Suppose we are thinking about a good that provides a positive externality to society. Winter is coming, so we will focus on snow shovels. We will first think about the private equilibrium. The firms who produce snow shovels have a supply curve given below. This is the private supply of snow shovels. Qs-Private = 2p Consumers have a (private) demand for snow shovels given by: QD-Private = 100 -0.5p 1. Plot both the private demand and supply with Q on the x-axis and p on the y-axis. Label the private market equilibrium p* and Q*. Also label the y-intercept for both demand and supply and the x-intercept for demand. Show your work for the calculation of p* and Q*. [3 points] Now suppose that society wants more snow shovels out there, because people shoveling their own sidewalk 2. When we say that a private individual will only take into account their own personal interest when deciding if to buy a snow shovel, what does this mean? [1 point] Now suppose therefore that the social demand curve for these snow shovels is given by: QD-Social = Qo-Private + 10 3. Given this social demand curve, solve for the socially optimal level of production (Q;) and the corresponding price level in this equilibrium (p*). Show your work. [2 points] 4. Is the private market overproducing or underproducing in this example? How do you know? [1 point] We talked in class about different solutions to these externality problems. Pigou had one solution. 5. What would the Pigouvian solution be in this case to push the private equilibrium to the socially optimal equilibrium. In this example, the Pigouvian solution would be to subsidize consumers' purchases of the snow shovels. What subsidy would they need to implement to solve this problem? (Be specific, including exact numbers associated with this solution. ) Show any work. (3 points]