Answer to Question #274123 in Microeconomics for Montosix

Question

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, Q, that would be pro duced 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 pro duce 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*)?

Answer 1

The above graph shows the monopoly with linear demand and a constant marginal curve. The vertical axis measures the price as P^* and horizontal axis measures the quantity as Q^*.Qc is the point at which the marginal cost and demand curve intersect each other. Consumer surplus is denoted as CS, producer surplus as PS and the dead weight loss as DWL.

The above curve shows the concave and the convex origin of demand curve. Since the demand curve is tangent to the marginal cost, then the slope of demand curve(Marginal revenue) is equal to the marginal cost. Thus the optimum production point occurs at Q^*. If the demand curve is concave to the origin then the producer surplus will decrease and the consumer surplus will increase. Therefore, if the demand curve is convex to the origin then the producer surplus will increase and consumer surplus would decrease