A new smartphone is just being released. The cost function is given by totalcost = 5x2, where x is the number of smartphones sold (in millions). The market demand for this smartphone is given by the inverse demand P = 300?10x. Assume that the market is competitive. Smartphones require superconductors, and the production of superconductors is heavily polluting due to the use of many chemicals in the process. The damages to society are given by Ds = 10x2.

a) Find the private marginal benefit, the private marginal cost, and the market equilibrium for this smartphone. What are the consumer surplus, producer surplus, total damage, and total surplus in this equilibrium?

b) Find the social optimum in the market for this smartphone. Compare total surplus in this case to that in part (a).