1. Suppose that the fisrt plant has constant MC=10, and the other plant has constant MC=15. How the equilibrium will look like in this case?
First of all, it should be noted that in this task the competition is based on Bertrand model, as two companies can not influence the market by changing the quantity, yet they can do so by changing the price of the product. Moreover, the electricity is a homogenous product which is also suits Bertrand model.
However, in this given example two plants have different marginal costs. This means that plant 2 can not set its price for electricity lower than 15, as it would be unprofitable for it. At the same time, plant 1 can afford to set the price lower than 15, which would eventually result in plant 1 grabbing the whole market.
What price should the plant 1 set? It is obvious that the price should be situated in the range 15>P≥10. Let’s exemplify this with some numbers:
P=70-Q
P(1)=14,9
Q=55,1
П(1)=(55,1*14,9)-(10*55,1)=269,99

2. Suppose that each plant has the next total cost function: TC=0.25q2+100. How the equilibrium will look like in this case?

Under the condition of increasing costs, we have to check whether the Bertrand trap is still intact.
First, we need to assume that this is still a Bertrand competition (since the product is homogenous) and thus we need to find a point below which it will have no sense for firms to cut the price. This point naturally is P=AC. We also assume that the firms will stop at this point and split the market.
P=70-Q
Q=2q
MC=0,5q
AC=TC/q=(0.25q2+100)/q=0,25q+100/q
P=AC
70-2q=0,25q+100/q q=29,61 Q=59,22
P=10,78
П(a,b)=(10,78-(0,25*29,61+100/29,61))*29,61=0

3. Suppose that each plant has the same constant MC=10, but their capacity is limited. Plant A can produce no more than 20, plant B can produce no more than 30. How the equilibrium will look like in this case? What