A senior student at SUNY Canton analyzed the private market of refined petroleum. She assumed that this specific market is competitive and estimated the following supply and demand relationships for refined petroleum products:

Supply (S) or Marginal Private Costs (MPC): MPC = 10+0.075Q,

Demand (D) or Marginal Private Benefits (MPB): MPB = 42-0.125Q,

where Q is measured in thousands of barrels per day and P is the price per barrel.

To complete her analysis of refined petroleum products, she estimated the Marginal External Costs (MEC) function as

MEC = 0.05Q

Based on the constant slope of 0.05, the MEC resulting from water pollution is increasing at a constant rate of 0.05 with respect to oil production. Because Q is measured in thousands of barrels per day, this value implies that for every additional 1,000 barrels of refined oil produced, the Marginal External Costs of pollution rise by $0.05 per barrel.

a). Derive the Marginal Social Costs (MSC) equation.

b). Find the socially optimal (efficient) levels for price and output graphically.