All problems below include an “unknown” parameter A, which is 1.5. Suppose that 2 firms are competing in a heterogeneous market whereby the demand functions of firm 1 and firm 2 are given by q1 = A − 3p1 + 2p2 and q2 = A − 3p2 + 2p1. Both firms have a marginal cost equal to 1. (a) [10] Calculate the optimal profits for the two firms when they compete in prices. (b) [20] If firm 1 spends an amount F to reduce its marginal cost to 0, what is the maximum value of F that it would be willing to pay? For the rest of the problem, suppose, instead, that firm 1 sets the quantity (q1) while simultaneously firm 2 sets the price (p2). (c) [15] Draw the two best response functions in a graph and indicate the Nash equilibrium. Be as detailed as possible in giving intuition. (Note: the graphs will be in the (p2, q1) space, but remember that you are not drawing any demand curves.) (d) [25] Compute both of the firms’ equilibrium prices, quantities, and profits. Which firm makes a higher profit? Explain the intuition of this
All problems below include an “unknown” parameter A,
which is 1.5.
Suppose that 2 firms are competing in a heterogeneous market whereby the demand
functions of firm 1 and firm 2 are given by q1 = A − 3p1 + 2p2 and q2 = A − 3p2 + 2p1.
Both firms have a marginal cost equal to 1.
(a) [10] Calculate the optimal profits for the two firms when they compete in prices.
(b) [20] If firm 1 spends an amount F to reduce its marginal cost to 0, what is the maximum
value of F that it would be willing to pay?
For the rest of the problem, suppose, instead, that firm 1 sets the quantity (q1) while simulta
neously firm 2 sets the price (p2).
(c) [15] Draw the two best response functions in a graph and indicate the Nash equilibrium.
Be as detailed as possible in giving intuition. (Note: the graphs will be in the (p2, q1)
space, but remember that you are not drawing any demand
(d) [25] Compute both of the firms’
makes a higher profit? Explain the intuition of this
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