If a representative firm with long-run total cost given by TC = 50 + 2q + 2q² operates in a competitive industry where the short-run market demand and supply curves are given by Q_D = 1,410 - 40P and Q_S = -390 + 20P,its long-run profit-maximizing level of output is:

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To find the long-run profit-maximizing level of output, we need to set the marginal cost (MC) of the representative firm equal to the market price (P) and solve for q. The long-run total cost of the representative firm can be written as: TC = 50 + 2q + 2q² Taking the derivative with respect to q, we get: MC = 2 + 2 Setting MC equal to the market price: P = MC = 2 + 2 Solving for P: P = 2 + 2 P - 2 = 2 P(1 - 2) = 2 P = 2/(1 - 2) Substituting the market price into the market demand equation: Q_D = 1,410 - 40P Q_D = 1,410 - 40(2/(1 - 2)) Q_D = 1,410 - 80/(1 - 2) Similarly, substituting the market price into the market supply equation: Q_S = -390 + 20P Q_S = -390 + 20(2/(1 - 2)) Q_S = -390 + 40/(1 - 2) At the long-run equilibrium, market demand must equal market supply: 1,410 - 80/(1 - 2) = -390 + 40/(1 - 2) Multiplying both sides by (1 - 2): 1,410(1 - 2) - 80 = -390(1 - 2) + 40 1,410 - 2,820 - 80 = -390 + 780 + 40 1,250 = 3,600 Solving for : = 1,250/3,600 = 0.3472 Substituting back into the market price: P = 2/(1 - 2) = 2/(1 - 2(0.3472)) = $3.07 Finally, substituting the market price back into the marginal cost equation: P = 2 + 2 $3.07 = 2 + 2(0.3472)q q = 5.06 Therefore, the long-run profit-maximizing level of output for the representative firm is 5 units.

If a Representative Firm with Long-Run Total Cost Given by TC