Hello, i'm currently studying economics and i experiment some difficulties doing this exercice.

An oil refinery is operating near a coastal town. The oil refinery can sell its refined oil at a fixed price equal to the global market price for refined oil. The oil refinery faces an upward sloping marginal cost curve and needs to decide on its optimal level of output. Oil refining however, has unintended side effects on the nearby coastal town under the form of pollution. For each unit of refined oil the refinery produces and sells, it imposes a health cost on the community's inhabitants, which is increasing in the total quantity of oil refined. The graph below shows the refinery's marginal private cost of production, its marginal external cost and its marginal social cost at different output levels. P, Refined Oil; MC Marginal social cost $250- $200 Marginal private cost $150 Marginal external cost $100 $50 100 200 300 400 500 600 700 Q, Refined Oil 1. In the absence of any intervention by the coastal town or government regarding the firm's operations: a. What is the firm's optimal level of output when the market price of refined oil is $150? b. What is the socially optimal level of output when the market price of refined oil is $150? 2. Explain and Illustrate using a graph how a well-chosen government tax on each unit of oil produced and sold can result in the firm producing the socially optimal level of output