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 S2(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, S3(P) = 50 for 12 hours each day and S3(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: From Firm's 1 perspective, the supply curve of the other firms includes both the supply from the wind farm, Firm 3, and the supply from the small competitive generation firms, Firm 2. (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 1 receives for its generation?