5. Take the two period general equilibrium model seen in attached notes and add a production externality (e.g. pollution):

a) Define the equilibrium.

b) Write down the household's optimization problem(s).

c) Generate and interpret the rst order conditions.

d) Show/argue that the second order conditions are satisfied.

e) Write down the firm's optimization problem.

f) Generate and interpret the first order conditions.

g) Show/argue that the second order conditions are satisfied.

h) Impose the market clearing conditions, as well as any conditions requiring

consistency between individual and aggregate quantities.

i) Solve the social planner's problem (only possible when there is a representative household)

remark: The answers should be similar to the attached pdf file notes