ECON 510 practice problems

Suppose a monopolist knows the own price elasticity of demand for its product is -3 and that its marginal cost of production is constant MC(Q) = 10 To maximize its profit, the monopoly price is:

-1 / -3 = (P - 10) / P 1 / 3 = (P - 10) / P P = 3P - 30 2P = 30 P = $15

In a monopoly where the marginal revenue and price are, respectively, given by $10 and $20, the price elasticity of demand is:

-2

Clark Industries currently spends 5 percent of its sales on advertising. Suppose that the elasticity of advertising for Clark is 0.25. Determine the optimal profit margin price (P-MC)/P.

20%

A firm with market power has an individual consumer demand of Q = 20 - 4P and costs of C = 4Q What is the optimal amount of this product to package in a single block?

4

You are the manager of a monopoly that faces a demand curve described by P=230-20Q. Your costs are C = 5 + 30Q . Your firm's maximum profits are:

495 Demand curve is P = 230 - 20Q So your TR = PQ = 230Q - 20Q2 MR = 230 - 40Q TC = 5 + 30Q MC = 30 So profit maximizing condition is MR =MC 230 - 40Q = 30 or, 200 = 40Q or, Q = 5 So profit = PQ - C = 230Q - 20Q2 - 5 - 30Q = (230*5) - (20*52) - 5 - (30*5) = 1150 - 500 - 5 - 150 = 495 So profit = 495

You are the manager of a firm that sells its product in a competitive market at a price of $50. Your firm's prime s cost function is C = 40 + 5Q ^ 2 . The profit - maximizing output for your firm is:

5

You are the manager of a firm that sells its product in a competitive market at a price of $40. Your firm's cost function is C = 60 + 4Q ^ 2 . The profit -maximizing output for your firm is:

5 C = 60+4Q^2 So, MC = 8Q (found derivative) For profit maximization, 40 = 8Q Q = 5 units

You are the manager of a monopoly that faces a demand curve described by P = 230 - 20Q . Your costs are C = 5 + 30Q . The profit-maximizing output for your firm is:

5 Demand curve: P = 230-20Q Calculate MR = dTR/dQ = 230-40Q Total cost: TC = 5+30Q Calculate MC = dTC/dQ = 30 Now, a monopolist maximizes profits by producing at the point MR = MC That is, 230-40Q = 30 200 = 40Q Q* = 5 units P* = 230-20(5) = $130 So profit maximizing output is 5 units

You are the manager of a monopoly that faces a demand curve described by P = 63 - 5Q . Your costs are C = 10 + 3Q The revenue -maximizing output is:

6.3

Suppose two types of consumers buy suits. Consumers of type A will pay $100 for a coat and $50 for pants. Consumers of type B will pay $75 for a coat and $75 for pants. The firm selling suits faces no competition and has a marginal cost of zero. The optimal commodity bundling strategy is:

Charge $150 for a suit

In a competitive industry with identical firms, long-run equilibrium is characterized by:

P=AC, P=MC, MR=MC All are correct

Which of the following statements is true regarding a simple pricing rule for monopoly and monopolistic competition?

P[(1 + Ef)/Ef] = MC

A monopoly has two production plants with cost functions C1 = 50 + 0.1Q1 ^ 2 and C2 =30+0.05Q2 ^ 2 The demand it faces is Q = 500 - 10P. What is the profit maximizing level of output?

Q1=Q2=125

Cinemas sometimes give senior citizens discounts . What is the possible privately motivated purpose for them to do so?

Senior citizens have a more elastic demand for movies than ordinary citizens

A monopoly has produced a product with a patent for the last few years. The patent is going to expire. What will happen after the patent expires?

Some firms will enter the industry.

You are a manager in a perfectly competitive market. The price in your market is $14 . Your total cost curve is C(Q) = 10 + 4Q + 0.5Q ^ 2 What will happen in the long run if there is no change in the demand curve?

Some firms will enter the market eventually

Which of the following is a correct statement?

The less elastic the demand, the higher the profit-maximizing markup.

Manufacturers of laundry detergent and dishwashing soap reinvest a relatively large percentage of their sales revenues on advertising campaigns . Most of these advertisements that appear on television stress the fact that their product is "New and Improved ." Why ?

The market for many of these products is monopolistically competitive, and this the tendency os for the firms to earn long-run economic profits of zero. The firms hope that by continually advertising new and improved features of their products, they can reap some short-term profits.

Which of the following statements is true?

The more elastic the demand, the lower the profit-maximizing markup

A linear demand function exhibits:

less elastic demand as output increases.

Differentiated goods are a feature of a

monopolistcally competitive market

Which of the following market structures would you expect to yield the greatest product variety?

monopolistic competition

There is no market supply curve in:

monopolistically competitive and monopolistic markets.

A monopolist claims his profit-maximizing markup factor is 10. What is the price elasticity of demand for the firm's product ?

none of the above

In a competitive market the inverse demand for milk is Pd=62-2.6Q. the inverse supply for milk is Ps=38.7+3.2Q. what is the equilibrium price of milk?

p=62-2.6Q p=62- 10.4 p=51.6

In a competitive market the inverse demand for milk is Pd=62-2.6Q. the inverse supply for milk is Ps=38.7+3.2Q. what is the equilibrium quantity of milk?

pd =ps 62-2.6Q=38.7+3.2Q 23.3= 5.8Q Q=4.01

There is a market supply curve in a:

perfectly competitive market

In a competitive market the inverse demand for milk is Pd=62-2.6Q. the inverse supply for milk is Ps=38.7+3.2Q. what is the producers surplus in the competitive market?

producer surplus = 1/2 x price at equilibrium x quantity 1/2 x 51.6x 4.01 =103.32

"Monopolistic competition is literally a kind of competition. Hence, there is no deadweight loss in a monopolistically competitive market."

statement is incorrect

To circumvent the problem of double marginalization:

transfer prices must be set that maximize the overall value of the firm rather than the profits of the upstream division.

A local video store estimates its average customer's demand per year is Q = 7 - 2P and it knows the marginal cost of each rental is $0.5. How much should the store charge for each rental if it engages in optimal two-part pricing?

$0.5

Suppose seP = 20 - 2Q is the market demand function for a local monopoly. The marginal cost is 2Q. The local monopoly tries to maximize its profits by equating MC = MR and charging a uniform price. What will be the equilibrium price and output ?

$13.33, 3.33 units

You are a manager in a perfectly competitive market. The price in your market is $14. Your total cost curve is C(Q) = 10 + 4Q + 0.5Q ^ 2. What price should you charge in the short run?

$14

A firm with market power has an individual consumer demand of Q = 20 - 4P and costs of C = 4Q . What is optimal price to charge for a block of 4 units?

$18

You are the manager of a gas station and your goal is to maximize profits. Based on your past experience, the elasticity of demand by Texans for a car wash is -4, while the elasticity of demand by non-Texans for a car wash is -6. If you charge Texans $20 for a car wash, how much should you charge a man with Oklahoma license plates for a car wash ?

$18.00

Suppose that initially the price is $20 in a perfectly competitive market. Firms are making zero economic profits. Then the market demand shrinks permanently, some firms leave the industry, and the industry returns to a long-run equilibrium. What will be the new equilibrium price, assuming cost conditions in the industry remain constant?

$20

A monopoly produces widgets at a marginal cost of $8 per unit and zero fixed costs. It faces an inverse demand function given by P = 38 - Q The monopoly price is:

$23

Suppose seP = 20 - 2Q is the market demand function for a local monopoly. The marginal cost is 10. If fixed costs are zero and the firm engages in two-part pricing , the most profits the firm will earn is:

$25

You are the manager of a firm that sells its product in a competitive market at a price of $60. Your firm's cost function is C = 50 + 3Q ^ 2 Your firm's maximum profits are:

$250 Given that C = 50+3Q2; P = $60 Marginal Cost (MC) = d/dC = d/dQ (50+3Q2) MC = 6Q In competitive market, at equilibrium point, P = MR = MC = AR = AC Therefore, Equating MC with given P value will give Q i.e., P = MR = MC; 6Q = 60 Therefore Q = 10 Total Cost (TC) = 50+3(10)2 TC = $350 TR = Q * P i.e., 10 * $60 = $600 Profit = TR - TC Plugging TR and TC values into the above formula; Profit = 600 - 350 = $250 Therefore, the firm's maximized profits are $250

During spring break, students have an elasticity of demand for a trip to Florida of -3. How much should an airline charge students for a ticket if the price it charges the general public is $360? Assume the general public has an elasticity of -2.

$270

During spring break, students have an elasticity of demand for a trip to Cancun, Mexico, of -4. How much should an airline charge students for a ticket if the price it charges the general public is $420? Assume the general public has an elasticity of -2.

$280

The average consumer at a firm with market power has an inverse demand function of P = 10 - Q The firm's cost function is C = 2Q If the firm engages in optimal two-part pricing, it will earn profits of:

$32

The average consumer at a firm with market power has an inverse demand function of P=10-Q. The firm's cost function is C = 2Q . If the firm engages in two-part pricing, what is the optimal fixed fee to charge each consumer?

$32

You are the manager of a firm that produces output in two plants. The demand for your firm's product is P = 78 - 15Q where Q = Q1 + Q2 The marginal costs associated with producing in the two plants are M*C1 =; 3Q1 and M*C2 = 2Q2 What price should be charged in order to maximize revenues?

$39

You are the manager of a Mom and Pop store that can buy milk from a supplier at $3.00 per gallon. If you believe the elasticity of demand for milk by customers at your store is -4, then your profit-maximizing price is:

$4.00

Consider a monopoly where the inverse demand for its product is given by P = 60 - 2Q Total costs for this monopolist are estimated to be C(Q) = 100 + 2Q + Q ^ 2 At the profit-maximizing combination of output and price, consumer surplus is:

$64

What price should a firm charge for a package of two shirts given a marginal cost of $2 and an inverse demand function P = 6 - 2Q by the representative consumer?

$8

A local video store estimates its average customer's demand per year is Q = 7 - 2P and it knows the marginal cost of each rental is $0.5. How much should the store charge for an annual membership in order to extract the entire consumer surplus via an optimal two part pricing strategy ?

$9

A local video store estimates its average customer's demand per year is Q = 7 - 2P and it knows the marginal cost of each rental is $0.5. What is the annual profit that the video store expects to make on an average customer if it engages in optimal two-part pricing?

$9

Suppose two types of consumers buy suits. Consumers of type A will pay $100 for a coat and $50 for pants. Consumers of type B will pay $75 for a coat and $75 for pants. The firm selling suits faces no competition and has a marginal cost of zero. If the firm sells coats and pants for $25 each , but offers a bundle containing both a coat and pants for $150 , how many bundles will the firm sell?

0

You are the manager of a firm that produces output in two plants. The demand for your firm's product is P = 78; - 15Q where Q = Q1 + Q2 . The marginal costs associated with producing in the two plants are M*C1 =; 3Q1 and M*C2 = 2Q2 How much output should be produced in plant 1 in order to maximize profits?

1 otal Revenue= PQ= 78Q-15Q2 Marginal Revenue= d(TR)/dQ = 78-30Q where Q = Q1 + Q2 To maximise profit in a monopoly, MR=MC1= MC2 78-30Q= 3Q1= 2Q2 (As given in the question) For MR= MC1 78-30(Q1+Q2)= 3Q1 33Q1 +30Q2 = 78 Q2= (78-33Q1)/30. -----(i) For MR= MC2 78-30(Q1+Q2)= 2Q2 32Q2+30Q1=78 Q2= (78-30Q1)/32 -----(ii) By (i) and (ii) (78-33Q1)/30= (78-30Q1)/32 30(78-30Q1) =32(78-33Q1) 33*32Q1- 900Q1= 2*78 156Q1=156 Q1=1

Eric provides cheese (H) and milk (M) to the market with the following total cost function: C(H,M)=10+0.4H^ 2 +; 0.2M ^ 2 The prices of cheese and milk in the market are $2 and $5 respectively. Assume that the cheese and milk markets are perfectly competitive. What output of milk maximizes profits?

12.5

You are the manager of a firm that produces output in two plants . The demand for your firm's product is P =; 96 - 15Q where Q = Q1 + Q2. The marginal costs associated with producing in the two plants are M*C1 =; 6Q1; 1 and M*C2 = 3Q2 How much output should be produced in plant 2 in order to maximize profits?

2

You are the manager of a monopoly that faces a demand curve described by P = 85 - 5Q . Your costs are C = 20 + 5Q The profit-maximizing output for your firm is:

8 P = 85 − 5Q Total Revenue(TR) = P xQ = 85P - 5Q2 Marginal Revenue(MR) = d(TR) / dQ = 85 - 10Q Total Cost(TC) = 20 + 5Q Marginal Cost (MC) = d(TC) / dQ = 5 Profit maximizing output can be derived when MR = MC. So, 85 - 10Q = 5 10Q = 80 So, Q = 80/10 = 8

You are the manager of a monopoly that faces a demand curve described by P = 85 - 5Q Your costs are C = 20 + 5Q The revenue- maximizing output is:

8.5 None of the answers are correct

Suppose two types of consumers buy suits. Consumers of type A will pay $100 for a coat and $50 for pants Consumers of type B will pay $ 75 for a coat and $75 for pants. The firm selling suits faces no competition and has a marginal cost of zero. If the firm charges $ 75 for pants and $ 75 for a coat, the firm will sell a coat to:

A consumers and type B consumers

Suppose two types of consumers buy suits. Consumers of type A will pay $100 for a coat and $50 for pants. Consumers of type B will pay $75 for a coat and $75 for pants. The firm selling suits faces no competition and has a marginal cost of zero. If the firm charges $100 for a suit ( which includes both pants and a coat), the firm will sell a suit to:

A consumers and type B consumers

Which of the following statements concerning monopoly is NOT true?

A monopoly is always undesirable.

The source(s) of monopoly power for a monopoly may be:

All of the following statements associated with this question are correct

In the long run , monopolistically competitive firms produce a level of output such that:

All of the statements associated with this question are correct.

Suppose two types of consumers buy suits. Consumers of type A will pay $100 for a coat and $50 for pants . Consumers of type B will pay $75 for a coat and $75 for pants. The firm selling suits faces no competition and has a marginal cost of zero. If the firm can identify each consumer type and can price discriminate, what is the optimal price for a pair of pants?

Charge type A consumers $50, and type B consumers $75.

Suppose that a monopolistically competitive market is at the long-run equilibrium. Based on this information, which of the following conclusions is NOT true?

Deadweight loss is zero.

What contributes to the existence of multiproduct firms?

Economies of scope and cost complementarity

Why does the government grant patents to investors? Why does the government give monopoly power to utility companies?

Government grants patents to investors in order to incentivize them to invest and engage in R&D in order to come up with new and innovation technology to increase output using fewer and less expensive resources. This acts as a way of motivating investors to invest in R&D and thus enjoy the benefits in the form of patents granted by the government and the reputation which comes with it. Govt gives monopoly powers to utility companies, as these companies require very high setup and fixed costs to operate and if government does not provide them with monopoly status, Competition would enter the market and these utility companies would get into losses. This will make other large firms also fearful pf entering the utility markets, thereby leading to no producers eventually.

In the long run, monopolistically competitive firms:

Have excess capacity

The number of efficient plants compatible with domestic consumption of the refrigerator industry in Sweden is 0.7. Which of the following implications is (are) correct?

In the absence of imports, the refrigerator industry in Sweden is monopolistic.

U.S. Airways experienced huge losses for several years in the 1990s , yet it continued to operate its fleets. Why didn't U.S. Airways shut down its operations to avoid the losses?

It was covering its variable costs (the cost of fuel, pilots, mechanics, flight attendants, and the like). Had it shut down its operations, losses would have been even higher, due to the high fixed costs associated with its fleet of aircraft.

Which of the following is a correct representation of the profit maximization condition for a monopoly?

MC = MR

Consider a monopoly where the inverse demand for its product is given by P = 200 - 5Q Based on this information, the marginal revenue function is:

MR(Q) = 200 - 10Q

Which of the following statements is NOT correct about monopoly?

Monopolists always make positive profits in the long run.

The average consumer at a firm with market power has an inverse demand function of P = 10 - Q The firm's cost function is C = 2Q If the firm engages in two-part pricing, what is the optimal price to charge a consumer for each unit purchased?

None of the answers are correct

Suppose you are the manager of Alpha Enterprises, a firm that holds a patent that makes it the exclusive manufacturer of bubble memory chips. Based on the estimates provided by a consultant, you know that the relevant demand and cost functions for bubble memory chips are Q = 25 - 0.5P ; C = 50 + 2Q a . What is the firm's inverse demand function ? b . What is the firm's marginal revenue when producing four units of output? . What are the levels of output and price when you are maximizing profits? d . What will be the level of your profits?

P = 50 - 2Q MR(Q) = 50 - 4Q; MR(4) = 50 - 4(4) = $34. Setting MR = MC yields 50 - 4Q = 2, or Q = 12. P = 50 - 2(12) = $26. Profits are ($26)(12) - 74 = $238

In the long run, perfectly competitive firms produce a level of output such that:

P = MC and P = minimum of AC

Which of the following industries is best characterized as monopolistically competitive?

Toothpaste There are many buyers and sellers of toothpaste, but each seller sells a slightly differentiated product (variants of toothpaste).

Beta Industries manufactures floppy disks that consumers perceive as identical to those produced by numerous other manufacturers . Recently , Beta hired an econometrician to estimate its cost function for producing boxes of one dozen floppy disks. The estimated cost function is C = 20 + 2Q ^ 2 a . What are the firm's fixed costs? b . What is the firm's marginal cost? Now suppose other firms in the market sell the product at a price of $ 10. c. How much should this firm charge for the product? d . What is the optimal level of output to maximize profits ? e . How much profit will be earned? f . In the long run, should this firm continue to operate or shut down? Why?

a. Firms fixed costs are the one that do not depend on Q. Hence, fixed costs = 20 b. MC = dC/dQ = d(20 + 2Q^2)/dQ = 4Q c. Many firms means that the market is perfectly competitve. The firm is a price taker in such a market and must charge the same price of $10 as other firms in the market to sell its goods. P = $10 d. Many firms means that the market is perfectly competitve. Hence, MR = Price = $10. At profit max: MC = MR, hence 4Q = 10 => Q = 10/4 = 2.5 Optimal level of output to maximize profits = 2.5 units e. Profits = Revenue - Costs = price * Q - (20 + 2Q^2) = 10 * 2.5 - 20 - 2*(2.5)^2 = 25 - 32.5 = -7.5 Hence profits are - $7.5 (loss of $7.5). f. Since the firm is earning losses, in the long-run it will shut down if the market conditions do not change.

The following table contains different consumers' values for three software titles: PowerPoint, Excel, and Word. Suppose there are 100 consumers of each type. It costs Microsoft $5 to produce each piece of software. If Microsoft wants to devise a pricing strategy that is incentive compatible between consumer types and will maximize its profit , then it should:

charge a single price of $300 for the bundle of Powerpoint, Excel, and Word

When two or more divisions mark up prices in excess of marginal cost:

double marginalization occurs.

A firm has a total cost function of C(Q) = 75 + 25Q ^ (1/2) The firm experiences :

economies of scale