Imagine a world with two goods: good x and a cash m. In this world, the consumption of x; units of good x causes a quantity of pollutants to be released s - x,. Cash consumption does not cause pollution. There are n identical consumers in this economy, each with an income of y and all having the following preferences: Ui(z;,m;) = alnz; + m; + BE, T F n Where B o= B Zil 5% is the quality of the air that the consumer breathes. Suppose that the price of the good x is p and that the price of cash mis 1. a) Mathematically calculate the quantity of the good x consumed by each individual at the Nash equilibrium of this game? b) If individuals could coordinate their decision to consume the good x, calculate mathematically, the quantity of good x would they agree to consume each one? c) Suppose a government seeks to encourage people to individually choose the quantity of x which would be obtained by the cooperation in (b). Calculate mathematically the amount of tax on the property x should he impose