The pricing of pharmaceutical products can be controversial. A recent example is EpiPen
produced by Mylan which is used to treat anaphylaxis. The retail price of an EpiPen is
$300, while industry sources estimate that it costs around $30 to produce each unit (i.e.
one dose). Despite this high price, Mylan sells 1 million units a year.
Questions
1) Use the Lerner index to determine the elasticity of demand for the EpiPen at its
equilibrium price. Is this elasticity consistent with the producer of the EpiPen, Mylan,
maximizing profits? Explain your answer. [2 points]
2) Assume Mylan's indirect demand function is linear: P = a – bQ, where Q is measured
in millions of units. Using the definition of the point elasticity of demand, the elasticity
you calculated in part 1 and the unit sales of EpiPen, find the values of “a” and “b” in the
above equation. [4 points]
3) Derive the marginal revenue function. If the marginal cost of production is constant at
$30, calculate the producer surplus, consumer surplus, and deadweight loss from
monopoly pricing. [4 points]
4) Use a diagram to illustrate the profit maximizing price, quantity sold, producer surplus,
consumer surplus and deadweight loss. [3 points]
5) Analyze the implications for the EpiPen market if the government imposes a price
ceiling on the EpiPen. Assume that the price ceiling is below $300 but above $30. [2
points]
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1) To determine the elasticity of demand for the EpiPen at its equilibrium price, we can use the Lerner index formula. The Lerner index is calculated as (P - MC) / P, where P is the price and MC is the marginal cost. In this case, the price is $300 and the cost is estimated to be $30.
Lerner index = (300 - 30) / 300 = 0.9
The Lerner index gives us a measure of market power, with higher values indicating less competition and more pricing power. This means that the demand for EpiPen is relatively inelastic, as consumers continue to purchase it even at the high price.
Based on this elasticity, Mylan can be seen as maximizing its profits. With a relatively inelastic demand, Mylan can set a higher price and still sell a significant amount of EpiPens, resulting in higher profits.
2) Assuming the indirect demand function is linear: P = a - bQ, we can use the concept of point elasticity of demand to find the values of "a" and "b".
Point elasticity of demand is calculated as the percentage change in quantity divided by the percentage change in price: (dQ/Q) / (dP/P).
Given that the elasticity from part 1 is 0.9 and that Mylan sells 1 million units a year, we can substitute these values into the point elasticity formula:
0.9 = (dQ/1 million) / (dP/P)
To continue solving for "a" and "b", we need more information such as the actual values of quantity (Q) and price (P) or the rate of change of quantity and price.
3) To derive the marginal revenue function, we need to use the inverse demand function. In this case, the inverse demand function is P = a - bQ. Taking the derivative of this function with respect to Q will give us the marginal revenue function:
MR(Q) = a - 2bQ
Since the marginal cost of production is constant at $30, we have the marginal cost function as MC(Q) = $30.
To calculate the producer surplus, we need to integrate the area between the marginal cost curve and the marginal revenue curve from 0 to the quantity sold.
Consumer surplus, on the other hand, is the difference between what consumers are willing to pay (P) and the market price (MC). In this case, it would be the area above the marginal cost curve and below the demand curve, from the quantity sold to the demand curve intercept.
Deadweight loss from monopoly pricing is the loss of economic efficiency due to the monopolistic control of a market. It is represented by the area of lost welfare between the demand curve and the marginal cost curve.
4) To illustrate the profit-maximizing price, quantity sold, producer surplus, consumer surplus, and deadweight loss, a diagram can be used. However, as an AI text-based bot, I am unable to create or display visual diagrams. It would be better to refer to a textbook or online resource that can provide a visual representation of the diagram.
The profit-maximizing price and quantity occur where marginal revenue equals marginal cost, corresponding to the point where the marginal cost curve intersects the marginal revenue curve.
Producer surplus is the area above the marginal cost curve and below the price line, up to the quantity sold.
Consumer surplus is the area above the marginal cost curve and below the demand curve, down to the quantity sold.
Deadweight loss occurs due to the difference between the socially optimal quantity and the quantity produced by the monopolistic firm. It represents the loss of efficiency in the market.
5) If the government imposes a price ceiling on the EpiPen below $300 but above $30, it would result in a few implications for the EpiPen market:
- The price ceiling would set a maximum price that Mylan can charge for the EpiPen, which would be below its current market price. This could help alleviate concerns about high prices and make the product more affordable for consumers.
- However, if the price ceiling is set too low, closer to the production cost of $30, it may discourage Mylan from producing and supplying the product. This could lead to shortages in the market and limited availability of the EpiPen.
- The price ceiling could also impact Mylan's profits, as the company may not be able to make as much profit per unit sold if the price is constrained by the ceiling.
- It is important for the government to strike a balance between ensuring affordability for consumers and incentivizing producers to continue supplying the product. Regular monitoring and adjustments may be necessary to achieve the desired outcomes in the market.