In this question we will combine a very simplied model of an externality that has long-lasting

impacts with the model of discounted utility that we learned in our game theory topic. Consider

a hypothetical environmental externality: produced as the byproduct of industrial activity, each

unit of emission of a pollutant that is emitted once, today, causes $10 of external harm to society

each and every year, starting immediately, forever. Let's say that policymakers apply a discount

factor of 2 (0; 1) to future gains and losses, in an analog of the discounted utility model except

for cash payos rather than utilities.

What would the socially ecient Pigouvian tax on the emission of this pollutant be if we applied

a discount factor of (i) = 0:5, (ii) = 0:9, and (iii) = 0:99? Give an intuitive explanation

of how to interpret the parameter in this context, and explain precisely but in simple terms

what the goal and eect of the Pigouvian tax would be.