A bakery produces bread. The production function of bread is q(e)=24e, where is e is the baker’s effort.

The baker can sell each loaf of bread (i.e. each q) for 2.

Baking bread creates effort costs for the baker which are given by c(e)=2e2.

The bread also produces a very nice smell, which creates a positive externality worth s(q) = 0.5 q to the local residents.

a. What number of loaves (i.e. q) maximizes the baker’s profits and what are the baker’s profits in this case?

b. What number of loafs (i.e. q) maximizes social welfare and what are the baker’s profits in this case?

c. What is – in general – the Pigouvian solution to undersupply of positive externalities?

d. The local government decides to tax or subsidize the production of bread in order to get the baker to produce the social welfare maximizing number of loaves (i.e. q). How high is the tax or subsidy per loaf of bread?

e. What are the baker’s profits with the tax / subsidy from d)?

Please show method and steps for the answer,