Demand is given by:   Q = 1000 – 3P
Supply is given by:      Q = P

1. Find the market equilibrium price and quantity, graph it, and calculate consumer and producer surplus.
Set quantity supplied equal to quantity demanded.
P*=250, Q*=250
CS = 1/2 (333.33-250)(250) = $10,416.25
PS = 1/2 (250)(250) = $31,250
Total Social Welfare = $41,666.25

2. Now assume that there is a $50 (negative) externality; that is, every unit produced creates $50 worth of pollution.

a. What is the equation of the social marginal cost curve?
P = 50 + Q  (or Q = -50 + P)

b. What is the efficient price and quantity? Calculate consumer and producer surplus.
P** = 262.50, Q** = 212.50

c. What is the deadweight loss if the quantity in part 1.  is produced?
First, calculate new social welfare.
CS = 1/2 (333.33-262.50)(212.50) = $7,525.69
PS = 1/2 (262.5-50)(212.5) = $22,578.12  (this is net of the externality)
Total Social Welfare = $30,103.81
Original SW - Externality Cost = $41,666.25 - (50)(250) = $29,166.25
Thus, the DWL is $937.56

d. Graph your results.