The market for authentic poutine in Vancouver is controlled by two shops, PierrePoutine (i = P) and Mean Poutine (i = M). The market demand is given by p = 12−q, where p is the price, and q is aggregate output. Both shops produce at constant marginal cost of $ 2 per dish of poutine.
a) Suppose first that each firm i = 1, 2 chooses its output qi , taking the output of the other firm as given [Cournot Competition]. Aggregate output is thus q = qP + qM. Determine the best-response functions q br 1 (q2) and q br 2 (q1). Calculate the Nash equilibrium quantities, the market price, and profits (Note that everything is symmetric here).
b) Now suppose firm i = 1,2 chooses its price pi , taking the price of the other firm as given [Bertrand Competition]. Give the Nash equilibrium prices and quantities. Explain carefully why i) this is a Nash equilibrium and why ii) there is no other equilibrium. Note: most of the credit will be for your explanation.
c) What if Pierre Poutine finds a cheaper cheese curd supplier, which reduces its marginal cost to $1 instead (MeanPoutine continues to have $ 2 production cost). Assuming that prices are quoted in dollars and cents (the smallest unit of measurement is a cent), determine new Nash equilibrium prices and quantities for the Bertrand Competition situation. Explain