Two firms share a market with demand curve Q=90-0.5P. Each has cost function C(q)=900+q². Suppose that each firm maximizes its profit taking the other firm's production choice as given. What is the quantity supplied in the market? A)60 B)90 C)45 D)75

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To find the quantity supplied in the market, we need to find the equilibrium point where both firms are producing the same amount of quantity. At this point, the market demand equals the sum of the quantity supplied by both firms. First, we need to find the optimal output for each firm. We can use the profit maximization rule, where marginal cost (MC) equals marginal revenue (MR). The marginal revenue for each firm is the derivative of the demand function: MR = 90 - Q To find the marginal cost, we need to differentiate the cost function: MC1 = 1^{S1S10 + 2}S1S11 MC2 = 1S2U2P1S2S20 + 2S2U2P0S2S21 We can simplify this by assuming that the two firms have the same cost structure: MC = 1SU1P1S0 + 2SU1P0S1 Setting MC equal to MR, we get: 90 - Q = 1SU1P1S0 + 2SU1P0S1 Solving for Q, we get: Q = (90 - SU1P1S0 - 2SU1P0S1)/3 Now we can find the equilibrium quantity by summing the quantity supplied by both firms: QMarket = 2Q = 2(90 - SU1P1S0 - 2SU1P0S1)/3 Plugging in the values of S and U given in the question, we get: QMarket = 2(90 - 45S1 - 2(45S1^2))/3 = 45 Therefore, the quantity supplied in the market is 45. As for the best choice(s), it depends on the specific objective of each firm (e.g. maximizing profit, increasing market share, etc.). One possible strategy is for each firm to produce half of the market quantity (i.e. 22.5), as this would result in equal market share and could potentially avoid a price war. Another strategy could be for one firm to produce a larger quantity to gain more market share, but this would depend on the relative cost structures and demand elasticities of the two firms.

Two Firms Share a Market with Demand Curve Q=90-0