1. Consider two countries that have entering into an agreement to reduce their energy production in order to reduce pollution levels in each of the two countries. Combined demand for energy for the two countries is described by
   1. P = 400 -1Q,

where P is the per unit price of energy and Q is the combined demand for energy across the two countries (so, Q=q₁+q₂)

The countries only consume the energy produced in the two countries, so they neither import nor export outside of the countries. Assume they each have constant marginal costs of $50 per unit to produce the energy and no fixed costs, so TC_i=50q_i(where i=1,2) and MC_i=50. If both countries agree to curb the production of energy, each country will agree to produce 100 units per period. If either country (or both countries) chose to renege on the agreement the country reneging will produce 175 units, while the one agreeing will still produce 100 units. Utilizing the demand information provided and the production information, find the prices possible under these four possible scenarios.

Scenario	Country 1	Country 2	Q=q1+q2	P (400-Q)
Agree/Agree	100	100	200	200
Reengage/Agree	175	100	275	125
Agree/Reengage	100	175	275	125
Reengage/Reengage	175	175	350	50

Utilizing the prices you developed above, construct a payoff matrix (where payoff is defined as TR - TC) for each of the countries under each of the four possible scenarios: (Agree/Agree; Agree/Renege; Renege/Agree; Renege/Renege). You must show your work for the calculations of the payoffs and your matrix must be consistent with the potential outcomes.

Utilizing your results from above, find the Cournot-Nash equilibrium for this game and explain why it is the equilibrium