S7. Two carts selling coconut milk (from the coconut) are located at 0 and 1, 1...

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S7. Two carts selling coconut milk (from the coconut) are located at 0 and 1, 1 mile apart on the beach in Rio de Janeiro. (They are the only two coconut-milk carts on the beach.) The carts-Cart 0 and Cart 1-charge prices po and p, respectively, for each coconut. One thousand beach- goers buy coconut milk, and these customers are uniformly distributed along the beach between carts 0 and 1. Each beachgoer will purchase one coconut milk in the course of her day at the beach, and in addition to the price, each will incur a transport cost of 0.5 x d2, where d is the distance (in miles) from her beach blanket to the coconut cart. In this system, 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. Location x is then defined by the expression: Po + 0.5x = P +0.5(1-x). The two carts will set their prices to maximize their bottom-line profit figures, B; profits are determined by revenue (the cart's price times its number of customers) and cost (each cart incurs a cost of $0.25 per coco- nut times the number of coconuts sold). (a) For each cart, determine the expression for the number of custom- ers served as a function of p, and p. (Recall that Cart 0 gets the cus- tomers between 0 and x, or just x, while Cart 1 gets the customers between x and 1, or 1 - x. That is, cart 0 sells to x customers, where x is measured in thousands, and cart 1 sells to (1-x) thousand.) Write the profit functions for the two carts. Find the two best-response rules for each cart as a function of their rival's price. (b) (c) Graph the best-response rules, and then calculate (and show on your graph) the Nash equilibrium price level for coconut milk on the beach. S7. Two carts selling coconut milk (from the coconut) are located at 0 and 1, 1 mile apart on the beach in Rio de Janeiro. (They are the only two coconut-milk carts on the beach.) The carts-Cart 0 and Cart 1-charge prices po and p, respectively, for each coconut. One thousand beach- goers buy coconut milk, and these customers are uniformly distributed along the beach between carts 0 and 1. Each beachgoer will purchase one coconut milk in the course of her day at the beach, and in addition to the price, each will incur a transport cost of 0.5 x d2, where d is the distance (in miles) from her beach blanket to the coconut cart. In this system, 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. Location x is then defined by the expression: Po + 0.5x = P +0.5(1-x). The two carts will set their prices to maximize their bottom-line profit figures, B; profits are determined by revenue (the cart's price times its number of customers) and cost (each cart incurs a cost of $0.25 per coco- nut times the number of coconuts sold). (a) For each cart, determine the expression for the number of custom- ers served as a function of p, and p. (Recall that Cart 0 gets the cus- tomers between 0 and x, or just x, while Cart 1 gets the customers between x and 1, or 1 - x. That is, cart 0 sells to x customers, where x is measured in thousands, and cart 1 sells to (1-x) thousand.) Write the profit functions for the two carts. Find the two best-response rules for each cart as a function of their rival's price. (b) (c) Graph the best-response rules, and then calculate (and show on your graph) the Nash equilibrium price level for coconut milk on the beach.

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S7 Coconut Milk Carts in Rio a Number of Customers Cart 0 Customers located between 0 and x will buy from Cart 0 Since the beachgoers are uniformly distributed the number of customers for Cart 0 in th... View the full answer