A profit-maximizing monopoly faces an inverse demand function described by the equation p(y) = 40 - y and its total costs are c(y) = 7y, where prices and costs are measured in dollars. In the past it was not taxed, but now it must pay a tax of 6 dollars per unit of output. After the tax, the monopoly will

Question

Quizplus · Accepted Answer

After tax, the new total cost function would be c(y) = 7y + 6y = 13y. 
To maximize profit, the monopoly would produce where marginal revenue (MR) equals marginal cost (MC): 
MR = 40 - 2y 
MC = 13
Setting MR = MC: 
40 - 2y = 13 
Solving for y: 
y = 13.5 
Therefore, the monopoly would produce 13.5 units of output after the tax. 
To determine the new price, substitute y = 13.5 into the demand function: 
p(y) = 40 - y = 40 - 13.5 = 26.5 
Therefore, the new price after tax would be $26.50. 
Comparing it to the price before tax, $40 - $13.50 = $26.50, the price would decrease by $3. Therefore, the correct answer is C. The monopoly would leave its price constant, as it does not make sense to increase prices when demand decreases due to a tax.

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