Suppose the following:
• The demand function for both products 1 and 2 has a constant elasticity: Q1 = k1 p1-ε1 and Q2 = k2 p2-ε2 where εi is the absolute value of the elasticity of demand for product i and ki is a parameter that reflects the size of the market. Suppose that ε1 = 6, ε2 = 1.1, and k1 = k2 = 20.
• The cost function is C(q1, q2) = f + f1 + f2 + q1 + q2, where f is a fixed common cost and fi is product-specific or attributable fixed costs. Marginal cost of production for each product is constant and equal to 1. Suppose that f = 2, f1 = .5 and f2 = .5. A firm that produces both products is a natural monopolist. Splitting up production would entail duplicating the fixed
common costs and thereby raise total costs.
Find the Ramsey prices.