Question

There are only two producers of Bumblebee Bandanas in the world, firm 1 and firm 2 . Suppose that inverse demand for this product is given by the function p=104.00−7Q, where p is the per-unit price, q i is the output for firm i (either firm 1 or 2 ), and Q=q1+q2. Firm 1 is the Stackelberg follower in this industry and has a constant marginal cost of $6 per unit, while the leader (firm 2) has a constant marginal cost of $3 per unit. Assume no fixed costs. What is firm 1 's reaction function? Give your answer to one decimal. Firm 1's reaction function: q1=_______- _________q2

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Answer 1

Firm 1's reaction function in this scenario is q1 = 52.00 − 3.5q2.

Step-by-step explanation:

Firm 1's reaction function can be determined by finding the profit-maximizing quantity of firm 1, given the quantity produced by firm 2. To maximize its profit, firm 1 should set its marginal cost equal to the marginal revenue it receives from selling an additional unit. In this case, firm 1's marginal cost is $6 per unit and the inverse demand function is p=104.00−7Q. By substituting these values, we can solve for firm 1's reaction function:

Quantity demanded by firm 1 (q1) = (104.00−7(q1+q2)) / (2)

By simplifying this equation, firm 1's reaction function is q1 = 52.00 − 3.5q2.