Consider a wholesale electricity market with three types of generators: nuclear plants, natural gas plants and oil-fired peak shavers. There are 3 plants in this market: one 10,000 MW nuclear plant, one 10,000 MW gas plant and one 4,000 MW oil plant (i.e., peak shaver). Marginal costs vary across generation types: $10 per MWh for nuclear, $15 per MWh for natural gas, and $50 per MWh for oil. During peak hours, demand is given by Q = 35,000 - 100P (measured in MWh). During off-peak hours, demand is given by Q = 20,000 - 100P. Assume for simplicity that a day consists of one peak hour and one off-peak hour. For now, assume that the market is competitive.

a. Calculate the peak and the off-peak prices of electricity in this market.

Oil and natural gas prices have suddenly increased, leading to a doubling of the marginal costs for the gas-fired plants and the peak shavers. The marginal cost of nuclear is unchanged.

b. Calculate the new peak and the new off-peak prices of electricity in this market.

c. How do the profits of the peak shavers change now that input costs are higher?

d. Give an example of a case in which input costs increase and the profits of the peak shavers move in a different direction than in part c.