Consider the competitive (private) market for widgets described by the following marginal benefit (MB) and private marginal cost (PMC) curves: MB = 100? 0.1Qd PMC = 4 + 0.06Qs, where Qs and Qd vary from 0 to 1000. Complete the following questions. (This question requires graphing for several parts – you can put all of your curves on the same figure.)
a) Generate a graph of these MB and PMC curves.
b) Using basic algebra, solve for the optimal private level of production, Qm, and the optimal private market-clearing price, Pm, and plot these values on your graph.
c) Calculate both the consumer and producer surplus (social welfare) for the private market outcome and indicate their location on your graph. (It is easiest to divide the area of the graph into subsections and indicate the different values using the sums of these different areas.)
d) Now, assume that each widget that is produced generates a pollution externality equal to $16 per unit. Incorporate this externality into the private-market problem, plot the new “social marginal cost curve”, SMC, and calculate the value of the externality as well as the Net Social Benefits that takes account of this externality (Net Social Benefits = CS+PS Externality).
e) Now, assume that the government implements a tax on widgets that fully internalizes the pollution externality. Using social marginal cost curve, SMC, and the $16 tax, calculate the new consumer and producer surplus, the new externality, the total tax revenue, and the net social benefits from the implementation of the tax. Indicate the tax revenue and externality areas following the implementation of the tax using your graph. Is society better or worse off following the tax?