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A demand-based approach to menu pricing
~Restaurant Managementj~
A Demand-Based Approach to
Menu Pricing ff menu prices can be increased slightly without reducing sales, restaurant owners can enjoy higher profits. This pilot study indicates that prices can, indeed, be raised
by Thomas J. Kelly, Nicholas M. Kiefer, and Kenneth Burdett AN INTEREST IN maximizing prices seems to imply an evil intent on the part of the person setting those prices. But setting prices is an important part of product merchandising. We believe t h a t implementation © 1994, Cornell University
of any restaurant-merchandising concept must be managed through setting prices appropriately. This means r e s t a u r a t e u r s m u s t grasp menu-item demand and the elasticity of t h a t demand. That is, not only should they know how
strong the demand is for a given item, but they should have an idea of how the demand for t h a t item will change as the price changes. In this context, they should think of menu-item pricing as a method of managing revenue.
T h o m a s J o h n Kelly is an associate professor at Cornell University's School of Hotel Administration and N i e h o l a s M. Kiefer, Ph.D., is the Henry Scarborough Professor of Social Science in the department of economics at Cornell University. K e n n e t h B u r d e t t , Ph.D., is professor of economics at the University of Essex.
48
THE CORNELL H.R.A. QUARTERLY
Increasing prices without loss of volume is an important method of boosting profitability. Marn and Rosiello point out t h a t a typical m a n u f a c t u r i n g firm t h a t can achieve a 1-percent improvement in price with no loss of volume will increase profits 11.1 percent.1 Considering the r e s t a u r a n t industry's high fixed costs, a 1-percent improvement in price can yield as much as a 20-percent improvement in profitsF Another reason for paying careful attention to price is t h a t in m a n y cases your customers are focusing on value more t h a n on price. In its publication Price-Value Relationships at Restaurants, the National Restaur a n t Association suggests t h a t "consumers view themselves as being more quality and value conscious as opposed to price conscious--they w a n t quality and are willing to pay for it. "3 That report further notes t h a t consumers generally are in a spending mood when they dine out. Those observations indicate the value of having available a reliable method for determining a m e n u item's m a x i m u m price. F o r m e r a p p r o a c h e s . In m a n y regions of the United States, the demand for r e s t a u r a n t services through the 1970s was strong enough t h a t the old standby of multiplying food cost by a factor of three or even four sufficed. Some managers viewed price increases in a similar light as t a x e s - - a n y increase was bad. In either case, profitability was m a i n t a i n e d by cutting expenses, often by using inexpensive labor or reducing the quality of food products. Michael V. Marn and Robert L. Rosiello, "Managing Price, Gaining Profit," Harvard Business Review, September-October 1992, p. 85. 2Deloitte Touche, Restaurant Industry Operations Report 1991 (Washington, DC: National Restaurant Association, 1992), p. 25. :3National Restaurant Association, Price-Value Relationships at Restaurants, February 1992, pp. 8-9.
FEBRUARY 1994
As a result, r e s t a u r a n t managers of the past might be forgiven for not having implemented a sophisticated approach to pricing. Today, however, consumers have m a n y r e s t a u r a n t choices available and m e n u prices are demand driven--as predicated by the consumers' view of r e s t a u r a n t value. In this article, we explain our proposal for achieving appropriate menu prices using experimental data and consumers' responses. At this point, our proposal has not been implemented in a restaurant, but we believe it would be effective, judging from the pilot study described below.
Defining the Ideal Price Pricing individual items is a problem facing managers in m a n y wholesale and retail businesses. Generally speaking, the price of an item should sufficiently exceed the costs associated with the item to allow for an excess r e t u r n or profit. Consequently, m a n y purveyors use cost as the basis of price, adding a m a r k u p to provide the desired return. Part of the problem with t h a t cost-driven approach is t h a t in m a n y cases the cost of stocking and distributing individual items comprises expenses incurred in common with other items, so individualitem costs are difficult to allocate. Moreover, pricing based on the a m o u n t charged for similar products offered by competitors doesn't work well because the items are often not exactly alike. The r e s t a u r a n t m a n a g e r who is trying to price m e n u items faces considerable diversity of product. Other r e s t a u r a n t s compete with similar but not identical items, and competitors' decor, selection, service, and quality differ as well. Thus, a r e s t a u r a n t m a n a g e r is not in the setting of neoclassical economics in which the price is 49
given by the m a r k e t and the sole decision of the m a n a g e r is production. Typical menu-pricing schemes include a fixed m a r k u p over food cost, a m a r k u p over total cost, and pricing to meet a grossmargin requirement. 4 The importance of knowing demand in setting prices also has been noted for some time2 Some writers in this journal and elsewhere have proposed taking into account the menu mix (i.e., demand), as well as contribution margins in setting prices. 6 In the end, the effectiveness of any pricing strategy depends on how well managers u n d e r s t a n d consumers' responses to price changes. We suppose t h a t an individual entering the r e s t a u r a n t looks at the m e n u and orders an entree based at least partly on the prices of all of the entr~es. Of course, the decision will depend not only on prices but on the customer's characteristics. However, the kinds of customers entering the r e s t a u r a n t depend largely on m a r k e t i n g decisions other t h a n relative pricing of m e n u items, so we will assume t h a t the m a n a g e r is satisfied with his customer mix and is interested in optimizing his pricing for this mix. Additionally, the propensity t h a t any particular item is ordered will depend on the competition. Items t h a t are the subject of fierce competition by local r e s t a u r a n t s ~Jack E. Miller, Menu Pricing and Strategy (New York: Van Nostrand Reinhold, 1980). 5Andre Gabor and C.W.J. Granger, "Price Sensitivity of the Consumer," Journal of Advertising Research, 4 (1964), pp. 4 0 4 4 . 6See: Michael Kasavana and Don Smith, Menu Engineering (Lansing, Michigan: Hospitality Publishers, 1982); responses to Kasavana and Smith included: David K. Hayes and Lynn Huffman, "Menu Analysis: A Better Way," The Cornell Hotel and Restaurant Administration Quarterly, Vol. 25, No. 4 (February 1985), pp. 64-70; and David V. Pavesic, "Prime Numbers: Finding Your Menu's Strengths," The Cornell Hotel and Restaurant Administration Quarterly, Vol. 26, No. 3 (November 1985), pp. 70-77.
(e.g., chicken wings, pizza) are likely to be much more price sensitive t h a n signature items t h a t are unique to a particular restaurant.
Restaurant managers are not in the setting of neoclassical economics in which the price is given by the market.
Modeling the Menu We attempted to create a mathematical model of the effect of price changes on the likelihood t h a t a customer would order a given item. Although we recognize t h a t changes in the price of one menu item in relation to the others will affect the customers' propensity to order the other items, t h a t change is small. For simplicity, we assumed no such change. We first built and tested our model to focus on the price and profit effect of a single item, item i. We used n to indicate the propensity or likelihood of an order. The likelihood t h a t an individual entering the restaur a n t will order item i is given by ~i" The number of orders for i will be equal to xi times the number of customers. So, if ~i is 0.2 and 100 clients enter the restaurant, we can expect 20 orders for item i. In simple terms, profits are equal to revenues less costs. In turn, revenues are calculated by multiplying the number of each item sold by its price and then summing all revenues from the items. Costs work the same way. Direct costs are allocated to each item, multiplied by the number sold, and summed over items. Indirect or fixed costs t h a t cannot n a t u r a l l y be allocated to individual m e n u items m u s t also be considered, but t h a t amount is subtracted after the gross profit (revenues minus direct costs) is totalled for all items. Mathematically, the above description for calculating variable profits per individual item i
50
is expressed by Ei~i (pi%) - C, or the sum for all sales of item i of the propensity to order i times the contribution margin, which is price less cost. The term ci excludes fixed costs, which are captured in total by the extra term, C, t h a t does not depend on prices. The q u a n t i t y (Pi - ci) is the contribution margin of item i. For this purpose, we will not consider fixed costs, C. To determine the appropriate price for item i, consider the effects of a small increase in price from the current level. Two things might occur. The first is a likely decrease in the number of orders for the item. The second is an increase in profit per unit each time the item is ordered. (Although we are not considering the substitution effect, a reduction in the number ordered of item i should result in an increase in other items' being ordered.) If the loss in revenue from the decrease in the number of orders for item i is less t h a n the gain in revenue resulting from the price increase in the item, then it may be appropriate to raise the price. Conversely, if the loss in revenue from the decrease in orders is greater t h a n the gain from the increased price per unit, then it m a y be appropriate to consider a price decrease. The effects of a change in the price of item i can be summarized in a compact mathematical formula. We will represent the change in price by ~p and the change in propensity to order as ~ . If we continue to assume t h a t the dominant effect of the price (pi) is on the propensity to order i (~) so t h a t we can ignore the "cross price" effect, the optimality condition could be shown by this function t h a t expresses the relative changes in those values: ~Ki/~Pi (Pi- Ci) = -~i" The change (2)
THE CORNELL H.R.A. QUARTERLY
in the propensity to purchase i (~) divided by the change in the price of i multiplied by the contribution margin of i (p~ - ci) equals any reduction in the propensity to purchase item i (-~i)" Since we expect the accum u l a t e d cross effects, though individually small in magnitude, to be positive, a necessary condition for optimality is t h a t the reduction in the propensity to purchase i is less t h a n or equal to the increased revenue resulting from the price change, stated m a t h e m a t i c a l l y as:
~i/~pi(Pi -
Prices 8.95
9.50
9.95
10.95
Total
Friday:
Fish Total entrees Proportion
34 240 14
58 242 .24
31 184 .17
47 200 .24
170 866 .20
Saturday:
Fish Total entrees Proportion
16 199 .08
10 143 .07
9 138 .07
10 175 .06
45 655 .07
Total:
Fish Total entrees Proportion
50 439 .11
68 385 ~, .18
40 322 .12
57 375 .18
215 1521 .14
Ci) ~ -~I~i.
In this paper we focus on the m e a s u r e m e n t of ~i and the price effect of the change in propensity to buy against the change in price (~Xi/~Pi) for a particular entr6e. The ~ is fairly easy to estimate: in a large sample, n~ is approximated by the percentage of customers ordering item i. Though crucial, the other factor is more tricky to measure. That is the effect o n Tci of a change in the price of item i. In our example with 100 clients, 100(3~/ ~pi ) represents the change in the number of orders for item i. To measure 3~/3p~, we collected experimental d a t a on the effects of different prices. This was a pilot study to indicate the feasibility of our approach. The results of our simple design and analysis are useful in pointing the way to more research.
The Restaurant and the Design Our study was carried out at a medium-price family r e s t a u r a n t t h a t offered a range of entr6es (including steak, seafood, and chicken) and specialty sandwiches t h a t are all available at dinnertime. We chose to study the demand for the friedhaddock dinner. This popular F E B R U A R Y 1994
EXHIBIT 1 Summary statistics
item's price, $8.95, was in the middle of the range of entr6e prices. After consultation with the r e s t a u r a n t management, we chose to study the effects of raising the price to $9.50, $9.95, and $10.95 on four different menus. We felt t h a t the highest price, more t h a n a 22percent increase, would be large enough to show a drop in dem a n d (with all other m e n u prices held constant). The decision to test four price levels was determined in part by convenience. On weekend nights there are four waitstaff members. With four menus, we could assign a m e n u to each server for the entire evening. To control for the possibility t h a t the waitstaff members would influence orders, we set out a 4x4x2 Latin-square design, controlling for menu, server, and day of the week (Friday or Saturday). The data were collected over four winter weekends. At the end of the meal, the customers paid the original $8.95 price regardless of which m e n u they received and which price they were given at the beginning of the meal. In this way, consumers did not suffer any monetary loss due to our experiment. 51
Data and Analysis Exhibit 1 shows a s u m m a r y of the data we collected over the four weekends. Of a total of 1,521 orders, 215 were for the fish fry. The "Friday effect" is easily seen, with the fish fry averaging 20 percent of the orders on Friday and j u s t 7 percent on Saturday. The price effects do not seem to exhibit any specific pattern, certainly not the monotonic decrease in order probability as a function of increasing price t h a t we expected. Orders for the fish fry dropped off at higher prices on Saturday, but the price did not seem to affect order levels on Friday. We judged t h a t waitstaff effects were not systematic and so did not report them. An analysis of variance (ANOVA)table including all main effects (staff, day, and price) with the dependent variable being the proportion of entr6es t h a t are fish is shown in Exhibit 2. The ANOVAtable indicates t h a t only the Friday effect is statistically significant. That is, the data we see would be extremely surprising if there were no Friday effect (p < .001). An interesting
EXHIBIT 2 A n a l y s i s of v a r i a n c e
SOURCE
Model
Price Friday Staff Residual Total
NUMBER OF OBS
:
ROOT M S E
: ,073875
28
R-SQUARE
= =
ABJ R-SQUARE
PARTIALSS
OF
MS
F
.11121 .01066 .08442 .00547 .10915 .22036
7
.01589 .0036 .08442 .00182 .00546 .00816
2.91 0.65
3
1 3
20 27
0.5047
0.3313 i PROB :> F
0.0286 0.5915
15.47
4
0.33
i 0.8009
0.0008
Note: The dependent variable is the proportion of fish-fry orders.
question for future researchers is what the data would look like if an item other than the fish fry were tested. The data clearly indicate that a substantial negative effect of price on the amount of the fish fry ordered is quite unlikely in the range of prices we tested. That means the r e s t a u r a n t might be able to raise its price and its profit without hurting demand. These data indicate no significant systematic price effect. This holds both overall and for each day separately. The apparent small decline in orders on Saturday is not significant.
Reconsidering Prices The full-service segment of the r e s t a u r a n t industry has experienced little or no real growth in recent years. 7 At 3.2 percent of gross volume, median profits continue to be low by historical standards. 8 This is an appropriate time for r e s t a u r a n t owners and managers to reevaluate their pricing strategies. Clearly, future menu-pricing strategies 7,R&I Annual Forecast, Full Service Segment," Restaurants & Institutions (January 9, 1991), p. 48. 8Deloitte Touche, p. 25.
will incorporate some consideration of the demand function. The best-known effort that addresses demand issues is the concept of menu engineering as postulated by Kasavana and Smith2 This simple model analyzes menu item preference by contrasting popularity of the item (quantity sold) with item contribution margin (profit) in a grid format. The informed r e s t a u r a t e u r adjusts menu prices based on this information. As prices are adjusted, the concept of elasticity must be considered. In the Kasavana and Smith typology, for instance, "Stars" are high-margin items for which demand is relatively inelastic. That idea was reinforced by Daniel Nimer, who chastised quick-service r e s t a u r a n t s (QSR) for timorous pricing? ° He stated that the consumer is not nearly as price elastic as most firms in the QSR segment seem to think, given their propensity to merchandise by discounting price. Moreover, based on industry-
rants (as opposed to quickservice operations) m a y experience inelastic demand as an aggregate sector. 11 It is clear that some consideration of the demand function will become increasingly important in r e s t a u r a n t operations. Our research indicates that an experimental approach is feasible and potentially informative. R e s t a u r a t e u r s m a y have much more latitude in raising the prices of popular items than is commonly thought. F u t u r e research should examine menuitem price elasticity across r e s t a u r a n t categories (quick service, midscale, upscale casual, and upscale formal) and in different geographical markets. F u r t h e r research should also involve examining the elasticity issue relative to the total dining expense (per-person gross check). In principle our methods and suitable variations could be used routinely by restaurants, especially those with sophisticated point-of-sale systems, to determine the local shapes of demand curves and to set prices appropriately, c o
9For a summary of the Kasavana and Smith model, see: Hayes and Huffman, pp. 65-67. lo Daniel A. Nimer, "Executing Effective Pricing Strategies to Maximize Profit," Miami, FL: Presentation at Chain Operators Exchange (COEX), 1989.
11Douglas M. Brown, "The Restaurant and Fast Food Race: Who's Winning?," Southern Economic Journal, Vol. 56, No. 4 (April 1990), pp. 984-995.
52
THE CORNELL H.R.A. QUARTERLY
A Demand-Based Approach to
Menu Pricing ff menu prices can be increased slightly without reducing sales, restaurant owners can enjoy higher profits. This pilot study indicates that prices can, indeed, be raised
by Thomas J. Kelly, Nicholas M. Kiefer, and Kenneth Burdett AN INTEREST IN maximizing prices seems to imply an evil intent on the part of the person setting those prices. But setting prices is an important part of product merchandising. We believe t h a t implementation © 1994, Cornell University
of any restaurant-merchandising concept must be managed through setting prices appropriately. This means r e s t a u r a t e u r s m u s t grasp menu-item demand and the elasticity of t h a t demand. That is, not only should they know how
strong the demand is for a given item, but they should have an idea of how the demand for t h a t item will change as the price changes. In this context, they should think of menu-item pricing as a method of managing revenue.
T h o m a s J o h n Kelly is an associate professor at Cornell University's School of Hotel Administration and N i e h o l a s M. Kiefer, Ph.D., is the Henry Scarborough Professor of Social Science in the department of economics at Cornell University. K e n n e t h B u r d e t t , Ph.D., is professor of economics at the University of Essex.
48
THE CORNELL H.R.A. QUARTERLY
Increasing prices without loss of volume is an important method of boosting profitability. Marn and Rosiello point out t h a t a typical m a n u f a c t u r i n g firm t h a t can achieve a 1-percent improvement in price with no loss of volume will increase profits 11.1 percent.1 Considering the r e s t a u r a n t industry's high fixed costs, a 1-percent improvement in price can yield as much as a 20-percent improvement in profitsF Another reason for paying careful attention to price is t h a t in m a n y cases your customers are focusing on value more t h a n on price. In its publication Price-Value Relationships at Restaurants, the National Restaur a n t Association suggests t h a t "consumers view themselves as being more quality and value conscious as opposed to price conscious--they w a n t quality and are willing to pay for it. "3 That report further notes t h a t consumers generally are in a spending mood when they dine out. Those observations indicate the value of having available a reliable method for determining a m e n u item's m a x i m u m price. F o r m e r a p p r o a c h e s . In m a n y regions of the United States, the demand for r e s t a u r a n t services through the 1970s was strong enough t h a t the old standby of multiplying food cost by a factor of three or even four sufficed. Some managers viewed price increases in a similar light as t a x e s - - a n y increase was bad. In either case, profitability was m a i n t a i n e d by cutting expenses, often by using inexpensive labor or reducing the quality of food products. Michael V. Marn and Robert L. Rosiello, "Managing Price, Gaining Profit," Harvard Business Review, September-October 1992, p. 85. 2Deloitte Touche, Restaurant Industry Operations Report 1991 (Washington, DC: National Restaurant Association, 1992), p. 25. :3National Restaurant Association, Price-Value Relationships at Restaurants, February 1992, pp. 8-9.
FEBRUARY 1994
As a result, r e s t a u r a n t managers of the past might be forgiven for not having implemented a sophisticated approach to pricing. Today, however, consumers have m a n y r e s t a u r a n t choices available and m e n u prices are demand driven--as predicated by the consumers' view of r e s t a u r a n t value. In this article, we explain our proposal for achieving appropriate menu prices using experimental data and consumers' responses. At this point, our proposal has not been implemented in a restaurant, but we believe it would be effective, judging from the pilot study described below.
Defining the Ideal Price Pricing individual items is a problem facing managers in m a n y wholesale and retail businesses. Generally speaking, the price of an item should sufficiently exceed the costs associated with the item to allow for an excess r e t u r n or profit. Consequently, m a n y purveyors use cost as the basis of price, adding a m a r k u p to provide the desired return. Part of the problem with t h a t cost-driven approach is t h a t in m a n y cases the cost of stocking and distributing individual items comprises expenses incurred in common with other items, so individualitem costs are difficult to allocate. Moreover, pricing based on the a m o u n t charged for similar products offered by competitors doesn't work well because the items are often not exactly alike. The r e s t a u r a n t m a n a g e r who is trying to price m e n u items faces considerable diversity of product. Other r e s t a u r a n t s compete with similar but not identical items, and competitors' decor, selection, service, and quality differ as well. Thus, a r e s t a u r a n t m a n a g e r is not in the setting of neoclassical economics in which the price is 49
given by the m a r k e t and the sole decision of the m a n a g e r is production. Typical menu-pricing schemes include a fixed m a r k u p over food cost, a m a r k u p over total cost, and pricing to meet a grossmargin requirement. 4 The importance of knowing demand in setting prices also has been noted for some time2 Some writers in this journal and elsewhere have proposed taking into account the menu mix (i.e., demand), as well as contribution margins in setting prices. 6 In the end, the effectiveness of any pricing strategy depends on how well managers u n d e r s t a n d consumers' responses to price changes. We suppose t h a t an individual entering the r e s t a u r a n t looks at the m e n u and orders an entree based at least partly on the prices of all of the entr~es. Of course, the decision will depend not only on prices but on the customer's characteristics. However, the kinds of customers entering the r e s t a u r a n t depend largely on m a r k e t i n g decisions other t h a n relative pricing of m e n u items, so we will assume t h a t the m a n a g e r is satisfied with his customer mix and is interested in optimizing his pricing for this mix. Additionally, the propensity t h a t any particular item is ordered will depend on the competition. Items t h a t are the subject of fierce competition by local r e s t a u r a n t s ~Jack E. Miller, Menu Pricing and Strategy (New York: Van Nostrand Reinhold, 1980). 5Andre Gabor and C.W.J. Granger, "Price Sensitivity of the Consumer," Journal of Advertising Research, 4 (1964), pp. 4 0 4 4 . 6See: Michael Kasavana and Don Smith, Menu Engineering (Lansing, Michigan: Hospitality Publishers, 1982); responses to Kasavana and Smith included: David K. Hayes and Lynn Huffman, "Menu Analysis: A Better Way," The Cornell Hotel and Restaurant Administration Quarterly, Vol. 25, No. 4 (February 1985), pp. 64-70; and David V. Pavesic, "Prime Numbers: Finding Your Menu's Strengths," The Cornell Hotel and Restaurant Administration Quarterly, Vol. 26, No. 3 (November 1985), pp. 70-77.
(e.g., chicken wings, pizza) are likely to be much more price sensitive t h a n signature items t h a t are unique to a particular restaurant.
Restaurant managers are not in the setting of neoclassical economics in which the price is given by the market.
Modeling the Menu We attempted to create a mathematical model of the effect of price changes on the likelihood t h a t a customer would order a given item. Although we recognize t h a t changes in the price of one menu item in relation to the others will affect the customers' propensity to order the other items, t h a t change is small. For simplicity, we assumed no such change. We first built and tested our model to focus on the price and profit effect of a single item, item i. We used n to indicate the propensity or likelihood of an order. The likelihood t h a t an individual entering the restaur a n t will order item i is given by ~i" The number of orders for i will be equal to xi times the number of customers. So, if ~i is 0.2 and 100 clients enter the restaurant, we can expect 20 orders for item i. In simple terms, profits are equal to revenues less costs. In turn, revenues are calculated by multiplying the number of each item sold by its price and then summing all revenues from the items. Costs work the same way. Direct costs are allocated to each item, multiplied by the number sold, and summed over items. Indirect or fixed costs t h a t cannot n a t u r a l l y be allocated to individual m e n u items m u s t also be considered, but t h a t amount is subtracted after the gross profit (revenues minus direct costs) is totalled for all items. Mathematically, the above description for calculating variable profits per individual item i
50
is expressed by Ei~i (pi%) - C, or the sum for all sales of item i of the propensity to order i times the contribution margin, which is price less cost. The term ci excludes fixed costs, which are captured in total by the extra term, C, t h a t does not depend on prices. The q u a n t i t y (Pi - ci) is the contribution margin of item i. For this purpose, we will not consider fixed costs, C. To determine the appropriate price for item i, consider the effects of a small increase in price from the current level. Two things might occur. The first is a likely decrease in the number of orders for the item. The second is an increase in profit per unit each time the item is ordered. (Although we are not considering the substitution effect, a reduction in the number ordered of item i should result in an increase in other items' being ordered.) If the loss in revenue from the decrease in the number of orders for item i is less t h a n the gain in revenue resulting from the price increase in the item, then it may be appropriate to raise the price. Conversely, if the loss in revenue from the decrease in orders is greater t h a n the gain from the increased price per unit, then it m a y be appropriate to consider a price decrease. The effects of a change in the price of item i can be summarized in a compact mathematical formula. We will represent the change in price by ~p and the change in propensity to order as ~ . If we continue to assume t h a t the dominant effect of the price (pi) is on the propensity to order i (~) so t h a t we can ignore the "cross price" effect, the optimality condition could be shown by this function t h a t expresses the relative changes in those values: ~Ki/~Pi (Pi- Ci) = -~i" The change (2)
THE CORNELL H.R.A. QUARTERLY
in the propensity to purchase i (~) divided by the change in the price of i multiplied by the contribution margin of i (p~ - ci) equals any reduction in the propensity to purchase item i (-~i)" Since we expect the accum u l a t e d cross effects, though individually small in magnitude, to be positive, a necessary condition for optimality is t h a t the reduction in the propensity to purchase i is less t h a n or equal to the increased revenue resulting from the price change, stated m a t h e m a t i c a l l y as:
~i/~pi(Pi -
Prices 8.95
9.50
9.95
10.95
Total
Friday:
Fish Total entrees Proportion
34 240 14
58 242 .24
31 184 .17
47 200 .24
170 866 .20
Saturday:
Fish Total entrees Proportion
16 199 .08
10 143 .07
9 138 .07
10 175 .06
45 655 .07
Total:
Fish Total entrees Proportion
50 439 .11
68 385 ~, .18
40 322 .12
57 375 .18
215 1521 .14
Ci) ~ -~I~i.
In this paper we focus on the m e a s u r e m e n t of ~i and the price effect of the change in propensity to buy against the change in price (~Xi/~Pi) for a particular entr6e. The ~ is fairly easy to estimate: in a large sample, n~ is approximated by the percentage of customers ordering item i. Though crucial, the other factor is more tricky to measure. That is the effect o n Tci of a change in the price of item i. In our example with 100 clients, 100(3~/ ~pi ) represents the change in the number of orders for item i. To measure 3~/3p~, we collected experimental d a t a on the effects of different prices. This was a pilot study to indicate the feasibility of our approach. The results of our simple design and analysis are useful in pointing the way to more research.
The Restaurant and the Design Our study was carried out at a medium-price family r e s t a u r a n t t h a t offered a range of entr6es (including steak, seafood, and chicken) and specialty sandwiches t h a t are all available at dinnertime. We chose to study the demand for the friedhaddock dinner. This popular F E B R U A R Y 1994
EXHIBIT 1 Summary statistics
item's price, $8.95, was in the middle of the range of entr6e prices. After consultation with the r e s t a u r a n t management, we chose to study the effects of raising the price to $9.50, $9.95, and $10.95 on four different menus. We felt t h a t the highest price, more t h a n a 22percent increase, would be large enough to show a drop in dem a n d (with all other m e n u prices held constant). The decision to test four price levels was determined in part by convenience. On weekend nights there are four waitstaff members. With four menus, we could assign a m e n u to each server for the entire evening. To control for the possibility t h a t the waitstaff members would influence orders, we set out a 4x4x2 Latin-square design, controlling for menu, server, and day of the week (Friday or Saturday). The data were collected over four winter weekends. At the end of the meal, the customers paid the original $8.95 price regardless of which m e n u they received and which price they were given at the beginning of the meal. In this way, consumers did not suffer any monetary loss due to our experiment. 51
Data and Analysis Exhibit 1 shows a s u m m a r y of the data we collected over the four weekends. Of a total of 1,521 orders, 215 were for the fish fry. The "Friday effect" is easily seen, with the fish fry averaging 20 percent of the orders on Friday and j u s t 7 percent on Saturday. The price effects do not seem to exhibit any specific pattern, certainly not the monotonic decrease in order probability as a function of increasing price t h a t we expected. Orders for the fish fry dropped off at higher prices on Saturday, but the price did not seem to affect order levels on Friday. We judged t h a t waitstaff effects were not systematic and so did not report them. An analysis of variance (ANOVA)table including all main effects (staff, day, and price) with the dependent variable being the proportion of entr6es t h a t are fish is shown in Exhibit 2. The ANOVAtable indicates t h a t only the Friday effect is statistically significant. That is, the data we see would be extremely surprising if there were no Friday effect (p < .001). An interesting
EXHIBIT 2 A n a l y s i s of v a r i a n c e
SOURCE
Model
Price Friday Staff Residual Total
NUMBER OF OBS
:
ROOT M S E
: ,073875
28
R-SQUARE
= =
ABJ R-SQUARE
PARTIALSS
OF
MS
F
.11121 .01066 .08442 .00547 .10915 .22036
7
.01589 .0036 .08442 .00182 .00546 .00816
2.91 0.65
3
1 3
20 27
0.5047
0.3313 i PROB :> F
0.0286 0.5915
15.47
4
0.33
i 0.8009
0.0008
Note: The dependent variable is the proportion of fish-fry orders.
question for future researchers is what the data would look like if an item other than the fish fry were tested. The data clearly indicate that a substantial negative effect of price on the amount of the fish fry ordered is quite unlikely in the range of prices we tested. That means the r e s t a u r a n t might be able to raise its price and its profit without hurting demand. These data indicate no significant systematic price effect. This holds both overall and for each day separately. The apparent small decline in orders on Saturday is not significant.
Reconsidering Prices The full-service segment of the r e s t a u r a n t industry has experienced little or no real growth in recent years. 7 At 3.2 percent of gross volume, median profits continue to be low by historical standards. 8 This is an appropriate time for r e s t a u r a n t owners and managers to reevaluate their pricing strategies. Clearly, future menu-pricing strategies 7,R&I Annual Forecast, Full Service Segment," Restaurants & Institutions (January 9, 1991), p. 48. 8Deloitte Touche, p. 25.
will incorporate some consideration of the demand function. The best-known effort that addresses demand issues is the concept of menu engineering as postulated by Kasavana and Smith2 This simple model analyzes menu item preference by contrasting popularity of the item (quantity sold) with item contribution margin (profit) in a grid format. The informed r e s t a u r a t e u r adjusts menu prices based on this information. As prices are adjusted, the concept of elasticity must be considered. In the Kasavana and Smith typology, for instance, "Stars" are high-margin items for which demand is relatively inelastic. That idea was reinforced by Daniel Nimer, who chastised quick-service r e s t a u r a n t s (QSR) for timorous pricing? ° He stated that the consumer is not nearly as price elastic as most firms in the QSR segment seem to think, given their propensity to merchandise by discounting price. Moreover, based on industry-
rants (as opposed to quickservice operations) m a y experience inelastic demand as an aggregate sector. 11 It is clear that some consideration of the demand function will become increasingly important in r e s t a u r a n t operations. Our research indicates that an experimental approach is feasible and potentially informative. R e s t a u r a t e u r s m a y have much more latitude in raising the prices of popular items than is commonly thought. F u t u r e research should examine menuitem price elasticity across r e s t a u r a n t categories (quick service, midscale, upscale casual, and upscale formal) and in different geographical markets. F u r t h e r research should also involve examining the elasticity issue relative to the total dining expense (per-person gross check). In principle our methods and suitable variations could be used routinely by restaurants, especially those with sophisticated point-of-sale systems, to determine the local shapes of demand curves and to set prices appropriately, c o
9For a summary of the Kasavana and Smith model, see: Hayes and Huffman, pp. 65-67. lo Daniel A. Nimer, "Executing Effective Pricing Strategies to Maximize Profit," Miami, FL: Presentation at Chain Operators Exchange (COEX), 1989.
11Douglas M. Brown, "The Restaurant and Fast Food Race: Who's Winning?," Southern Economic Journal, Vol. 56, No. 4 (April 1990), pp. 984-995.
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THE CORNELL H.R.A. QUARTERLY