Suppose that only one firm produces and sells soccer balls in the world. The following equations describe its demand, marginal revenue, total cost, and marginal cost curves:

Demand: P=10-Q

MR=10-2Q

TC=3+Q+0.5Q^2

MC=1+Q

where Q is the quantity of soccer balls (in millions) and P is the pricer per soccer ball.

a) How many soccer balls does the monopolist produce? At what price are they sold? What is the monopolist's profit?

b) Illustrate the monopolist's production choice graphically, and mark the area that corresponds to the monopolist's profit.

c) What is the socially optimal quantity of soccer balls that should be sold? Calculate teh size of the deadweight oss created by the monopolist's decision, and mark it on your graph from part b).