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New York University - ECON ECON-UA 10 Intermediate Microeconomics Q1)Suppose there are 100 identical firms in a perfectly competitive industry

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New York University - ECON ECON-UA 10

Intermediate Microeconomics

Q1)Suppose there are 100 identical firms in a perfectly competitive industry. Each firm has a short-run total cost function of the form

C(q) =  (1/300)q³ + 0.2q² + 4q + 10:

1. Calculate the firm’s short-run supply curve with q as a function of market price (P).
2. On the assumption that there are no interaction effects among costs of the firms in the industry, calculate the short-run industry supply curve.
3. Suppose market demand is given by Q = -200P + 8,000. Calculate equilibrium price and quantity for both the firm, and the industry. Also calculate total, and average costs, along with profits.

 

Q2.

A perfectly competitive industry has a large number of potential entrants. Each firm has an identical cost structure such that long-run average cost is minimized at an output of 20 units (q_i =  20). The minimum average cost is $10 per unit. Total market demand is given by Q = 1,500 - 50P.

1. What is the industry’s long-run supply schedule?
2. What is the long-run equilibrium price (P*)? The total industry output (Q*)? The output of each firm (q*)? The number of firms? The profits of each firm?
3. The short-run total cost function associated with each firm’s long-run equilibrium output is given by C(q) = 0.5q² - 10q + 200.

Calculate the short-run average and marginal cost function. At what output level does short-run average cost reach a minimum?

4. Calculate the short-run supply function for each firm and the industry short-run supply function.
5. Suppose now that the market demand function shifts upward to Q = 2,000 - 50P. Using this new demand curve, calculate price and quantity (for the firm as well as the industry) for the very short run if firms cannot change their outputs.
6. In the short run, use the industry short-run supply function (from part (d)) and the new market demand function to recalculate equilibrium price, total industry output, firm output, firm profit.
7. What is the new long-run equilibrium for the industry with the new market demand curve?

Q3.

The handmade snuffbox industry is composed of 100 identical firms, each having short-run total costs given by STC = 0.5q² + 10q + 5 and short-run marginal costs given by SMC = q + 10, where q is the output of snuffboxes per day.

1. What is the short-run supply curve for each snuffbox maker? What is the short-run supply curve for the market as a whole?
2. Suppose the demand for total snuffbox production is given by Q = 1,100 - 50P.

What will be the equilibrium in this marketplace? What will each firm’s total short-run profits be? c. Graph the market equilibrium and compute total short-run producer surplus in this case.

Show that the total producer surplus you calculated in part (c) is equal to total industry profits plus industry short-run fixed costs.

Suppose the government imposed a $3 tax on snuffboxes. How would this tax change the market equilibrium?

How would the burden of this tax be shared between snuffbox buyers and sellers?

Calculate the total loss of producer surplus as a result of the taxation of snuffboxes. Show that this loss equals the change in total short-run profits in the snuffbox industry. Why do fixed costs not enter into this computation of the change in short-run producer surplus?

 

Q4.

9.9.  Ron’s Window Washing Service is a small business that operates in the perfectly competitive residential window washing industry in Evanston, Illinois. The short-run total cost of production is STC(Q) = 40+ 10Q + 0.1Q², where Q is the number of windows washed per day. The corresponding short-run marginal cost function is SMC(Q) = 10 + 0.2Q. The prevailing market price is $20 per window.

1. How many windows should Ron wash to maximize profit?
2. What is Ron’s maximum daily profit?
3. Graph SMC, SAC, and the profit-maximizing quantity. On this graph, indicate the maximum daily profit.
4. What is Ron’s short-run supply curve, assuming that all of the $40 per day fixed costs are sunk?
5. What is Ron’s short-run supply curve, assuming that if he produces zero output, he can rent or sell his fixed assets and therefore avoid all his fixed costs?

Q5.

9.10.  The bolt-making industry currently consists of 20 producers, all of whom operate with the identical shortrun total cost curve STC(Q) = 16 + Q², where Q is the annual output of a firm. The corresponding short-run marginal cost curve is SMC(Q) = 2Q. The market demand curve for bolts is D(P) = 110 − P, where P is the market price.

1. Assuming that all of each firm’s $16 fixed cost is sunk, what is a firm’s short-run supply curve?
2. What is the short-run market supply curve?
3. Determine the short-run equilibrium price and quantity in this industry.

 

Q6.

9.24.  The global propylene industry is perfectly competitive, and each producer has the long-run marginal cost function MC(Q) = 40 − 12Q + Q². The corresponding long-run average cost function is AC(Q) = 40 − 6Q + Q²/3. The market demand curve for propylene is D(P) = 2200 − 100P. What is the long-run equilibrium price in this industry, and at this price, how much would an individual firm produce? How many active producers are in the propylene market in a long-run competitive equilibrium?

Q7.

9.34.  The semiconductor market consists of 100 identical firms, each with a short-run marginal cost curve SMC(Q) = 4Q. The equilibrium price in the market is $200. Assuming that all of the firm’s fixed costs are sunk, what is the producer surplus of an individual firm and what is the overall producer surplus for the market?

 

Q8.

9.35.  Consider an industry in which chief executive officers (CEOs) run firms. There are two types of CEOs:

exceptional and average. There is a fixed supply of 100 exceptional CEOs and an unlimited supply of average CEOs. Any individual capable of being a CEO in this industry is willing to work for a salary of $144,000 per year. The longrun total cost of a firm that hires an exceptional CEO at this salary is

 

 

where Q is annual output in thousands of units and total cost is expressed in thousands of dollars per year. The corresponding long-run marginal cost curve is MC_E(Q) = Q, where marginal cost is expressed as dollars per unit. The long-run total cost for a firm that hires an average CEO for $144,000 per year is TC_A(Q) = 144 + Q². The corresponding marginal cost curve is MC_A(Q) = 2Q. The market demand curve in this market is D(P) = 7200 − 100P, where P is the market price and D(P)  is the market quantity, expressed in thousands of units per year.

1. What is the minimum efficient scale for a firm run by an average CEO? What is the minimum level of long-run average cost for such a firm?
2. What is the long-run equilibrium price in this industry, assuming that it consists of firms with both exceptional and average CEOs?
3. At this price, how much output will a firm with an average CEO produce? How much output will a firm with an exceptional CEO produce?
4. At this price, how much output will be demanded?
5. Using your answers to parts (c) and (d), determine how many firms with average CEOs will be in this industry at a long-run equilibrium. f ) What is the economic rent attributable to an exceptional CEO?

7. If firms with exceptional CEOs hire them at the reservation wage of $144,000 per year, how much economic profit do these firms make?
8. Assuming that firms bid against each other for the services of exceptional CEOs, what would you expect their salaries to be in a long-run competitive equilibrium?

Q9.

The major oil spill in the Gulf of Mexico in 2010 caused the oil firm BP and the U.S. government to greatly increase purchases of boat services, various oil-absorbing materials, and other goods and services to minimize damage from the spill. Use side-by-side firm and market diagrams to show the effects (number of firms, price, output, profits) of such a shift in demand in one such industry in both the short run and the long run. Explain how your answer depends on whether the shift in demand is expected to be temporary or permanent.