A rock-climbing school faces two demand curves. The demand by local residents is Q = 400 - 0.5P, and the demand by others is Q = 500 - 0.5P. The marginal cost of serving either local or nonlocal residents is constant at $100. If the rock-climbing school cannot practice third-degree price discrimination and must charge a single price to all customers, it will charge:

Question

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To find the single price the school will charge, we first need to find the combined demand curve by adding the quantities demanded by locals and nonlocals at any price P. The combined demand is Q_combined = (400 - 0.5P) + (500 - 0.5P) = 900 - P. To maximize profit, we set marginal revenue (MR) equal to marginal cost (MC). The inverse demand curve is P = 900 - Q. Differentiating this with respect to Q gives us MR = 900 - 2Q. Setting MR = MC, we have 900 - 2Q = 100. Solving for Q gives Q = 400. Substituting Q back into the inverse demand curve, P = 900 - 400 = $500.

A Rock-Climbing School Faces Two Demand Curves