Question: Punggol Power Co. (PPC) operates two power plants: a 15,000 kWh fuel oil plant, and a 5,000 kWh natural gas plant. The kWh figures refer to the plant's maximum generating capacity. At current fuel prices, it costs $0.15 to generate 1 kWh from the fuel oil plant, and $0.20 to generate 1 kWh from the natural gas plant. PPC can buy any amount of fuel and generate any amount of power (up to the operating capacity of each power plant). PPC also faces costs which do not vary with output: these are depreciation of $1,500 for the fuel oil plant, $1,000 for the natural gas plant, and $2,000 for management costs. It is not possible to sell any plants or change management. If Punggol Power Co. needs to supply electricity above their maximum operating capacity, PPC has a contract with another power generator to purchase as much power as needed (for resale) for $0.30 per kWh.
(a) Write down Punggol Power Co.'s fixed cost, marginal cost, and total cost function. Briefly explain your answer for each cost component. Hint: You should think about the order in which power plant(s) should be used, to minimise the costs of supplying a given quantity of power; your final answer may have multiple total cost functions.
(b) Using a well-labelled graph, illustrate and examine Punggol Power Co.'s marginal cost function for the range Q = 0 to Q = 25000.
(c) Market demand for electricity is given by P = 2 - 0.0001Q. If Punggol Power Co. set prices as though it were a perfectly competitive firm, what would be the market price and quantity?
(d) Suppose Punggol Power Co. set prices as though it were a monopoly. Market demand remains the same at P = 2 - 0.0001Q. What would be the market price and quantity?