EXERCISE

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:

P = 800 -1.5Q,

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 $75 per unit to produce the energy and no fixed costs, so TC_i=75q_i (where i=1,2) and MC_i=75.

a) If both countries agree to curb production of energy, each country will agree (A) to produce 100 units per period. If either country (or both countries) chose to renege (R) on the agreement the country reneging will produce 175 units, while the one agreeing will still produce 100 units. If both countries renege, each will produce 175 units.

Utilizing the demand information provided and the production information, find the prices possible under these four possible scenarios. Show calculations.

Price for AA =

Price for AR=

Price for RA=

Price for RR=

b) Utilizing the prices 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). Show the calculations of the payoffs and matrix must be consistent with the potential outcomes. The first (top) value in the matrix represents the payoff for the Row Player and the second (bottom) represents that for the Column Player. When one enters each value, please include a dollar sign ($), use commas, and ifthere are centsinvolved includes those as well. For example, if one calculates 1025.75 for an answer, enter it as $1,025.75 .

	Agree	Renege
Agree
Renege

c) Utilizing the results from above, find the Cournot-Nash equilibrium for this game and explain why it is the equilibrium. One's explanation should include a definition of what constitutes an equilibrium and if each of the four potential outcomes is or is not an equilibrium and why this is the case by utilizing the definition.