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)
(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?