A profit-maximizing monopoly faces an inverse demand function described by the equation p(y) = 30 - y and its total costs are c(y) = 5y, where prices and costs are measured in dollars. In the past it was not taxed, but now it must pay a tax of 2 dollars per unit of output. After the tax, the monopoly will

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The tax increases the marginal cost by $2, from $5 to $7. The monopoly sets marginal revenue equal to marginal cost to maximize profit. The marginal revenue derived from the demand function is MR = 30 - 2y. Setting MR = MC gives 30 - 2y = 7, solving for y gives y = 11.5. The new price is p(11.5) = 30 - 11.5 = 18.5. The original price was 17.5, so the price increases by $1.

A Profit-Maximizing Monopoly Faces an Inverse Demand Function Described by the Equation