Han is a biochemist in planet Toolong were patents last forever. He has developed a medicine for which the inverse demand curve is given by $P(Q)=20-\frac{Q}{100},$ where $Q$ is the number of doses demanded and $P$ is the price of one dose.

The chemicals and excipients needed for production, alongside labor costs, result in a fixed marginal cost of $$4$ per dose. Assume these are Han's only costs.

Han is a profit$-$maximizer and has obtained a patent for his medicine, making him the monopolist in the market for this drug.

a$)$ What is Han's $($total$)$ revenue function, $R(Q)?$ Recall that the revenue function provides revenue as a function of quantity sold. $[$Hint: As a monopolist, Han chooses how much to charge for his medicine. That said, the number of doses he sells at that price is$,$ of course, determined by the demand curve.$]$

b$)$ Complete the table

c$)$ If Han wants to maximize profits, approximately how many doses of his medicine

should he sell? In a few words, explain your reasoning.

d$)$ If Han wants to maximize profits, how much should he charge for his medicine? In a few words, explain your reasoning.

e$)$ What is Han$$s profit when he is a monopolist?

For part f$)$ and g$),$ suppose there are no patents in Toolong and that knowledge of all newly discovered medicinal formulations is shared for free, without regard for profit.

f$)$ At what price would doses of Han$$s medicine be sold in a competitive market? In

other words, what is the equilibrium price if there were many sellers with access to

the technology needed to produce Han$$s medicine?

g$)$ What would Han$$s profit be in a competitive market?

Food for thought $[$no need to write up an answer$]$: Compare prices in a monopoly and a competitive market. Compare profits in both scenarios. In a world without patents, would Han work on new medicinal formulations?