Assignment
1. 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.
2. Assume there is a firm which is currently producing with a cost functionC(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.
3. 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.
4. 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.
5. 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.
|
|
Kelsey
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Dave
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Jim
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|
Tech
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Capacity
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MC
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Capacity
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MC
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Capacity
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MC
|
|
1
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1000
|
5
|
2000
|
10
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5000
|
40
|
|
2
|
500
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10
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1000
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20
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1000
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10
|
|
3
|
300
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0
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500
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5
|
600
|
20
|
|
4
|
200
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20
|
500
|
30
|
400
|
5
|
Draw supply curves for each producer and the market supply for electricity in Davis.
6. 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) Howareyouranswers from(a)through(d)thesameordifferent? Why do we care?
7. 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.