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 1, specify a linear functional form for the demand for Combination 1
meals, and run a regression to estimate the demand for Combo 1 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 1, 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.
(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
104ORDER WITH US FOR AN A+ QUALITY PAPER….
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
104ORDER WITH US FOR AN A+ QUALITY PAPER….
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.
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.
