Question

Two firms are producing identical goods in a market characterized by the inverse demand curve P = 120 – 4Q, where Q is the sum of Firm 1's and Firm 2's output, q₁ + q₂. Each firm's marginal cost is constant at $20.

Graph the reaction function for each firm and indicate the Nash equilibrium.

Answer 1

P= 120-4G and me, = mc2 = 20 We can determine the reaction function for firm 1 as follows. To maximize profit, it sets mRi= me. Given that, P = 120-4Q 7 P = 120-4(qit q2) 7 P = 120 - 42 - 492 multiplying both sides with q, we get P2i = 1204,- 49,² - 49122 TRI = 1209,- 49, ² - 49122 > MRI= d(TRI) = 120 - 89,- 492

Setting mRi= me, we get 120-891 - 492 = 20 → 89, = 100 - 492 191 = 12.5-0.592 firm 1's reaction I curve The same appling cakulation applies for firma: Firm 2's reaction curore : 192 = 12.5 -0.5911 firm z's Reaction curve 12 .5 A Nash equilibrium Firon t's Reaction Curve 12.5 25