Bertrand model and stackelberg equilibrium

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Reference no: EM1316069

Firms in some industries with a small number of competitors earn normal economic profit. The Wall Street Journal (Lee Gomes, "Competitors Lives On in Just PC Sector," March 17, 2003, B1 reports that the computer graphics chips industry is one such market. Two chip manufacturers, nVidia and ATI, "both face the prospect of razor-thin profits, largely on account of other's existence."

a. Consider the Bertrand model with no product differentiated in which each firm has a positive and fixed sunk cost F and zero marginal cost. What are the equilibrium prices and profits? Illustrate your result on a proper diagram.

b. Assume that nVidia and ATI produce differentiated products and are Bertrand competitors. The demand for nVidia's chip is Q_V = 2 - 3P_V + P_A, the demand for ATI's chip is Q_A = 2 - 3P_A + P_V, where P_V is nVidia's price, P_A is ATI's price. Suppose each manufacturer's marginal dost is constant at $1 and fixed sunk cost is zero. What are the equilibrium prices, quantities and profits in this market? Does "razor-thin" profit result imply that two manufacturers necessarily produce chips that are nearly perfect substitutes? Explain.

c. Now consider a more general version of the model where the demand for nVidia's chips is Q_V = α - βP_V + γP_A; the demand for ATI's chips is Q_A = α - βP_A + γP_V, and the marginal cost of each firm is given by m and fixed sunk cost is zero. What must be the relationship between α, β, γ and m so that each firm makes zero profits even though they produce differentiated products.

d. Determine the Stackelberg equilibrium with one leader firm and n follower firms if the market demand curve is linear and each firm has a constant marginal cost, m, and no fixed cost.

Reference no: EM1316069

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