final exam prices and markets - insead · exam number section number final exam prices and markets...

Exam number

Section number

Final Exam

Prices and Markets

P1 Sep–Oct 2011

Timothy Van Zandt

24 October 2011

9:00–12:00

PLEASE READ THESE INSTRUCTIONS

• The following is probably different from your other exams. This exam does notuse separate answer books. Instead, you must write your answers only on the examitself. Do not unstaple the pages. Do not attach extra pages. Try to use only thespace allocated. However, if you need to continue an answer on the back of anypages or on the blank pages included at the end of the exam, indicate this clearly.

• You have three hours to complete this exam.

• This is a closed book exam. Two “A4 cheat sheets” (total 4 sides) are allowed.

• As stated in the MBA regulations, a non-communicating calculator is allowed(though unlikely to be needed).

• In case of doubt about the interpretation of any question, state your interpretationand proceed. (Professors are not allowed, by MBA regulations, to answerquestions during the exam.)

• The exam has 23 questions worth 97 points, on 18 numbered pages, plus 2 blanknumbered pages. Check that your exam is complete before proceeding.

• I have tried to make this exam longer and harder than the sample exams. (Out ofkindness, of course. I think you all understand the benefit of a not-too-highaverage grade.) Pace yourself so that you get through the entire exam. There arequestions that are meant to stump a good number of (good) students. Don’t letthem cloud your thinking about the easy questions.

Which brings me to the next page …

P&M Sep/Oct 2012 Sample Exam 3

Prices & Markets • Final Exam • 24 October 2011

Do not write on this page.

Problem 1. [4]

Problem 2. [3]

Problem 3. [3]

Problem 4. [4]

Problem 5. [4]

Problem 6. [4]

Problem 7. [3]

Problem 8. [4]

Problem 9. [8]

Problem 10. [2]

Problem 11. [4]

Problem 12. [4]

Problem 13. [4]

Problem 14. [4]

Problem 15. [4]

Problem 16. [3]

Problem 17. [4]

Problem 18. [4]

Problem 19. [3]

Problem 20. [6]

Problem 21. [4]

Problem 22. [8]

Problem 23. [6]

TOTAL: [97]


Prices & Markets • Final Exam • 24 October 2011 1

Part I Multiple choices without explanations

For each problem, circle any of the options that are true—which may include all options

or none.

No explanations are necessary. However, you may provide clarifying interpretations

or brief explanations if you are in doubt. These may be used for giving partial credit, in

your favor or against.

Problem 1. [4 points] Consider the Cournot model of quantity competition withhomogeneous goods. Compared to the Nash equilibrium values, which of thefollowing are true of the cooperative (collusive) outcome?

a. Market price is higher.

b. Total output is higher.

c. The firms’ profits are higher.

d. Total surplus is higher.

Problem 2. [3 points] Which of the following statements about elasticities arealways true?

a. If two goods are substitutes, then their cross-price elasticities are negative.

b. A steeper demand curve is less elastic than a flatter demand curve (when drawnas we usually do, with quantity on the horizontal axis and price on the verticalaxis).

c. For a given linear demand curve, demand becomes more elastic as the pricerises.



Problem 3. [3 points] Consider a profit-maximizing firm with market power—thinkof price competition with differentiated products and a small number of competingfirms. This firm produces a product whose production is electricity-intensive. A newlocal geothermal power source has been developed, which has signifantly lowered thefirm’s cost of power whereas other firms in the market do not benefit from this newsource.

a. The firm will lower its price.

b. The firm will produce more.

c. The other competing firms will reduce their prices.

Problem 4. [4 points] When the demand elasticity of a firm’s good is equal to 1,which of the following obtain their maximum value?

a. The firm’s profit.

b. Consumers’ surplus.

c. Total surplus.

d. Revenue.



Problem 5. [4 points] In a Nash equilibrium,

a. the total well-being of all players might not be maximized;

b. players collude to achieve the best possible outcome;

c. each player is happy with his decision, given the decisions of the other players;

d. one player convinces the others to follow a course of action that will be in his orher own self interest.

Problem 6. [4 points] Which of the following result in a deadweight loss?

a. Equilibrium in a perfectly competitive market.

b. Competitive equilibrium with a tax on the good.

c. Uniform pricing with market power.

d. Pricing with market power and perfect price discrimination.



Problem 7. [3 points] Consider the simultaneous-move game shown below.

Player B1 2

16

3

4

9Player A

29

4

7

7

(The names of the actions are important. In particular, action 2 is higher than action 1.)Observe that player B’s payoff is always higher in the bottom row than in the top rowand player A’s payoffs is always higher in the right column than in the left column.This shows that …

a. … the actions are strategic complements.

b. … the game has positive externalities.

c. … each player has a dominant action.

Problem 8. [4 points] In which cases does a profit-maximizing single-product firmequate marginal revenue to marginal cost?

a. If the firm is perfectly competitive.

b. If the firm plays the Nash equilibrium of a price-competition game.

c. If the firm plays the Nash equilibrium of a quantity-competition game.

d. If the firm is a monopolist with no threat of entry.



Part II Multiple choices with explanations

Problem 9. [8 points] Which of the following hold:

a. Supply is less elastic in the short run than in the long run.

b. Marginal cost is higher in the short run than in the long run.

c. Following a shift in the market demand curve: if a firm operating in the marketdoes not anticipate the actions of other firms, then it will overreact.

d. A firm in a competitive market may set price above short-run marginal cost.



Part III Short Answers

Problem 10. [2 points] Suppose your firm offers three kinds of financial services toindividual investors and you decide to only sell them as a bundle. Is this an example ofscreening? Explain.



Problem 11. [4 points] Go back in time to the development of high-definition TVstandards. Europe and North America are each designing their own standards. Supposethat a range of technologies are available and that they can be ordered according tohow “European” or “American” they are. For example, being more European means(a) developed by European firms and (b) closer to existing European technology andhence easier for European broadcasters to adapt to; being more American means theopposite. Measure this characteristic by a variable T which ranges from 0 for“all-American” to 1 for “all-European”.

0 1

All-American All-European

T measures “Europeanness”

Let TE be the technology adopted by Europe and let TA be the technology adoptedby North America. Europe’s and North America’s payoffs have the forms

uE (TE, TA) = ΠE (TE) − c(TE, TA)

uA (TA, TE) = ΠA (TA) − c(TE, TA),

where

• c(TE, TA) measures the cost of not be standardized — if TE = TA, thenc(TE, TA) = 0, and otherwise c(TE, TA) is an increasing function of the distancebetween the two technologies.

• ΠE (TE ) is increasing and ΠA (TA) is decreasing (other things equal, a moreEuropean standard is better for Europe and worse for North America).

11.1. [1 points] Which do you consider most likely: that the actions are strategiccomplements or strategic substitutes? (No explanation should be given.)

11.2. [3 points] Explain why, if TE is a best response by Europe to TA, thenTE ≥ TA.



Part IV Exercises

Problem 12. [4 points] Consider a competitive market with demand and supply,respectively, given by

QD = 100 − P

QS = P

where P is the price. Suppose the government levies a per-unit tax of €10. How muchrevenue is generated?

Problem 13. [4 points] A firm (A) is engaged in price competition with anotherfirm (B). Firm A’s demand function is d(PA, PB) = 40 − 2PA + PB , where PA is it ownprice and PB is the price charged by firm B. Firm A’s marginal cost is 10. Find theformula for firm A’s reaction curve.



Problem 14. [4 points] Consider a firm with market power that has constantmarginal cost. Its current demand curve is d1(P ) and it’s profit maximizing price andquantity are P1 and Q1, respectively. The demand curve shifts to d2, which is lesselastic than d1. Yet d1 and d2 intersect at the point (Q1, P1).

14.1. [2 points] Draw an graph that illustrates this situation, using linear demand.You graph has to show (a) d1, (b) d2, (c) and the intersection point (Q1, P1).

14.2. [2 points] What happens to the quantity sold following the shift in demand?



Problem 15. [4 points] The makers of Fanta and Orangina are engaged in pricecompetition. (Imagine that these are the only drinks they produce and the only softdrinks on the market.) They face the same constant marginal cost. You are given noinformation about the demand functions, and so you should not assume that they arelinear nor that the game is symmetric. You observe that the price of Fanta is 2.10 andthe price of Orangina is 2.60. Furthermore, the (own-price) elasticity of demand ofFanta is 3 and that of Orangina is 2. Based on this information, can you determinewhether these prices are a Nash equilibrium of this price competition game?

Problem 16. [3 points] A monopolist can price discriminate across two marketsegments, A and B, with the following demand curves:

QA = 100 − PA

QB = 150 − 2PB .

In which market will it charge a higher price? Explain.



Problem 17. [4 points] You are a monopolist selling two different types of concerttickets. You have zero marginal cost and hence your objective is to maximize revenue.You face three groups of potential customers, with an equal number of customers ineach group. The following table summarizes the valuation of each group for eachconcert. (Each customer’s valuation of going to both concerts is just the sum of hisindividual valuations.)

Valuation

Type Rock World

A 5 60

B 35 65

C 40 70

17.1. [2 points] Pure bundling: What is the optimal price for the bundle of bothtickets? What is your profit?

17.2. [2 points] Mixed bundling: Find one mixed bundle pricing strategy that givesyou higher profit than your answer with pure bundling.



Problem 18. [4 points] A home-delivery spring-water distributor has a monopoly ina residential market. A second distributor, which sells a differentiated product, isconsidering entry. Assume that once entry takes place, the firms play a Nashequilibrium of a pricing game. Describe what data you need in order to determinewhether entry would be profitable, and outline how you would determine the answer.(Follow as closely as possible the simple models in this course, rather than extendingthe analysis.)



Problem 19. [3 points] The first graph shows the MC and AC curves for some firm.On the second graph, draw a total cost curve that is consistent with these AC and MCcurves.

(No explanation required if drawn correctly, but an explanation may count towardspartial credit. The shape is what matters; no need to get out a ruler to produce an exactcost curve.)

€

Output

Marginal cost

Average cost

€

Output

Total cost



Problem 20. [6 points] A firm i is engaged in Cournot competition. It hasconstructed the following spreadsheet to show the relationship between its output andvarious other variables, given decisions of the other firms:

Answer the following questions based on the data in the cells.

20.1. [2 points] What is approximately the value of MRi for Qi between 60 and 65?

20.2. [2 points] What quantity is the firm’s best response? (No explanation needed.)

20.3. [2 points] What is approximately the elasticity of the market demand curvebetween the prices of 30.15 and 30.20?



Problem 21. [4 points] Consider a competitive market with free entry. Each firmhas the following cost curves:

C = 400 +Q2

MC = 2Q

The market demand is 2800 − 30P . Calculate the equilibrium price, the quantityproduced by each firm, and the number of firms.



Problem 22. [8 points] Suppose your firm is in a competitive industry with freeentry (many identical firms and potential entrants). The industry experiences anunanticipated permanent increase in demand. (Assume the industry is small and so anyshift has no impact on input prices.) Assume that it takes a year or more for entry orexit to take place, but otherwise there is no inertia in the production by existing firms inthe market.

Analyze in which direction (“up”, “down”, “stay the same”) the following move inthe before any exit/entry takes place and after the market settles into an equilibriumwith exit/entry: (a) equilibrium price; (b) number of firms; (c) output per firm; (d) profitper firm.

22.1. [4 points] Fill in each cell with “up”, “down”, or “no change”.

Variable Before exit/entry After exit/entry

P up no changeN no change upQi up no changeΠi up no change

22.2. [2 points] Explain, for before any exit/entry takes place:

22.3. [2 points] Explain, for after the market settles into an equilibrium withexit/entry:



Problem 23. [6 points] The following is a typical consequence of economicintegration, such as the removal of trade and currency barriers in Europe and such asthe formation of a free-trade zone among the ASEAN countries:

• there is industry consolidation, meaning that firms merge or exit the market andthus fewer firms remain;

• yet at the same time prices fall due to increased competition.

Let’s use our model of imperfect competition with free entry to illustrate andunderstand this. We consider the simplest scenario. The world consists of twocountries, say France and Germany. We are looking at the market for one good, such aswashing machines. Initially there is no trade between the countries. Then all tradebarriers are removed. This could have many consequences, but we suppose that theonly effect is on competition in the market for washing machines.

Assume that the model of imperfect competition with free entry applies both foreach country before trade and for the combined market with free trade. The marketsare identical in the two countries, both on the demand side and because the existingand potential firms have the same cost structures.

We therefore use an example we looked at in class (for which I did the calculationsbut we interpreted the tables together), which compared the outcome of imperfectcompetition with free entry for two different market sizes, one twice as large as theother—as captured by the two demand curves d1 and d2 shown on the next page. Thesmall market size corresponds to each of the individual markets, France and Germany.The large market size corresponds to the integrated market.

The tables on the next page show the outcome of imperfect competition for a fixednumber of firms, for a range of number of firms in the market. (Profit per firm meansvariable profit, i.e., not taking into account the fixed cost.) Assume that the fixed cost is350. Treat this as an on-going yearly fixed cost (and all fgures in the table are also on ayearly basis) so that it is both the cost of entering the market and what is saved byexiting the market. Answer the following questions based on the table.



d1 d2

Number

of firms

Total

OutputPrice

Output

per firm

Profit per

firm

Q = 1500 - 50P || P = 30 - Q/50

Number

of firms

Total

OutputPrice

Output

per firm

Profit per

firm

Q = 3000 - 100P || P = 30 - Q/100

1 500 20.00 500 5,000 1 1,000 20.00 1,000 10,000

2 667 16.67 333 2,222 2 1,333 16.67 667 4,444

3 750 15.00 250 1,250 3 1,500 15.00 500 2,500

4 800 14.00 200 800 4 1,600 14.00 400 1,600

5 833 13.33 167 556 5 1,667 13.33 333 1,111

6 857 12.86 143 408 6 1,714 12.86 286 816

7 875 12.50 125 313 7 1,750 12.50 250 625

8 889 12.22 111 247 8 1,778 12.22 222 494

9 900 12.00 100 200 9 1,800 12.00 200 400

10 909 11.82 91 165 10 1,818 11.82 182 331

11 917 11.67 83 139 11 1,833 11.67 167 278

12 923 11.54 77 118 12 1,846 11.54 154 237

13 929 11.43 71 102 13 1,857 11.43 143 204

14 933 11.33 67 89 14 1,867 11.33 133 178

15 938 11.25 63 78 15 1,875 11.25 125 156

d1 d2

23.1. [1.5 points] In each country before trade is opened up, how many firms are inthe market? What is therefore the total number of firms across the two countries beforeintegration?

23.2. [1.5 points] Following integration, how many firms are in the integratedmarket? Therefore, compared to before integration, who many firms enter or exit themarket?

23.3. [1.5 points] What is the market price in each country before integration? Whatis the market price after integration?

23.4. [1.5 points] Suppose that it takes some time for firms to exit or enter followingintegration, so that, for the first year after trade is opened up, the total number of firmsin the integrated market is the same as existed in the countries before integration. Whatis the market price price? How is each firm earning or losing, net of the fixed cost?



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