1. The market demand curve for heroin is said to be highly inelastic. Heroin

supply is also said to be monopolized by the Mafia, which we assume to be
interested in maximizing profits. Are these two statements consistent?

Yes, these two statements are consistent. If the demand for heroin is highly inelastic, then the Mafia will be able to charge a higher price for the drug, resulting in higher profits. This is because the demand for heroin is not very sensitive to changes in price, so the Mafia can increase the price without significantly reducing the quantity of heroin demanded.