In a small town, there are two bakeries, Poilne and Tartine, selling sourdough bread. It costs Poilne

Bakery $4 to produce one loaf of bread and it costs Tartine Bakery $3 to produce one loaf of bread. Both

bakeries are trying to maximize their profits by choosing how much bread to produce simultaneously. De-

note the number of loaves produced by Poilne Bakery by qp and the number of loaves produced by Tartine Bakery by qt . Assume that Poilne Bakery and Tartine Bakery do not have any market power. Price of one loaf of sourdough bread is determined by the demand curve which is given by

P = 30 ( qt + qp)

a) (1 points) Write down the profit function of Poilne bakery.

b) (1 points) Write down the profit function of Tartine bakery.

c) (5 points) Find the best reply function of Poilne bakery.

d) (5 points) Find the best reply function of Tartine bakery.

e) (5 points) Find the Nash equilibrium using the best reply functions you derived in part c and d.

f) (4 points) Draw the best reply functions you found in part c and d in the same graph. Show the Nash

equilibrium on your graph.

g) (4 points) Calculate equilibrium profits of the two bakeries.