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?