The demand for lithium is given by P = 500 0.2L, where L is the quantity of mined lithium and P is the price. Lithium is mined at a constant marginal cost of $50 and sold in a competitive market. a) What is the quantity of lithium sold in equilibrium? b) If lithium mining generates a marginal external cost of $0.1L, what is the socially optimal level of lithium? c) Draw a diagram illustrating the private and social marginal cost curves, and the demand curve. Determine and place on the diagram the private market quantity, the socially optimal quantity, and the social welfare cost