Suppose that amsterdam is forced to charge the same price

Question

Managerial Economics Practice Problems

Pricing -

Accounting and Consulting Group Inc.

Accounting and Consulting Group (ACG) has two divisions, Accounting and Consulting. ACG employs 20 consultants, a number that cannot be changed in the short run, and consultants are paid in the following way: they are given a salary of $2,500 per week, and, for each hour the consultant works, she is paid an additional $150 / hour. Consultants always work exactly 50 hours per week (no more or less); if there is no work, consultants are expected to be at their desks on standby for when work comes in. Other than the wage difference, consultants are equally happy working or waiting.

1. The Consulting division (C) currently faces a weekly external demand for its services which is best estimated by the equation Q = 1500 - P, where Q is consulting hours and P is the price (in dollars per hour) that it charges for consulting. The Accounting (A) division needs some help and has requested that the C division supply it with 100 hours of consulting per week. If the A division compensates the C division so that C is no worse off after supplying the 100 consulting hours per week, how much should A pay C for the consulting?

2. External demand for consulting increases sharply, so that C faces a new weekly external demand for its services of Q = 3000 - P. C's staffing levels and compensation scheme are the same as before. A still requests 100 consultant hours per week. What should A pay in order for C to be no worse off than they would be without supplying A with these 100 hours of service?

Boehringer Ingelheim

Boehringer Ingelheim (BI), a German pharmaceutical company, is bringing to market a new anticoagulant, dabigatran (brand name Pradaxa). Dabigatran has fewer interactions and requires less in-office monitoring than warfarin, the main competing product, and BI has built a €120 million plant to produce what promises to be a blockbuster drug. The plant has been tailored to the Pradaxa production process and hence has little other use. Given the company's cost of capital, this works out to be the equivalent of €20 million per year.

Annual costs of operating the plant are around €25 million, due to the high cost of continued regulatory compliance. However, marginal cost is relatively low, €5 per daily dose of Pradaxa. The plant has the capacity to produce up to 5,000,000 doses per year, and given the long process for approval of its facilities, further production will not come online in the near future.

Due to regulatory complications with the U.S. Food and Drug Administration, BI sees Europe as essentially its only market for this year. Different countries within Europe have differing price thresholds for giving approval for Pradaxa's use in their national health systems, but due to centralized negotiation, the same price must be charged across all of Europe. In other words, if BI charges a lower price for Pradaxa it will have higher sales by meeting the price requirements of additional countries, but it cannot charge high prices in some countries and low prices in others within Europe. The price points (WTP) in each country and the expected sales if sold in each country are given in the table.

Country	WTP	Projected Sales
Austria	19.50 €	83,000
Belgium	16.50 €	107,000
Bulgaria	6.50 €	76,000
Cyprus	8.50 €	8,000
Czech Republic	12.80 €	104,000
Denmark	18.25 €	55,000
Estonia	8.75 €	13,000
Finland	17.20 €	53,000
France	14.75 €	640,000
Germany	16.00 €	822,000
Greece	13.00 €	112,000
Hungary	8.00 €	100,000
Italy	13.80 €	596,000
Latvia	7.50 €	23,000
Lithuania	8.25 €	34,000
Luxembourg	30.00 €	5,000
Malta	12.23 €	8,000
Poland	7.25 €	381,000
Portugal	12.50 €	106,000
Romania	6.75 €	215,000
Slovakia	9.50 €	54,000
Slovenia	12.75 €	20,000
Spain	13.20 €	453,000
Sweden	17.50 €	92,000
The Irish Republic	22.00 €	44,000
The Netherlands	23.00 €	164,000
UK	15.50 €	612,000

1. Should BI operate its Pradaxa facility to sell to the European market in 2012?  If so, what should it set as its price in Europe, what are its expected sales, and how much profit will it expect to make?

2. Suppose BI overcomes the FDA hurdles in the U.S. and plans to use its current (European) plant to produce Pradaxa for the U.S. market, where the sole focus will be selling to Medicare, the U.S. program that provides health insurance for the elderly. Medicare negotiates prices, and BI will only  be able to sell to them at €10 (we ignore any issues of currency conversion), but BI estimates that it could sell up to 4,000,000 doses in the U.S. at that price. How will the ability to sell in the U.S. affect the price charged in the European market in 2013? What fraction of output should BI target to sell in each market in 2013?

Restaurant Pricing

Amsterdam Restaurant is considering having a "late-night special," i.e., a discount for individuals who are willing to dine late in the evening. One reason a restaurant might consider such a plan is because it gets too full at peak times. Let's assume that Amsterdam does not have this problem; Amsterdam is considering the special purely as a targeted pricing strategy. Assume the costs of serving customers are constant throughout the night and are equal to $10 per customer.

Amsterdam Restaurant serves two types of customers, Columbia students and non-students. There are 100 customers of each type. Within each group, the consumers are identical. The total willingness to pay for dinner at Amsterdam depends on the time of night. Each customer will only dine once per night.

	Students	Non-Students
Dinner @ or after 10:00 pm	$31	$46
Dinner before 10:00 pm	$35	$58

1. Suppose that Amsterdam is forced to charge the same price for dinner at all hours of the night. Amsterdam is also forced to charge the same price to students as to non-students. How much should Amsterdam charge? How much profit will Amsterdam earn?

2. Now suppose that Amsterdam can have different menus with different prices before and after 10 o'clock, and can have "student prices" and regular prices. It can achieve this consumer group price differential by asking students for their ID. What will be the student and regular prices at different times of the night, and what will Amsterdam's profits be?

3. Now suppose that Amsterdam cannot charge different prices to students and non-students but it can charge different prices at different times. How much should Amsterdam charge for dinner before and after 10pm? How much profit will it earn?

Standard and Luxury Products

A company is looking to sell its product in two versions, Standard and Luxury. Producing the standard version costs $5 per unit and producing the luxury version costs $30 per unit. Market research shows that there are two types of consumers interested in buying the products: high spending and low spending. There are 400 low-spending consumers and 200 high-spending consumers. The willingness to pay (WTP) for the standard and luxury versions of the product for each consumer group are reported in the table below.  Consumers will buy at most one unit of the product.

	Standard	Luxury
High-Spending	$90	$110
Low-Spending	$60	$90

What version(s) should the company produce and at what price(s)? Be sure to explain your rationale.

Markets -

Market for Selenium

Selenium is a chemical element used in glassmaking, the production of pigments, and various metal production processes such as electrolysis. Selenium is extracted as a byproduct in the refining of other ores, such as copper.

Selenium Producers
Producer	Pounds Capacity	WTS (Cost) Per Pound
A	4,000	$11
B	3,000	$38
C	2,500	$8
D	2,500	$17
E	2,500	$45
F	2,000	$12
G	1,500	$23
H	1,500	$26
I	1,500	$32
J	1,000	$13
K	1,000	$28

 

Selenium Consumers
Consumer	Potential Quantity Demanded	WTP
L	3,000	$64
M	2,500	$71
N	2,500	$13
O	2,000	$20
P	2,000	$36
Q	2,000	$45
R	1,500	$65
S	1,500	$70
T	1,000	$52
U	1,000	$51
V	1,000	$14
W	500	$48
X	500	$28
Y	500	$61
Z	500	$19

1. The capacity of selenium producers and their willingness to sell (WTS), i.e. production cost, per pound of Selenium and can be summarized by the table above (left). A second table (right) provides the willingness to pay (WTP) of selenium consumers (who are mostly glass manufacturers and metals producers) and the quantity that they would potentially purchase if the price is at or below their WTP. What would you predict for the equilibrium price and quantity in the selenium market?

2. A $22 tax on the sale of selenium is being proposed-all producers of selenium would have to pay $22 to the government for every pound of selenium that they sell. A representative from the Selenium Producers' Consortium (which represents the industry) claims: "Selenium producers cannot afford to have their margins cut by $22. This tax will put most of us out of business!" Evaluate this statement. In particular, estimate how much selenium producers will earn per pound after paying the tax and which selenium producers will no longer find it profitable to produce selenium.

Roses and the Mayor

In Diblasioville, a small progressive city, there is a highly competitive local market for fresh cut, long- stem roses on Valentine's Day, which are always sold by the dozen. There are diverse sets of consumer groups whose members would potentially buy one (and only one) dozen if the price were at or below their willingness to pay (WTP). There are a number of firms selling identical roses, but the firms differ in their production capacities and their costs (and therefore their willingness to sell roses to consumers). Information on consumers and firms is given in the following tables (which can be downloaded).

Consumer Group	Group Size	WTP
A	31	$28.80
B	126	$23.00
C	75	$22.30
D	86	$20.90
E	33	$61.60
F	78	$54.90
G	172	$48.10
H	129	$40.00
I	75	$63.40
J	74	$24.60
K	86	$57.30
L	23	$31.80
M	69	$26.00
N	180	$42.60
O	44	$30.00

a. What would you predict for the equilibrium price and quantity in this market for roses? Please support your answer, using text, tables, and/or figures as you see fit.

The new mayor of Diblasioville is concerned that not enough low income residents of the city are able to afford roses on Valentine's Day. The mayor identifies the following consumer groups as having low incomes: B, C, D, J, L, and M.

In order to create a more equitable distribution of roses, the mayor is considering two policies to intervene in the rose market. The first policy is a subsidy to rose producers of $10 per dozen roses that they sell during Valentine's day. The second policy is providing a $15 voucher to each low income consumer which can be used towards the purchase of a dozen roses from any firm.

Firm Name	Capacity	Unit Cost (WTS)
P	20	$30.00
Q	175	$11.00
R	100	$36.00
S	235	$45.00
T	65	$22.00
U	185	$41.00
V	265	$16.00
W	125	$38.00
X	100	$26.00
Y	85	$27.00
Z	110	$19.00

b. Evaluate the impact of each of these policies on this market for roses. How successful is each policy in achieving the mayor's goal of increasing the percentage of low income consumers that are able to buy a dozen roses on Valentine's Day, and how costly is each policy to the city government? Which policy would you recommend the mayor choose? Support your answer using text, tables, and/or figures as you see fit.

For Part (b), assume consumers and firms are totally honest: firms would accurately report sales when claiming the subsidy and only low income consumers buying a dozen roses would use the voucher. In recommending a policy, assume the mayor's goals are increasing rose purchases by low income residents and not spending too much of the city government's money.

Having considered the policies above, the mayor is still not satisfied, and decides to take the drastic measure of expropriating all local rose producing firms and merging them to create a single rose producer - effectively creating a government-run citywide monopoly on roses. The mayor directs this new city-run rose producer to sell roses to the public at whatever price maximizes its profits, and then to distribute all profits to low income residents on a per capita basis. For simplicity, assume that the conglomerate of vendors retains the cost structure of each underlying vendor.

c. Suppose you are appointed CEO of the new city-wide rose monopoly. You have control over the production of all the individual firms that previously sold roses in the competitive market, and you can choose any price for roses that you see fit. What price would you charge, how many roses would you expect to sell, and what would your profits be? Be sure to support your answer with text, tables, and/or figures as you see fit.

d. Given your answer to part (c), how much would each low income resident receive as a per capital distribution of the firm's profits? Would the low income residents be better or worse off under this new scheme compared with the original market equilibrium in Part (a)?

Buying Local

A national grocery chain is looking to expand into a new metropolitan area and is considering purchasing small supermarkets currently owned and operated by local independent grocers.

The net present value (NPV) of local supermarkets' current stream of profits is either high ($2 million), moderate ($1.5 million), or low ($1 million). Each owner knows the profitability of the local supermarket which he or she operates and would sell their supermarket to the national chain as long as the offered purchase price was at least 10% higher than their current NPV. For example, an owner of a highly profitable supermarket would need an offer of at least $2.2 million in order to be willing to sell.

The national chain believes that better management, scale economies, and other synergies would allow it to raise the NPV of each of the local supermarkets by 40% if it were to purchase them. For example, if it purchased a highly profitable local supermarket, the NPV of future profits of the supermarket to the national chain would be $2 million *140% = $2.8 million. This increase in value does not depend on the number of supermarkets that the chain is able to purchase.

There are 60 local supermarkets under consideration. The national chain believes that 1/3 of the local supermarkets are highly profitable, 1/3 have moderate profits, and 1/3 have low profits, but the national chain cannot tell which of the local supermarkets fall into which category.

You are asked to provide advice to the national chain's management team on what price it should offer to the local independent grocers. Assume that the chain will make a single offer to all supermarkets, once and for all. Please make sure to provide (1) a clear explanation for the price that you suggest that they offer, (2) your prediction for the number and type of local supermarkets that will accept the chain's offer, and (3) the total NPV of the transaction to the national chain (i.e. the aggregate NPV of the supermarkets they purchase minus the total amount they pay).

Strategic Interaction -

Strategic Price Competition

Two firms, A and B, interact in a strategic price competition. Firms can select one out of two possible prices: low and high. The payoff matrix associated with each possible combination of prices is given below, where the lower number in each cell is the payoff for Firm A and the upper number in each cell is the payoff for Firm B.

Firm B	High	$20 $70	$65 $65
	Low	$55 $55	$70 $20
		Low	High
		Firm A

Firms interact once for all and they choose prices simultaneously. Based on the idea of "beating the competition" clauses in retail and B2B pricing, consider two automatic pricing contracts:

I. I automatically change price to Low if my competitor's price is equal to or below my price.

II. I automatically change price to Low if my competitor's price is below my price.

1. Suppose that both firms can adopt Contract I, "equal to or below my price," and not Contract II. Each firm now has three possible actions: low price, high price, high price + contract. Write down the payoff matrix of this interaction. Do firms have strictly or weakly dominated actions? Find the Nash equilibria. Can you select the most likely Nash equilibrium?

2. Suppose that both firms can adopt Contract II, "below my price," and not Contract I. Each firm now has three possible actions: low price, high price, high price + contract. Write down the payoff matrix of this interaction. Do firms have strictly or weakly dominated actions? Find the Nash equilibria. Can you select the most likely Nash equilibrium?

3. Discuss why the two contracts have different effects on the strategic interaction.

Bidders in a 2^nd Price Auction

Consider a second-price sealed bid auction for a single item. There are only two bidders, each of which has a private value of the object of either $100 or $300, which occur with equal and independent probabilities. If there is a tie for the highest bid, the winner is selected at random from among the highest bidders.

(a) What is the expected revenue from the auction?  Be sure to explain how you arrived at your answer.

(b) Suppose that, before the auction is conducted, a third bidder, identical to the original two, joins the bidding. There are now three bidders, each of which has a private value of the object of either $100 or $300, which occur with equal and independent probabilities. Does this change the expected revenue from the auction? If so, what is the expected revenue? Be sure to explain how you arrived at your answer.

(c) Briefly explain why changing the number of bidders affects or does not affect the expected revenue.

 Dealing with Dealers

A recent WSJ article discussed Tesla's move to sell cars directly to the public rather than sell through a network of dealers. Consider the following situation regarding a car manufacturer's choice of sales channel.

Tulsa Automotive Co. (TAC) has developed a hydrogen cell fueled car, called the HX1, which it is now preparing to sell to the public. The cost of manufacturing each HX1 vehicle is $26,000 and TAC estimates it has a manufacturing capacity of 500 vehicles per year. In addition to per-vehicle manufacturing costs, TAC has annual overhead costs of $7.5 million, of which marketing and sales costs constitute $3.5 million.

HX1  Price	Nationwide Annual Demand for HX1
$60,000	0
$57,500	50
$55,000	120
$52,500	220
$50,000	310
$47,500	390
$45,000	465
$42,500	535
$40,000	600
$37,500	660
$35,000	715
$32,500	760
$30,000	810
$27,500	855
$25,000	890

 

HX1 Price	Annual Demand for HX1 Broken Out By:
	CA	Rest of U.S.
$60,000	0	0
$57,500	40	10
$55,000	90	30
$52,500	155	65
$50,000	210	100
$47,500	250	140
$45,000	290	175
$42,500	325	210
$40,000	350	250
$37,500	370	290
$35,000	385	330
$32,500	395	365
$30,000	405	405
$27,500	410	445
$25,000	420	470

(a) Using market research, the company has determined the demand curve for the HX1, given in the following table. For simplicity, assume that TAC will only set prices for its cars at multiples of $2,500.

At what price would you recommend selling the HX1? Please provide a rationale for your recommendation. What are your predicted profits for TAC?

(b) Suppose that additional market research reveals that much of the demand for the HX1 is concentrated in California (see table). TAC believes that by requiring buyers to show a driver's license issued at least 1 year prior to the purchase date, it can effectively provide different prices in California than in the rest of the US.

Assume that TAC's plan to sell the HX1 at different prices in California than in the rest of the US would work. Using the demand curves for the HX1 in CA and the rest of the US (RoUS) given in the following tables, what would you recommend TAC set for the prices for these two groups of consumers? Please provide a rationale for your recommendation. What are your predicted profits for TAC?

Note: these parts are more difficult.

Instead of selling directly to the public, TAC can sell through a national network of car dealers. However, using the dealer network would negate the ability for the HX1 to be sold at different prices in California than in the rest of the country.  The demand curve for the HX1 by consumers (see table) is not affected by whether the cars are sold to them via dealers or directly by TAC (i.e. demand is the same is in part a).

A potential upside of selling via dealers is that there would be no fixed costs associated with starting up a dealer network (since they already sell other brands of automobiles) and TAC would save 100% of the marketing and sales costs given above, regardless of the number of cars sold. Dealers buy the HX1 from TAC at a wholesale price and do not incur any additional costs beyond buying the HX1 cars from TAC. However, the dealers have the right to set final retail prices (for simplicity, at multiples of $2,500) on cars sold to the public.

HX1 Price	Nationwide Annual Demand for HX1
$60,000	0
$57,500	50
$55,000	120
$52,500	220
$50,000	310
$47,500	390
$45,000	465
$42,500	535
$40,000	600
$37,500	660
$35,000	715
$32,500	760
$30,000	810
$27,500	855
$25,000	890

(c) Suppose that TAC decides to sell through the national dealer network and charges them a wholesale price equal to your solution from part (a). Put yourself in the position of the manager of the dealer network. How many cars would you order from TAC at that wholesale price, and how much higher would you set the retail price to sell the HX1 to the public?  Please provide a rationale for your recommendation.

(d) Now put yourself in the position of TAC. Given how the dealer network will mark up retail prices, at what wholesale price would you recommend TAC sell the HX1 to dealers? Please provide a rationale for your recommendation. What are your predicted profits for TAC and would you recommend they sell cars through the dealers or go back to selling directly to the public?

A Strategic Partnership

Two firms decide to form a partnership. The amount of revenue of the partnership depends on the quality of the work done by each firm, according to the following formula:

Revenue = $5*W₁ + $10*W₂

W₁ denotes the work quality chosen by Firm 1 and W₂ the work quality chosen by Firm 2. Each firm can choose from three possible levels of quality: 0, 1, and 2. The partnership contract stipulates that Firm 1 receives a share S (between zero and one) of the partnership's revenue and Firm 2 receives a share 1-S of the partnership's revenue. Both firms must pay a cost for their work equal to the quality level squared (e.g., the cost of quality level 2 would be 22 = $4).

(a) Suppose that S=10%. The payoff matrix of this strategic interaction is given in the following table. Does Firm 1 have any dominant or dominated actions? Does Firm 2 have any dominant or dominated actions? Provide your rationale.

(b) What is the Nash equilibrium of the interaction between the firms when S=10%? Why?

(c) You are hired to write down a contract that maximizes the revenues of the partnership. At what level of quality for the two partner firms is the revenue maximized? Find a value of S that achieves this goal. Make sure to explain the rationale for why this value of S maximizes revenue for the partnership (i.e., full credit will not be given just for solving by trial and error).

 Hiring a Manager

A firm needs to hire a manager to run a specific project. The weekly revenues generated by the project depend on the effort exerted by the manager, according to the rule:

Weekly Revenues = $600*(Manager Effort)

The goal of the firm is to maximize weekly profits, i.e., revenues minus manager compensation.

Effort is not observable or verifiable by the firm and is chosen by the manager. The manager can choose to exert one of 5 levels of effort. Effort is a whole number from 1 to 5, 1 = works very little; 5 = works very hard.  The weekly cost to the manager of exerting any given level of effort is equal to $100 times the square of that effort level (e.g., if 2 is the level chosen, the cost is $100*2²=$400). A qualified manager can get a job in a similar business earning $500 per week. The goal of the manager is to maximize weekly earnings.

The firm offers the manager a contract specifying weekly compensation, which can depend on the revenues generated by the project. The manager can accept or reject the offer. If the offer is accepted, the firm and the manager get the payoffs specified above. If it is rejected, the firm gets zero and the manager earns $500 in another job.

1. Suppose that the firm is offering an optimal contract. What level of effort would such a contract induce? What would be the value of the project generated by such a contract? What part of the value should the firm be able to capture? And what would the manager earn from this contract?

2. Suppose that the firm chooses a no-incentive contract, where only a flat weekly wage is paid to the manager. What effort level is the manager going to choose if such a contract is accepted? Should the firm ever offer such a contract? Why?

3. Suppose that the firm chooses a target contract, where the manager is given no salary/wage but is paid a weekly bonus for revenues reaching a set target. Advise the firm on the optimal target and the amount of money that should be paid to the manager if the target is met or surpassed. What do you predict would be the weekly profits of the firm and the weekly earnings of the manager under the contract? Is the target contract you propose an optimal contract? Why?

4. Suppose that the firm chooses a franchise type contract, where a fee is paid from the manager to the firm (or from the firm to the manager) and the manager receives a share of the project revenue. Advise firm on the optimal values of the fee/salary and of the manager's share of the weekly project revenues. What do you predict would be the weekly profits of the firm and the weekly earnings of the manager under the contract? Is the franchise contract you propose an optimal contract? Why?