Elasticity , profit maximizing price- output and social welfare effects of first degree price discrimination for the drug company Botox

The patented drug, Botox, is currently sold by Allergan, Inc. It was originally used as a "miracle drug" to treat two relatively rare eye conditions that led to functional blindness, but when its usefulness in cosmetic applications became apparent, its sales expanded rapidly. Prior to the FDA approval for cosmetic use, sales were in the ballpark of $400 million annually, but after approval in 2002, sales doubled. The current price for a vial of Botox, is $400, and the marginal cost to produce a vial is $25. Botox is usually injected under the skin around the eyes and in the forehead in order to paralyze the muscles and to smooth the appearance of wrinkles. These wrinkle-smoothing effects last approximately 120 days, requiring repeated injections to maintain the appearance of youth.

a) Utilizing the Lerner index, find out 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.

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 determine whether the current price and quantity Allergen is setting is maximizing its monopoly profits.

c) If Allergen is able to use first-degree price discrimination, what is the lowest price it will charge for a vial of Botox? describe 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.

d) In another recent article,[1] a different kind of product called a dermal filler used to "plump up folds and creases" and intended for facial use below the nose is becoming a hot seller, too. Allergan is beginning to roll out its version, called Juvederm, designed to compete with the current market leader, Restylane, produced by Medicis. Medicis is in the process of introducing its own injectable neurotoxin to compete directly with Botox for wrinkle-smoothing above the nose ("Reloxin"). Discuss the economies of scope in producing and marketing these two kinds of cosmetic products, and the competitive implications for this market if Medicis can successfully launch its "Reloxin" and Allergan can create demand for its Juvederm. How will this entry affect pricing power in this market? Discuss, being sure to cite any sources you use.