the quantity of customers served by Matt - the customer demand function for Matt's restaurant - was QM = 44 - 2PM + PS and the quantity of customers served by Sean was QS = 44 - 2PS + PM. The profits for each restaurant also depend on the cost of serving each customer. Suppose that Matt is able to reduce his costs to just $2 per customer by eliminating the wait staff. Suppose that Sean continues to incur a cost of $8 per customer.

a.) What is Sean's profit function, S?

b.) What is Matt's profit function (revenue per customer multiplied by number of customers), M?

c) Sean needs to choose his price to maximize his profit function. What is Sean's best response function?

d) Matt needs to choose his price to maximize his profit function. What is Matt's best response function? Explain what this best response function means.

e) Calculate the Nash equilibrium

f) Graph the two best response functions and indicate the location of the Nash equilibrium on the graph. To match what we did in class, plot Matt's price on the vertical axis and Sona's price on the horizontal axis.

g) Look at the graph of the best response functions that we came up with in class when the cost per consumer was $8 for both Matt and Sean. Indicate which best response function in your new graph has moved and by how much. Explain why these changes occurred in your graph.