# The coconut-milk carts from Exercise S7 set up again the next day. Nearly everything is exactly the.

The coconut-milk carts from Exercise S7 set up again the

next day. Nearly everything is exactly the same as in Exercise S7: the carts

are in the same locations, the number and distribution of beachgoers is

identical, and the demand of the beachgoers for exactly one coconut milk each

is unchanged. The only difference is that it is a particularly hot day, so that

now each beachgoer incurs a higher transport cost of 0.6d2 . Again,

Cart 0 sells to all of the beachgoers located between 0 and x, and Cart 1 sells

to all of the beachgoers located between x and 1, where x is the location of

the beachgoer who pays the same total price if she goes to 0 or 1. However, now

location x is defined by the expression:

Again, each cart has a cost of $0.25 per coconut sold.

(a) For each cart, determine the expression for the

number of customers served as a function of p0 and p1.

(Recall that Cart 0 gets the customers between 0 and x, or just x, while Cart 1

gets the customers between x and 1, or 12 x. That is, Cart 0 sells to x

customers, where x is measured in thousands, and Cart 1 sells to (12 x)

thousand.)

(b) Write out profit functions for the two carts and find

the two best-response rules.

(c) Calculate the Nash equilibrium price level for

coconuts on the beach. How does this price compare with the price found in

Exercise S7? Why?