A scientist has discovered the vaccine formula to the COVID-19
and received a patent for it (a legal monopoly). The scientist has
signed a contract with a pharmaceutical company that will produce
and sell the vaccine on the market.
The monopoly pharmaceutical supplier faces an inverse demand
curve P = 20 - (1/80)Q with marginal revenue MR = 20 – (1/40)Q,
where Q is the output of vaccine in units and P is the market price
per unit. The company desires to set a market price-quantity for
the vaccine to maximize its profits. The monopoly total cost to
supply the vaccine is C= (1/200)Q2 + 6Q + 200 with marginal cost
MC= (1/100)Q + 6.
Explain your work and show graphically each part below. (Don’t
worry if the numbers are not round.)
a. What price and quantity maximizes profit for the monopoly
pharmaceutical company?
b. If the vaccine were produced in a competitive market, what
would be the market price and quantity?
c. What is the profit/loss the monopoly pharmaceutical company
receives? What would be the profit/loss in a competitive market in
the long-run?
d. Find the welfare cost associated with the monopoly
pharmaceutical company’s price and quantity. Show graphically.
Explain the concept of the welfare cost as if you were talking to
someone who had not taken a microeconomics course.
e. Briefly, is there any justification that a such a legal
monopoly may benefit society?
f. Suppose the pharmaceutical company pays the scientist a
percentage of the vaccine total sales (revenues). Would the
scientist prefer a different price (than the monopoly profit
maximizing price) to set for the vaccines? Explain. (Think about
what you would want to maximize here.)