Question

Assume that consumers view tax preparation services as undifferentiated among producers, and that there are hundreds of companies offering tax preparation in a given market. The current market equilibrium price is $120. Jojo’s Tax Service has a daily, short-run total cost given by TC = 100 + 4Q². Answer the following questions:

How many tax returns should Jojo prepare each day if her goal is to maximize profits?

How much will she earn in profit each day?

A perfectly competitive firm has the following total cost and marginal cost functions:

     TC = 100 + 10q – q² + (1/3)q³

     MC = q² – 2q +10

     a)    For quantities from 0 to 10 determine: TC, TFC, TVC, and MC.

b)    For quantities from 0 to 10 determine: ATC, AFC, and AVC.

c)    Assume P (MR) equals 45. For quantities from 0 to 10 determine: TR and profit.

d)    At what quantity is profit maximized? At this quantity what is true about the relationship between MC and MR?

Assume that the industry for pickles is perfectly competitive. There are 150 producers. 100 of the firms are “high-cost,” with short-run supply curves Q_hc = 4P, while the others are “low-cost,” with short-run supply curves Q_lc = 6P. Quantities are measured in jars and prices in dollars.

Derive the short-run industry supply curve for pickles.

Assume the market demand curve for pickles is given by Q^d = 6,000 – 300P. Find the market equilibrium price and quantity.

At this price, how many pickles are produced by the high- and low-cost firms, respectively?

Determine total industry surplus at the equilibrium.

Suppose your firm, Jane & Joe’s Coffee Company, is in a competitive industry in which you are currently in long run equilibrium and making 0 economic profit.

a.    Illustrate this situation with a graph. Show how the graph for the market is related to the graph for the firm.

b.    Suppose the demand for coffee falls (the demand schedule shifts to the left). Illustrate this situation and discuss what happens in the market and to the firm.

c.    Describe and illustrate what will happen to your firm, and the industry, as it moves back toward a long run equilibrium.

If a firm decides it is in its best interest to shut down in the SR what must be true about: total revenue compared to total cost? Total revenue compared to total variable cost? Price compared to average total cost? Price compared to average variable cost?

Betty’s Bats (BB) sells baseball bats for children around the world. The firm faces a demand curve of Q = 10 – 0.4P, where Q is measured in thousands of bats and P is dollars per bat. BB has a marginal cost curve equal to MC = 5Q Answer the following questions:

What is BB’s profit-maximizing output? Show the profit-maximizing decision graphically.

What price will BB charge to maximize its profits?

What is a network good? How might a network good make it possible for a monopoly to emerge?

Suppose the local roofing company has market power and faces the following inverse demand curve: P = 2000 – 10Q where quantity is the number of roof jobs and price is in dollars. The marginal cost for this firm is: MC = 200 +16Q. Answer the following questions:

What are the profit-maximizing output and price?

If the firm’s demand declines to what are the new profit-maximizing output and price Demand declines to: P = 1400 - 12Q ?

The demand for slurpees in a competitive market is P=100-2Q and supply is P=Q. What is the equilibrium price and quantity? What is the value of the area of consumer surplus? What is the value of the area of producer surplus? What are the gains to trade in the market? Suppose the slurpee market is monopolized by one firm. Assume the supply function now represents the monopolist’s marginal costs schedule. The demand schedule is unchanged. What is the monopolist’s marginal revenue mathematically? With a monopoly, what is the equilibrium price and quantity? What is the value of the area of consumer surplus? What is the value of the area of producer surplus? What are the gains to trade in the market? What is the value of the area of deadweight loss?

As discussed in class, what three things must be true for a monopolist to earn durable (long run profits)?

Oil Can Henry’s (OCH) and Jiffy Lube (JL) are the only two firms that provide oil changes in a local market in a Cournot duopoly (a two-firm oligopoly). The inverse demand curve for oil changes is: P = 100 – 2Q where quantity is measured in oil changes per year in thousands and price is measured in dollars per job. Assume OCH has a marginal cost of $12 per job and JL has a marginal cost of $20. Answer the following questions:

Determine each firm’s reaction curve.

How many oil changes will each firm produce in Cournot equilibrium?

What will the market price of an oil change be?

How much profit does each firm earn?

  

Allstate Insurance and Aetna are fierce rivals in the insurance industry. The output of insurance policies issued by Allstate is an important factor in Aetna’s decision of how many policies to issue (the number of policies that maximize profits). Similarly, the output of insurance policies issued by Aetna is an important factor in Allstate’s decision of how many policies to issue (the number of policies that maximize profits). The reaction function for Allstate can be expressed as: Q_allstate = 100 – 0.5(Q_aetna). The reaction function for Aetna is: Q_aetna = 50 – 0.25(Q_allstate).

Graph both reaction functions. Be sure you indicate numerically the points at which each function intersects the horizontal and vertical axes.

At which output quantities do the reaction functions intersect?

Assume there are two firms, A and B. If they compete on the price of their product, they each set a price of $5. If they agree to collude (form a cartel) they set the price of their product at $10. Use the prisoner’s dilemma model to show why the firms have an incentive to cheat. Your model should illustrate the two strategies available to each firm are “cheat” (P=$5) and “don’t cheat.” (P=$10). The size of the payoffs are your choice but should support your conclusion that each firm has a dominant strategy and that strategy is to set P=$5.

Prior to 1978 the domestic passenger airline industry was a regulated monopoly/cartel. Yet even with regulated prices exceeding those that would obtain in a competitive market, each firm was barely breaking even. Why? Incorporate a graph to explain what was happening.

As discussed in class, there are seven “keys to success” for a cartel. What are they?

Suppose Adam Baum and Rhoda Dendron are a small town’s only producers of chlorine for swimming pools. The inverse demand curve for chlorine is: P = 32 – 2Q where quantity is measured in tons and price is measured in dollars per ton. The two firms have an identical marginal cost of $16 per ton. Answer the following questions:

If the two firms collude, splitting the work and profits evenly, how much will each firm produce at what price? How much profit will each firm earn?

Does Adam have an incentive to cheat by producing an additional ton of chlorine? Explain.

Does Adam’s decision to cheat affect Rhoda’s profit? Explain.

Suppose both firms agree to each produce 1 ton more than they were producing in part (a). How much profit will they earn? Does Rhoda have an incentive to cheat?

Answer 1

Question 1

Tax preperation services market is depicted as perfectly competitive market.

Total cost function -

TC = 100 + 4Q²

Calculate the marginal cost -

MC = dTC/dQ = d(100 + 4Q²)/dQ = 8Q

Market equilibrium price, P = $120

A perfectly competitive firm maximizes profit when it produces that level of output corresponding to which price equals marginal cost.

P = MC

120 = 8Q

8Q = 120

Q = 120/8 = 15

So,

Jojo should prepare 15 retruns each day if her goal is to maximize profit.

Calculate Profit -

Profit = Total Revenue - Total Cost

Profit = (P * Q) - (100 + 4Q²)

Profit = (120 * 15) - (100 + (4*15²))

Profit = 1,800 - 1,000 = 800

Thus,

Jojo will earn $800 as profit each day.