Economics 402 problem set 3 question. .Problem No. 5.

Problem 5: Suppose that the demand curve is now P (91 + (12) = 110 2011 + 92). Suppose that rms 1 and 2 simultaneously choose quantity q1 and (12 to supply and that the rms incur a marginal cost of production equal to 10. Assume that the quantities that each rm can supply are [0, 55]. As a result, each rm's utility function is given by: \"1((11,Q2) = (110 2(931 + 9'2))CI1 10(11 \"2(q1, r12) = (110 - 2(91 + q2))t12 - 10(12- Part a: If rm 2 produces quantity Q2, what is the best response for rm 1? Use this to solve for the best response function for rm 1, BR1(q2). Similarly solve for the best response function for rm 2, BR2(q2). Part I): What are the strictly dominated strategies of each rm in this game? Justify why each of these strategies are strictly dominated. Justify why all other strategies are not strictly dominated. Part c: After having eliminated the strictly dominated strategies found in part a, what are the strictly dominated strategies in the reduced game? Provide justication again. Part d: [Esctm Credit] What are the rationalizable strategies for each player? What are the ratio nalizable strategy proles