The demand for t-shirts is Q = 20 ( P/2, where Q is the number of t-shirts and P is their price. The private cost of producing t-shirts is C(Q) = Q2, with private marginal cost MCP = 2Q. Washing and dyeing the t-shirts causes water pollution with total damages CE(Q) = Q2/2, marginal external costs of MCE = Q. Let's see how we can use this information to develop a social supply curve, marginal benefit and cost of pollution curves, and marginal benefit and cost of abatement curves.
(a) First, let's figure out the market equilibrium when everyone ignores external costs. Remember that the supply curve is marginal cost above average variable costs. In this case it is the entire marginal cost curve. What is the private supply curve for t-shirts? Use that private supply curve plus the demand curve to find the equilibrium price and quantity. Draw a diagram showing the private supply, demand, and the equilibrium.
(b) Next, add the marginal external costs to your diagram. Then calculate the full-cost supply curve and add that to your diagram. Remember that in this case we first add (marginal) costs, not quantities, since these are the costs associated with each t-shirt. Finally, use the full-cost supply curve and the demand curve to find the efficient price and quantity. Show these on your diagram.