Thank you! Consider a market in which two firms {1, 2} compete in quantities {q1, q2}.

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Consider a market in which two firms {1, 2} compete in quantities {q1, q2}. The consumer inverse demand is given by P(A,Q) = A − Q, where Q is the total quantity Q = Q(q1, q2) := q1 + q2. Assume that each firm has a constant marginal cost c. Assume that A > c.
Suppose that firm 1 can make an investment prior to the start of competition in order to influence consumer demand. Assume that A = A(I) := c + √ I, where I is the number of units of investment and k(I) := I^2 is the cost of purchasing I units of investment. Firm 2 observes firm 1’s choice of I. What is a strategy for firm 1 in this game? For firm 2? What is the subgame perfect equilibrium of this game?
Now suppose that firm 1 and firm 2 merge into a single firm called firm A. Assume that firm A makes an investment in demand as firm 1 was able to do in part (1) and chooses a production quantity qA. What are its profit-maximizing choices of I and qA?
What is the difference between the equilibrium investment levels you found in parts (1) and (2)? What explains these differences? In your answer, you should consider how the benefits and costs of investment are distributed between the firms.

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