Consider a monopolist with a linear demand curve: q = a - bp, where a, b > 0. It produces at constant marginal cost c and has no fixed cost. Assume that 0 < c < a / b. 

1. Find the monopoly price, quantity, and profits.

2. Derive the inverse demand curve P (q). Draw P (q), the MR-curve, and the MC-curve in a diagram. Explain why we need the assumption c < a / b.

3. Does it matter that the monopolist sets price instead of quantity?

4. Calculate the deadweight loss of monopoly.

5. A change in b results in two opposing effects on the deadweight loss. Calculate the effect of a change in b on the deadweight loss.

6. Derive the price elasticity of demand η for any price. How does η change with p?