- Using the cost function C(q) = 2500 + 2q + q2 do the following.
· (a) Find the fixed, variable, average, and marginal cost equations for this firm.
· (b) Graph these and explain the important feat.
- Assume there is a firm which is currently producing with a cost function C(q) = 2500 + 2q + q2.
· (a) Given a market price of $150, should this firm exit the market in the long run? If not, find the quantity produced and profit.
· (b) Given a market price of $100, should this firm exit the market in the long run? If not, find the quantity produced and profit.
· (c) What is the lowest price that will keep this firm in the market? Show this graphically and explain two ways you find this point mathematically.
· (d) Draw this firm’s long run supply curve.
- Imagine all firms are identical to the one in the previous problem in a perfectly competitive market.
· (a) What will the market price be in the long run assuming free entry and exit? What will each firm’s profit be?
· (b) Suppose market demand is Qd = 3020 − 10p. What will be the quantity exchanged in the market in the long run? How many firms will operate?
· (c) Draw the long run supply curve and demand curve.
- There are two firms in a market with the following cost curves. C1(q1) = 2000 + 10q1 + 5q12 C2(q2) = 10, 000 + q2 (a) Find and graph the supply curve for each firm. (b) Write an equation and graph market supply.
Imagine there are three utility companies in the Boston market; Kelsey Gas and Electric, Dave Municipal Utility, and Jim Department of Water and Power. They have the following generation portfolios.
- Using the information from the previous problem, suppose there is only one producer of electricity in a market; only Kelsey.
· (a) If demand in this market is Qd = 1000 − 10p, what would the market price be? Explain.
· (b) If demand in this market is Qd = 1500 − 10p, what would the market price be? Explain.
· (c) If demand in this market is Qd = 2100 − 10p, what would the market price be? Explain.
· (d) If demand in this market is Qd = 3000 − 10p, what would the market price be? Explain.
· (e) How are your answers from(a)through(d)the same or different? Why do we care?
- Consider the electricity market in Boston from question 5 again. Imagine that off-peak demand is 5000 MW, part-peak demand is 7500 MW, and peak demand is 12,500 MW. In a year there are 4000 hours of off-peak, 3000 hours of part-peak, and 1760 hours of peak demand. Assume that if there is a tie in the cost of generation, generation is allocated proportional to the amount each offers at that price. For example, if demand were 2010 MW we need 90% of the production available at a marginal cost of 5. Kelsey would provide 300 MW plus 90% of 1000 MW, Dave would provide 90% of 500 MW, and Jim would provide 90% of 400 MW.
· (a) Suppose that all generators are required to supply electricity at marginal cost. What are the off-peak, part-peak, and peak prices?
· (b) Under the restriction in part (a), calculate yearly revenues for each utility company assuming all generation is sold at the market price.
· (c) Under the restriction in part (a), what is the maximum you would be willing to pay to lease each of these generation portfolios for a year?
· (d) Now consider a world where utilities are not required to price at marginal cost, but there is a price cap at 200. Will the prices during each period differ from part (a)?
· (e) Discuss how your answers to parts (b) and (c) would differ due to the ability of firms to exert market power.