The correct answer is: Both 1 and 2.
According to Prof. Schumpeter, monopolies are inefficient because they produce less output and charge higher prices than a perfectly competitive market would. However, he also argued that monopoly profits act as an incentive for innovation, as firms compete to be the first to introduce new products and services.
Option 1 is true because monopolies have a great deal of market power, which allows them to charge higher prices and produce less output than a perfectly competitive market would. This is because consumers have no other choice but to buy from the monopolist, and the monopolist can therefore charge whatever price it wants. As a result, monopolies are often seen as being inefficient.
Option 2 is also true because monopoly profits can act as an incentive for innovation. This is because firms that are able to innovate and introduce new products and services can earn monopoly profits for a period of time before other firms are able to copy their innovations. This gives firms an incentive to invest in research and development, which can lead to new and better products and services being developed.
Option 3 is false because AR is not equal to MR for a monopolist. This is because a monopolist faces a downward-sloping demand curve, which means that it can sell more units of its product by lowering its price. As a result, the marginal revenue curve for a monopolist lies below the demand curve.
In conclusion, both options 1 and 2 are true according to Prof. Schumpeter about a monopolist.