This is a homework problem, but I'm at my wit's end. I don't even know where to start on this, but I've tried a number of strategies.
Consider a regional market for wholesale electricity where there are 4 firms, who have submitted the following willingness-to-supply curve functions, where P represents the price in $/MWh, and Q is the quantity of MWh.
S1(P): Qs = 10 P P = .10 Qs
S2(P): Qs = 2.5 P P = .40 Qs
S3(P): Qs = 5 P P = .20 Qs
S4(P): Qs = 7.5 P P = .1333333 Qs
The total market demand is 2,000 MWh. Suppose that firm 1 and firm 2 decide to merge, and that the merged firm has a total cost function given by
C = 10,785 + 1.10 Q + .05 Q2
If the newly merged firm maximizes profits, then what is the profit maximizing price and quantity of electricity?
I tried setting Q1 and Q2 equal to zero. So I get (5+7.5)P = 2000 and therefore P= 160. I know that this is a step, but I have no idea where to continue.
Find the market supply function: sum of quantities supplied by all firms as a function of price. Set it equal to the fixed demand 2000 MWh (I assume this is perfectly inelastic) to find the equilibrium price. The quantity must be 2000 MWh.
The merged firm's willingness to supply function comes from price equalling marginal cost.