Two restaurantsXandYare competing for customers; therefore each has to set the prices for their menu. Prices are their strategic choices in the game of competing with each other; each restaurant's goal is to set price to maximize profit, the payoff in this game. LetX'sprice beandY'sprice be. Suppose each restaurant incurs a cost of 8 serving each customer. Market surveys have shown that whenX'sprice isandY'sprice isthe numbers of their customers areandrespectively, where

= 44 2 + (Measured in 00's per month)

= 44 2 + (Measured in 00's per month)

AssumeX'sprofit per week (in 00's of pounds) isand similarlyY'sprofit is.

1. SupposeYraises its price by two pounds, describe the effects that this will have on the customer numbers inXandY.
2. Using the originalandfunctions, determine the functional form of the profitfunctions(,)and(,).
3. Use suitable method to obtain the best response rule forXandY.
4. From the best response rule obtained in part (c), either use graphical method or
5. otherwise to determine the Nash equilibrium for the two restaurants.
6. Calculate the average price each customer will pay in each restaurant at the Nash equilibrium.
7. Determine what price is jointly best for the two restaurants if you assume that both restaurants will charge same price per customer. Is this arrangement sustainable? Explain.