We have learnt that in a perfectly Competitive market, all cost savings from a technological advance are passed along to cnsumer in the form of lower prices (Recall the genetically modified example in lecture notes notes "profit maximization and competitive supply in the long run") is the same true of monopoly? Let's see.

Now a more advanced technology is available and changes the total cost function of the monopolistn to be:

TC=0.5Q² + 10Q

Demand does not change.

Solve for the price and quantity that the monopolist would chose to maximize its profit under the more advanced technology. And also calculate the resulting profit.