you are working as an analyst for potential investor in a new wind farm. the wild farm will be looted in a small electricity market

Please show your work on all problems. Please also be considerate to the grader by writing neatly. If you cannot figure out how to solve a problem, write down what you tried and why you tried it. You are encouraged to work together but must write up your problem sets individually. 1. You are working as an analyst for a potential investor in a new wind farm. The wind farm will be located in a small electricity market. The market currently has one major generation firm and several small competitive generators. Your task is to predict the response of the major generation firm to the entry of the wind farm. This will provide predictions of the market price for the wind farm owner. Demand in the electricity market is fixed at 1200 MW. Firm 1 is the existing major generation firm in the market. It has a capacity of 500 MW and constant marginal cost of $20/MWh. Firm 2 can be considered the aggregate of the small competitive generation firms. The supply curve of Firm 2 is S, (P) = 350 + 10P. Call the new wind farm Firm 3. The planned capacity of the wind farm is 300 MW. Based on meteorological forecasts, the output of the wind farm will be 50 MW for 12 hours of the day and 200 MW for 12 hours of the day. Market regulations require this output to be offered at a price of zero. That is, S, (P) = 50 for 12 hours each day and S; (P) = 200 for the other 12 hours. The marginal cost of operation for the wind farm is $0/MWh. (a) Find the inverse residual demand facing Firm 1 during the hours in which the wind farm produces 200 MW. Hint: this calculation is similar to problem 2 on problem set 3. (b) Calculate the optimal generation quantity for Firm 1 during the hours in which the wind farm produces 200 MW. What will the market price be during these hours? (c) Find the inverse residual demand facing Firm 1 during the hours in which the wind farm produces 50 MW. (d) Calculate the optimal generation quantity for Firm 1 during the hours in which the wind farm produces 50 MW. What will the market price be during these hours? (e) Sketch the residual demand curves for Firm 1 from (a) and (c), and label the profit- maximizing price and quantity points that you found in (b) and (d). Sketch a possible step-function offer curve that would allow Firm 1 to produce at its optimal quantity, for either realization of Firm 3's wind generation.(f) Based on the prices you found in (b) and (d), calculate the daily revenue for the wind farm (Firm 3). What will be the average price that the wind farm receives for its generation? Is this higher or lower than the average price that Firm I receives for its generation? 2. GenPower operates in a small electricity market with no transmission constraints. Suppose the supply curve of other firms in the market is described by the equation: 500 + 5P if P 100 That is, the maximum capacity of the other firms in the market is 1000 MW. The demand for electricity in this market is 1500 MW. The market has a price cap of $500/MWh. GenPower has a generation capacity of 2000 MW and a constant marginal cost of $20/MWh. (a) Sketch a graph to show the supply curve of the other firms, the market demand, and the residual demand of GenPower. (b) The profit-maximizing generation quantity and price for GenPower are 500 MW at $500/MWh. Find GenPower's profits at this price and quantity. (c) Now suppose that GenPower has signed a fixed price forward contract with an electricity retailer in which it guarantees to supply 750 MW at a price of $50/MWh. If GenPower produces less than 750 MW, then it has to buy the difference in the wholesale market at the market price. If GenPower produces more than 750 MW, it can sell the difference in the wholesale market at the market price. Suppose Genpower produces 500 MW and the market price is $500/MWh. Given this contract, what is GenPower's profit? (d) Now suppose GenPower instead produces 825 MW. Find the market price. Given the forward contract, what is GenPower's profit? (e) Explain how your answer above contributes to our understanding of the causes of the Californian electricity crisis in 2000