Suppose that there are 2000 agents with a positive willingness to pay for a good

(say, cars). The agents are heterogenous in their willingness to pay. These willingness to pays are uniformly distributed between 1 and 1000. Hence, someone has willingness to pay 1000, someone has willingness to pay 999.50, someone has willingness to pay 999, someone has willingness to pay 998.50, someone has willingness to pay 998,..., someone has willingness to pay 2, someone has willingness to pay 1.50, someone has willingness to pay 1, and someone has willingness to pay 0.50.

The consumption of this good has a negative externality on others. The total size of this externality is e(q) = ?800000 ? 50q for all q > 0 and e(q) = 0 for q = 0; where q is the number of agents consuming the good.

The good is produced by a competitive industry. The total cost of producing the good is T(qi) = 100qi for all firms in the industry, where qi is the quantity produced by the firm.

a) Draw the market demand curve. and the industry supply curve (in the absence of taxes).

b) Solve for the competitive equilibrium allocation and price (in the absence of any taxes and other government interventions).

c) Determine the optimal policy.

lQuestion 4. {3 points) Suppose that there are 2000 agents with a positive willingness to pay for a good (say, cars). The agents are heterogencus in their willingness to pay. These willingness to pays are uniformly distributed between 1 and 1000. Hence, someone has willingness to pay 1000, someone has willingness to pay 999.50, someone has willingness to pay 090, someone has willingness to pay 903.50, someone has willingness to pay 098,..., someone has willingness to pay 2, someone has willingness to pay 1.50, someone has willingness to pay 1, and someone has willingness to pay 0.50. The consumption of this good has a negative externality on others. The total size of this externality is e(g] = 300000 50:1 for all :1 .'2 0 and e{q] = 0 for q = 0; where q is the number of agents consuming the good. The good is produced by a competitive industry. The total cost of producing the good is TIIqi) = 1009:; for all rms in the industry, where q:- is the quantityr produced by the rm. a) Draw the market demand curve. and the industry supply curve (in the absence of taxes]. b] Solve for the competitive equilibrium allocation and price [in the absence of any taxes and other govern ment interventions]. c) Determine the optimal policy.|