Question

Market demand for a retail product X in Our Town is given by Q^d = 42 – 0.4P (or P = 105 – 2.5Q_T). This market is shared by two firms, Mom & Pops and Walmart, whose cost structures are given by C_M&P = 15Q_M&P, and C_W = 100 + 5Q_W respectively. The two firms agree to share the market EQUALLY, and to collude on the price, which will be set by Walmart (as the dominant firm).

a. Determine Mom & Pop’s profit level under these conditions.

b. Walmart is considering pricing in a way that would force Mom & Pop’s to shut down its operations. Calculate Walmart’s profits as a monopolist as well as with Mom & Pop’s present (see assumption in (a) above), and advise Walmart whether or not it to do this. Set up your answers in a payoff matrix.

Profits Payoff Matrix		MOM & POP
		Present	Shut Down
Wal Mart	(Collude) High price:    P =
	(Compete) Low Price: P =

Answer 1

a. Determine Mom & Pop’s profit level under these conditions.

MR = MC (Walmart is the dominant firm)

105 – 5Q = 5

QT = 20, 10 units for both firms

P = 105 – 2.5*20 = 55

Walmart’s profit = 55*10 – (100 + 5*10) = $400

Mom & Pop’s profit = 55*10 – 15*10 = $400.

b. Walmart is considering pricing in a way that would force Mom & Pop’s to shut down its operations. Calculate Walmart’s profits as a monopolist as well as with Mom & Pop’s present (see assumption in (a) above), and advise Walmart whether or not it to do this. Set up your answers in a payoff matrix.

MR = MC (Walmart is a monopolist)

105 – 5Q = 5

QT = 20

P = 105 – 2.5*20 = 55

Walmart’s profit = 55*20 – (100 + 5*20) = $900

Mom & Pop’s profit = 0

In case the two compete and Mom & Pop does not shut down, Walmart produces = (105 – 2*5 + 15)/7.5 = 14.67 and Mom & Pop produces = (105 – 2*15 +5)/7.5 = 10.67. Market price P = (105 – 2.5*(14.67 + 10.67)) = 41.66. Profit for Walmart is 437.77 and that of Mom & Pop is 284.44.

Dominant strategy for Mom & Pop’s is to present and not shut down. It follows that Walmart will compete and have a higher profit

	Mom & Pop’s
Walmart		Present	Shut down
	Collude	(400, 400)	(900, 0)
	Compete	(437.77, 284.44)	(900, 0)