Consider the market of milk. The inverse demand for milk (private marginal benefit, PMB) is as follows:

where PMB and Q represent price and quantity respectively. Suppose the private marginal cost (PMC) of production is $2 per litre, namely

Since cows produce greenhouse gas, the social marginal cost (SMC) is $4 per litre, that is

1. Sketch (accurately) and label the PMC, SMC and PMB curves.
2. Use the appropriate equations to find the market equilibrium quantity and the socially optimal quantity. Illustrate your answers in the diagram.
3. How might the social optimum be achieved?