CONSULTING PROJECT

Estimation and Analysis of Demand for Fast Food Meals

You work for PriceWatermanCoopers as a market analyst. PWC has been hired by the owner of

two Burger King restaurants located in a suburban Atlanta market area to study the demand for its basic

hamburger meal package–referred to as “Combination 1? on its menus. The two restaurants face

competition in the Atlanta suburb from five other hamburger restaurants (three MacDonald’s and two

Wendy’s restaurants) and three other restaurants serving “drive-through” fast food (a Taco Bell, a

Kentucky Fried Chicken, and a small family-owned Chinese restaurant).

The owner of the two Burger King restaurants provides PWC with the data shown in Table 1. Q

is the total number of Combination 1 meals sold at both locations during each week in 1998. P is the

average price charged for a Combination 1 meal at the two locations. [Prices are identical at the two

Burger King locations.] Every week the Burger King owner advertises special price offers at its two

restaurants exclusively in daily newspaper advertisements. A is the dollar amount spent on newspaper ads

for each week in 1998. The owner could not provide PWC with data on prices charged by other

competing restaurants during 1998. For the one-year time period of the study, household income and

population in the suburb did not change enough to warrant inclusion in the demand analysis.

TABLE 1: Weekly Sales Data for Combination 1 Meals (1998)

week Q P A week Q P A

1 51,345 2.78 4,280 27 78,953 2.27 21,225

2 50,337 2.35 3,875 28 52,875 3.78 7,580

3 86,732 3.22 12,360 29 81,263 3.95 4,175

4 118,117 1.85 19,250 30 67,260 3.52 4,365

5 48,024 2.65 6,450 31 83,323 3.45 12,250

6 97,375 2.95 8,750 32 68,322 3.92 11,850

7 75,751 2.86 9,600 33 71,925 4.05 14,360

8 78,797 3.35 9,600 34 29,372 4.01 9,540

9 59,856 3.45 9,600 35 21,710 3.68 7,250

10 23,696 3.25 6,250 36 37,833 3.62 4,280

11 61,385 3.21 4,780 37 41,154 3.57 13,800

12 63,750 3.02 6,770 38 50,925 3.65 15,300

13 60,996 3.16 6,325 39 57,657 3.89 5,250

14 84,276 2.95 9,655 40 52,036 3.86 7,650

15 54,222 2.65 10,450 41 58,677 3.95 6,650

16 58,131 3.24 9,750 42 73,902 3.91 9,850

17 55,398 3.55 11,500 43 55,327 3.88 8,350

18 69,943 3.75 8,975 44 16,262 4.12 10,250

19 79,785 3.85 8,975 45 38,348 3.94 16,450

20 38,892 3.76 6,755 46 29,810 4.15 13,200

21 43,240 3.65 5,500 47 69,613 4.12 14,600

22 52,078 3.58 4,365 48 45,822 4.16 13,250

23 11,321 3.78 9,525 49 43,207 4.00 18,450

24 73,113 3.75 18,600 50 81,998 3.93 16,500

25 79,988 3.22 14,450 51 46,756 3.89 6,500

26 98,311 3.42 15,500 52 34,592 3.83 5,650

a. Using the data in Table 12, specify a linear functional form for the demand for Combination 1

meals, and run a regression to estimate the demand for Combo 1 meals.

b. Should you use the ordinary least-squares (OLS) method or the two-stage least-squares method

(2SLS) method for estimating industry demand for rutabagas? Explain briefly.

c. Using statistical software, estimate the parameters of the empirical demand function specified in

part a. Write your estimated industry demand equation for rutabagas.

d. Evaluate your regression results by examining signs of parameters, p-values (or t-ratios), and the

R2.

e. Discuss how the estimation of demand might be improved.

f. Using your estimated demand equation, calculate an own-price elasticity and an advertising

elasticity. Compute the elasticity values at the sample mean values of the data in Table 1.

Discuss, in quantitative terms, the meaning of each elasticity.

g. If the owner plans to charge a price of $4.15 for a Combination 1 meal and spend $18,000 per

week on advertising, how many Combination 1 meals do you predict will be sold each week?

h. If the owner spends $18,000 per week on advertising, write the equation for the inverse demand

function. Then, calculate the demand price for 50,000 Combination 1 meals.

CONSULTING PROJECT

Pricing and Production Decisions at PoolVac, Inc.

PoolVac, Inc. manufactures and sells a single product called the “Sting Ray,” which is a patent-protected automatic cleaning device for swimming pools. PoolVac’s Sting Ray accounts for 65 percent of total industry sales of automatic pool cleaners. Its closest competitor, Howard Industries, sells a competing pool cleaner that has captured about 18 percent of the market. Six other very small firms share the rest of the industry’s sales. Using the last 26 months of production and cost data, PoolVac wishes to estimate its unit variable costs using the following quadratic specification:

2=++AVCabQcQ

The monthly data on average variable cost (AVC), and the quantity of Sting Rays produced and sold each month (Q) are presented in the table below.

PoolVac also wishes to use its sales data for the last 26 months to estimate demand for its Sting Ray. Demand for Sting Rays is specified to be a linear function of its price (P), average income for households in the U.S. that have swimming pools (Mavg), and the price of the competing pool cleaner sold by Howard Industries (PH):

=+++davQdePfMgP g H

The table below presents the last 26 months of data on the price charged for a Sting Ray (P), average income of households with pools (MAVG), and the price Howard Industries charged for its pool cleaner (PH):

obs

AVC QPMAVG PH

1

109

1647

275

58000

175

2

118

1664

275

58000

175

3

121

1295

300

58000

200

4

102

1331

300

56300

200

5

121

1413

300

56300

200

6

102

1378

300

56300

200

7

105

1371

300

57850

200

8

101

1312

300

57850

200

9

108

1301

325

57850

250

10

113

854

350

57600

250

11

114

963

350

57600

250

12

105

1238

325

57600

225

13

107

1076

325

58250

225

14

104

1092

325

58250

225

15

104

1222

325

58250

225

16

102

1308

325

58985

250

17

116

1259

325

58985

250

18

126

711

375

58985

250

19

116

1118

350

59600

250

20

139

91

475

59600

375

21

152

137

475

59600

375

22

116

857

375

60800

250

23

127

1003

350

60800

250

24

123

1328

320

60800

220

25

104

1376

320

62350

220

26

114

1219

320

62350

220

1

PoolVac, Inc. incurs total fixed costs of $45,000 per month.

1. a. Run the appropriate regression to estimate the average variable cost function (AVC) for Sting Rays. Evaluate the statistical significance of the three estimated parameters using a significance level of 5 percent. Be sure to comment on the algebraic signs of the three parameter estimates.

b. Using the regression results from part 1 a, write the estimated total variable cost, average variable cost, and marginal cost functions (TVC, AVC, and MC) for PoolVac.

TVC = __________________________________________

AVC = __________________________________________

MC = ___________________________________________

c. Compute minimum average variable cost.

Qmin = ___________ AVCmin = ______________

2. a. Run the appropriate regression to estimate the demand function for Sting Rays. Evaluate the statistical significance of the three estimated slope parameters using a significance level of 5 percent. Discuss the appropriateness of the algebraic signs of each of the three slope parameter estimates.

2

3

b. The manager at PoolVac, Inc. believes Howard Industries is going to price its automatic pool cleaner at $250, and average household income in the U.S. is expected to be $65,000. Using the regression results from part 2 a, write the estimated demand function, inverse demand function, and marginal revenue function.

Demand: ____________________________

Inverse Demand: ____________________________

Marginal Revenue: ____________________________

3. Using your estimated cost and demand functions from parts 1 and 2, what price would you recommend the manager of PoolVac, Inc. charge for its Sting Ray? Given your recommended price, estimate the number of units PoolVac can expect to sell, as well as its monthly total revenue, total cost, and profit.

P: ___________

Q: ___________

TR: ___________

TC: ___________

Profit: ___________

4. For the profit-maximizing solution in question 3, compute the point elasticity of demand for Sting Rays.

E = ______________

In the profit-maximizing situation in question 3, a 5 percent price cut would be predicted to _______________ (increase, decrease) quantity demanded of Sting Rays by ___________ percent, which would cause total revenue to _____________ (rise, fall, stay the same) and profit to _____________ (rise, fall, stay the same).

5. For the profit-maximizing solution in question 3, compute the income elasticity of demand for Sting Rays.

EM = ______________

a. Is the algebraic sign of the income elasticity as you expected? Explain.

b. A 10 percent increase in Mavg would be predicted to _______________ (increase, decrease) quantity demanded of Sting Rays by ___________ percent.

4

6. For the profit-maximizing solution in question 3, compute the cross-price elasticity of demand for Sting Rays.

EXR = ______________

a. Is the algebraic sign of the income elasticity as you expected? Explain.

b. A 3 percent decrease in PH would be predicted to _______________ (increase, decrease) quantity demanded of Sting Rays by ___________ percent.

7. If total fixed costs increase from $45,000 to $55,000, what price would you now recommend in order to maximize profits at PoolVac? Compute the number of units sold at this price, total revenue, total cost and profit:

P: ___________

Q: ___________

TR: ___________

TC: ___________

Profit: ___________

8. If the manager of PoolVac wanted to maximize total revenue instead of profit (a bad idea), the manager would charge a price of $_____________. At this price, PoolVac’s profit would be $_______________, which is _______________ (higher than, lower than, the same as) the profit in question 3.