A community of electricity consumers have the following inverse demand function: 7 =-2g+60 [S/MWh]There are two power generating companies, A and B, supplying this community of consumers. The costfunctions are:Company A: c,(q)= 29% [S/h]Company B: c3(42) = 39; [S/h]Where, q, and q; are the production levels for Company A and B respectively. Note that the totalelectricity consumption is equal to the total production supplied by the two companies, i.e., q = 94+ 93 -Now please answer the following questions:1) Considering Cournot competition model, what are the production levels for company A andcompany B at the equilibrium? What is the electricity price z at the equilibrium?2) At the equilibrium, what is the marginal cost for each company? Comparing to the electricityprice z , what phenomenon do you observe and why?

Here, we have given two power-generating companies and the cost functions are given above. The inverse demand function is given. First, we have to calculate the production level for Company A and B. Then, we will calculate the electricity price π at equilibrium. Then, we will calculate the marginal cost for companies A and B. And, then compare the electricity price π with the marginal cost for companies A and B. Then, we will observe and conclude that if the market is earning profit or facing loss. The given Inverse Demand Function : π=-2q+60 $/MWh ∵q=qA+qB so, π=-2q+60 $/MWhπ=-2qA+qB+60 $/MWhπ=-2qA-2qB+60 $/MWh The cost function are : cAqA=2q2A$/hcBqB=3q2B$/h So, the profit function, M can be given by : For company A : MA=πqA-cA=-2qA-2qB+60 ×qA-2q2A=-2qA2-2qAqB+60qA -2q2A=-4qA2-2qAqB+60qA ∂MA∂qA=0∂∂qA-4qA2-2qAqB+60qA=0-8qA-2qB+60=08qA=-2qB+60 The reaction function of company A, qA=-2qB+608=RAqB→eq.1For company B : MB=πqB-cBMB=-2qA-2qB+60qB-3q2BMB=-2qAqB-2qB2+60qB-3q2BMB=-2qAqB-5qB2+60qB ∂MB∂qB=0 ∂∂qA-2qAqB-5qB2+60qB=0 -2qA-10q+60=0 The reaction function of company B, qB=2qA-6010=RBqA→eq.2so, from eq. 2, putting qB=2qA-6010 qB=2-2qB+608-6010qB=-qB+302-6010qB=-qB+30-120210qB=-qB-9020qB=-qB-9020qB+0.05qB=-4.51.05qB=-4.5qB=-4.51.05qB=4.2857 qA=-24.2857+608qA=-8.5714+608qA=6.4285 So, the production level for Company A : 6.4285 units And, the production level for Company B : 4.2857 units Hence, π=-2qA-2qB+60=-26.4285-24.2857+60 $/MWh=-12.857-8.5714+60=38.5716 So, at equilibrium, the electricity price, π=$38.5716We have, cA=2q2A$/h So, the marginal cost for company A, McA=∂cA∂qA=∂2q2A∂qA=4qA=46.4285=25.714 We have, cB=3q2B$/h So, the marginal cost for company B, McB=∂cB∂qB=∂3q2B∂qB=6qB=64.2857=25.714So, by using the Cournot competition model, from above, we can conclude that the marginal cost for both the companies is the same. And, the marginal cost is less than the price, i.e.;MCA<π and MCB<π . Which means the companies are earning profits. In reality, the condition for equilibrium never occurs.