charges $2 for per cone. Both vendors sell the same ice cream. Write the price function for a customer that is x distance from the closest vendor?