(In the following problems, do not use the letter A, but substitute it with A=1.5) Suppose that two firms are competing in a heterogeneous market where 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) [10] If firm 1 spends an amount F toreduce 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) [5] 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) [5] Compute both of the firms’ equilibrium prices, quantities, and profits. Which firm makes a higher profit? Explain the intuition of this. 4. [10] Overall quality of the submission. This will be allocated based on the quality of explanations, clarity of math equations and graphs, and tidy editing
(In the following problems, do not use the letter A, but substitute it with A=1.5)
Suppose that two firms are competing in a heterogeneous market where 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) [10] If firm 1 spends an amount F toreduce 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) [5] 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) [5] Compute both of the firms’
makes a higher profit? Explain the intuition of this.
4. [10] Overall quality of the submission. This will be allocated based on the quality of expla
nations, clarity of math equations and graphs, and tidy editing
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