Given an inverse demand function for hangars: $$P = 3 - \frac{Q}{16,000}$$ and constant marginal cost of $1$, what is the equilibrium price and quantity of hangars in a monopoly?
In a perfectly competitive market we need $P = MC$, which gives us an equilibrium price of $1$ and quantity of $32,000$. However, in a monopoly we need $MC = MR$, and in this case that equates simply to price = $1$. Then, the demand gives us, again, an equilibrium quantity of $32,000$. Am I making some mistake somewhere, or are the equilibrium prices and quantities in a monopoly and competitive market in this example equal simply by coincidence?