3. (This problem requires some knowledge of calculus.) Suppose there are two firms in a production economy, each using good 1 as an input to produce good 2. They are both located in the same town, and both are bad polluters, so each one's operation has a deleterious effect on the other. Firm I's production setYiis given by

6.1.

,3

yi2 < V-yn - jy'22'

Firm 2's production set I2 is given by

2/22 <V-y2i - jyi2'

Suppose the market prices of goods 1 and 2 are given by p = (1,1).

Assume that each firm takes the other's output as given and fixed.

a. Calculate the competitive equilibrium production plan for the economy.

b. Show that the competitive equilibrium is not an optimum.