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]
1) To determine the elasticity of demand for the EpiPen at its equilibrium price, we can use the Lerner index formula:
Lerner index = (P - MC) / P
Where P is the price, and MC is the marginal cost. In this case, the retail price of an EpiPen is $300, and the estimated cost to produce each unit is $30. Substituting these values into the formula:
Lerner index = (300 - 30) / 300 = 0.9
The Lerner index measures market power, and in this case, it indicates that Mylan has a high degree of market power. The higher the Lerner index, the lower the elasticity of demand. Therefore, the elasticity of demand for the EpiPen at its equilibrium price is relatively low.
This low elasticity of demand suggests that Mylan may be maximizing its profits by setting a high price for the EpiPen. When demand is inelastic, a firm can increase its profits by raising prices since the quantity demanded is not significantly affected.
2) Given the linear indirect demand function P = a - bQ, we can use the point elasticity of demand formula to find the values of "a" and "b" using the elasticity calculated in part 1 and the unit sales of EpiPen.
The point elasticity of demand formula is:
E = (1/slope) * (P/Q)
Where E is the elasticity of demand, slope is the coefficient of Q in the demand function, P is the price, and Q is the quantity.
In this case, we know that elasticity is 0.9 and the unit sales are 1 million. Substituting these values into the formula:
0.9 = (1/slope) * (300/1)
0.9 = 300/slope
Solving for slope:
slope = 300 / 0.9 = 333.33
Now we can substitute the slope into the demand function to solve for "a":
300 = a - (333.33 * 1)
300 = a - 333.33
a = 300 + 333.33
a = 633.33
Therefore, the values of "a" and "b" in the demand function are a = 633.33 and b = 333.33.
3) To derive the marginal revenue function, we need to differentiate the demand function P = a - bQ with respect to quantity Q:
MR = dP/dQ = -b
Since the demand function in this case is linear, the marginal revenue is constant and equal to the negative of the slope coefficient "b."
Given that the marginal cost of production is constant at $30, we can calculate the producer surplus, consumer surplus, and deadweight loss from monopoly pricing.
Producer surplus is the difference between the market price and the marginal cost of production. In this case, the market price is $300, and the marginal cost is $30. Therefore, the producer surplus per unit is:
Producer surplus = Market price - Marginal cost = $300 - $30 = $270
Consumer surplus is the difference between the market price and the willingness to pay. In this case, since the demand function is linear, willingness to pay can be calculated by rearranging the demand function:
P = a - bQ
Q = (a - P) / b
Substituting the given values of "a" and "b" into the equation and solving for Q:
Q = (633.33 - 300) / 333.33 = 0.99 million
Consumer surplus per unit is given by:
Consumer surplus = Willingness to pay - Market price = ($300 - $633.33) / 333.33 = -$0.99
Since the quantity sold is 1 million, the total consumer surplus is:
Consumer surplus = 1 million * -$0.99 = -$0.99 million
Deadweight loss represents the loss in economic efficiency due to monopoly pricing. It can be calculated as half the difference between the monopoly quantity and the socially optimal quantity (where marginal cost equals marginal valuation). In this case, since the marginal cost is constant at $30, the socially optimal quantity would also be 1 million units.
Deadweight loss = 0.5 * (1 million - 1 million) * ($300 - $30) = $0
Therefore, the deadweight loss is zero in this scenario.
4) To illustrate the profit-maximizing price, quantity sold, producer surplus, consumer surplus, and deadweight loss, we can use a diagram.
[Diagram explanation]
5) If the government imposes a price ceiling on the EpiPen, assuming it is below $300 but above $30, several implications for the market can arise. A price ceiling sets a maximum price that can be charged for a product.
Given that the current equilibrium price is $300, imposing a price ceiling below $300 would result in a price reduction. This would likely increase the quantity demanded as consumers can now purchase the EpiPen at a lower price. However, due to the low elasticity of demand calculated earlier, the quantity demanded may not increase significantly.
As a result of the price ceiling, there might be a shortage of EpiPens, as the quantity supplied may not be able to meet the increased demand at the lower price. This shortage could lead to rationing or black market activity.
In terms of the producer, imposing a price ceiling would reduce their ability to charge a higher price and hence lower their profits. This could potentially impact their willingness to produce and invest in the product.
Overall, the implications of a price ceiling on the EpiPen market would depend on the specific details of the price ceiling and its impact on both supply and demand dynamics.