You have just bought out your only competitor in the region for the supply of electrical power. With the acquisition you now have a second power generation plant (Q2), but one that operates slightly differently to the one you already had (Q1). Both power plants will generate an identical electrical product (voltage and frequency) and can be combined to supply the market, i.e. QT otal = Q1 + Q2. The inverse demand function you are faced ECON2001 - TAKE-HOME EXAM #2 3 with can be represented as P = 500 2Q, but the cost to run each plant is slightly different given by C1 = 25+(2Q1) 2 and C1 = 20+(2Q2) 2 .

(a) Calculate your marginal revenue and marginal cost functions.

(b) Calculate how much each plant should be producing in order to maximise profits.

(c) Calculate the price at which you will maximises your profits.

(d) Calculate what your maximum profits will be.