Draw an example of a monopoly with a linear demand curve and a constant marginal cost curve.
a. Show the profit-maximizing price and output, p* and Q*, and identify the areas of consumer surplus, producer surplus, and deadweight loss. Also show the quantity, Qc, that would be produced if the monopoly were to act like a price taker.
b. Now suppose that the demand curve is a smooth concave-to-the-origin curve (which hits both axes) that is tangent to the original demand curve at the point (Q*, p*). Explain why this monopoly equilibrium is the same as with the linear demand curve. Show how much output the firm would produce if it acted like a price taker. Show how the welfare areas change.
c. How would your answer in part a change if the demand curve is a smooth convex-to-the-origin curve (which hits both axes) that is tangent to the original demand curve at the point (Q*, p*)?