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# Lerner Index, Profit Maximization, first-degree price discrimination, etc.

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The patented drug, Botox, is currently sold by Allergan, Inc. The current price for a vial of Botox, is \$400, and the marginal cost to produce a vial is \$25.

a) Using the Lerner index, find the price elasticity of demand for Botox and interpret what this value means to total revenue if the price of Botox were increased one percentage point.

Note: Lerner Index is the difference between price and marginal cost dived by price. L = (p-MC)/P The larger the L the greater the degree if monopoly power.

b) The inverse demand for Botox is: P = 775 - 375Q, where Q represents millions of vials of Botox and P is in dollars per vial. Derive the marginal revenue curve and find the price and quantity Allergen will set in order to maximize its monopoly profits.

c) Draw a diagram of the firm's inverse demand, marginal revenue, MC, and optimal price and quantity. In addition, show the areas of consumer surplus, producer surplus, and deadweight loss and calculate their values (in dollars).

d) If Allergen is able to use first-degree price discrimination, what is the lowest price it will charge for a vial of Botox? Explain the concept of first degree price discrimination, and show how social welfare will be affected if Allergen is permitted to set price in this way.