There are two major producers of corncob pipes in the world, both located in Herman, Missouri.Suppose that the inverse demand function for corncob pipes is described by p  160  4q, where q is total industry output, and marginal costs are zero.What is the Cournot reaction function of firm 1 to the output, q₂, of firm 2?

A) 40  4q₂
B) 160  4q²₂
C) 20  .5q₂
D) 160  4q₂
E) 164  8q₂

Question

Maricris Yamuta · Accepted Answer

Final Answer : C, Explanation :  The Cournot reaction function for a firm in a duopoly setting, where firms choose quantities to maximize profits given the quantity chosen by the other firm, can be derived from the inverse demand function and the assumption of zero marginal costs. Given the inverse demand function p = 160 - 4q, where q is the total quantity produced by both firms, and assuming marginal costs are zero, the profit maximization problem leads to the derivation of the Cournot reaction function. The correct reaction function, considering the setup and simplifying the mathematical expressions, is q1 = 20 - 0.5q2, which matches choice C. This reflects firm 1's optimal output level (q1) as a function of firm 2's output level (q2), under the assumption of Cournot competition where each firm assumes the other's quantity as given and adjusts its own quantity to maximize profit.

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