9.) The case of a multi-plant monopoly. There is a monopoly which supplies electricity using two
power plants. One of the power plant makes use of conventional (uses fossil fuels) technology and has a
total cost function TC = 500X106 + 0.4Q2. The other power plant makes use of renewable sources to
generate electricity with a total cost function TC, = 50X10° + 2Q,². The market demand function for the
electricity generated out of these two power plants is P = 1X106-5QT. In the case of this monopoly using
two power plants, prices, revenues and costs are in pesos while quantities of electricity generated are in
kilowatt-hours. Using the information provided, answer the following questions.
i.)What will be the modified profit maximizing condition for this monopoly with two power
plants? [MR = MCT with MCT as the combined or horizontal sum of respective marginal costs of
the two power plants] What is the relevant MCT function for this monopoly power generating
firm considering the two power plants? [MC = 0.8QQ = 1.25MC, while MC, = 4QQ, =
1/4MC,; it follows that Q₁ = QC +Q, = 1.5MC and reverting in terms of marginal costs will result
in MCT = 2/3QT]
ii.) What will be the profit maximizing output of electricity for this monopoly with two power
plants? [using modified profit maximizing condition MR = MCT will result in 1X106 10QT =
2/3QT which when solved for quantities will result in QT = Qmax of 93,750 kilowatt hours of
electricity] What will be the profit maximizing price of electricity for this monopoly with two
power plants? [using Prtmax = 1X10° -5 Qmax = 531,250 pesos per megawatt or a thousand
kilowatt hour of electricity] What is the marginal revenue of this monopoly at the profit
maximizing output of electricity for this monopoly? [using MRmax = 1X106-10 Qmax = 62,500
pesos per megawatt hour of electricity generated]
iii.) How much electricity will be sourced from the power plant using conventional technology by
the monopoly? [using MRmax = MC, will result in 62,500 = 0.8Q, which when solved for
quantities will result in Qc πmax = 78,125 kilowatt hour of electricity from the conventional power
plant] How much electricity will be sourced from the power plant using renewable technology
by the monopoly?[ using MRmax = MC, will result in 62,500 = 4Q, which when solved for
quantities will result in Qr max = 15,625 kilowatt hours of electricity]
