Demand Equation Redux: The Design and Functionality of the Gold/Pray Model in Computerized Business Simulations Page 28 - Developments in Business Simulation and Experiential Learning, Volume 38, 2011 ABSTRACT This paper is a response to a paper entitled “Is the Gold/ Pray Simulation Model Valid and Is It Really Robust?" which was presented at the 2010 ABSEL conference by Kenneth Goosen. The Goosen paper called into question the validity and robustness of the Gold/Pray demand model. This paper is written as a response to the argu- ments advanced by Goosen. Goosen (2010) has raised five problems with the Gold/Pray (1983) model. The paper will proceed by listing and then replying to each of these al- leged problems. One of the purposes of the paper is to encourage simulation developers, especially total enter- prise simulation developers, to explain and discuss their underlying demand equations and how these equations have worked over the life of their simulation usage. INTRODUCTION AND PURPOSE In 1974, at the first annual ABSEL conference held in Oklahoma City, Churchill (1974) presented a small scale deterministic business game called DØG. In the paper he provided some of the details of the formulae and underly- ing demand functions that had been incorporated into the game. Since Churchill presented this information at the first annual ABSEL conference, it would not have been surprising to see a number of articles addressing demand functions over the course of ABSEL's thirty-seven year history. That has not been the case. Less than one percent of all the articles that have been published in the ABSEL's proceedings in the period of time 1974 to 2010 have fo- cused on the demand functions that are the heart of busi- ness simulations. They are several plausible explanations for the paucity of articles on this subject. In 1981, Goosen alluded to the challenges in designing appropriate algo- rithms faced by potential simulation developers, and Pray and Gold (1982) state the challenges more explicitly and specifically. In his chapter devoted to designing business simulations, Teach (1990) indicates in spite of the fact that a great deal of information is provided about several of the simulations, the details of the demand algorithms Mark- strat or Industrat have not been published. A perusal of the ABSEL literature draws one to the conclusion that simulation designers of business simulations have not been inclined to reveal the details of their demand functions in the literature; perhaps for proprietary reasons. Pray and Gold's use of the term black box is a result of the "secrecies of the internal workings" of simulations. To focus the discussion of demand functions in simu- lations, it might be useful to state which, of the full range of simulations that fall in the purview of ABSEL, must have an integrated demand function in their underlying software. Biggs (1990) utilizes the definition that Cohen and Rhenmann (1961) presented when he describes a total enterprise game as one "designed to give people experience in making decisions at a top executive level and in which decisions from one functional area interact with those made in other areas of the firm." Keys and Biggs (1990) describe a total enterprise game as "one which includes decisions in most of the main functions of business: marketing, produc- tion, finance and personnel." Obviously simulations that are not total enterprise simulations might not have a built-in demand function, but equally obviously, all true total enter- prise simulations have to address demand and have to have a demand function as an integral component. The follow- ing discussion of demand functions is limited to demand functions incorporated into total enterprise simulations. In 1983, Gold and Pray presented their work on simu- lating market-level and firm-level demand. In their paper DEMAND EQUATION REDUX: THE DESIGN AND FUNCTIONALITY OF THE GOLD/PRAY MODEL IN COMPUTERIZED BUSINESS SIMULATIONS Steven C. Gold Rochester Institute of Technology sgold@saunders.rit.edu Peter M. Markulis SUNY Geneseo markulis@geneseo.Edu Daniel R. Strang SUNY Geneseo strang@geneseo.edu mailto:sgold@saunders.rit.edu mailto:markulis@geneseo.Edu mailto:strang@geneseo.edu Page 29 - Developments in Business Simulation and Experiential Learning, Volume 38, 2011 they indicate several of the alternative functional forms for demand models including a linear form, a non-linear form and a multiplicative form. In their article they discuss the advantages and disadvantages of each form and ultimately suggest the multiplicative form for several reasons, not the least of which is its robustness. Elements of robustness include the ability to eliminate conventional wisdom on the part of players which would severely limit the effectiveness of a simulation if it were discovered. In 1990, Gold and Pray discussed the potential problems of a simulation "blowing up!" Clearly, a robust demand model will pre- vent this potential unfortunate result for simulation play. A perusal of the ABSEL literature indicates occa- sional interest in the modeling of demand functions in the period of time from 1974 to 2010. Each of articles pro- vided were at best a marginal extension or reflection of the basic Gold/Pray demand algorithm. Decker, LaBarre and Adler (1987) presented two distinct approaches to defining the underlying functions of simulations, the multiplicative and the interpolation model. In 1998, Lambert and Lam- bert considered the advertising response in the Gold/Pray algorithm and Carvalho addressed the theoretical derivation of a basic demand function. Over the years, Teach (1984, 1986, 1990) has explored various facets of demand func- tions. In 2006, Murff, Teach, Schwartz present an algo- rithm they developed to establish industry-level demand in simulations. Murff et al. argue that their algorithm resolves the monotonicity problems attendant to the Gold/Pray algo- rithm which they maintain require artificial constraint of several of the keys decision variables. To that point, when the Gold/Pray demand algorithm is incorporated in a simu- lation, additional algorithms utilizing exponential smooth- ing of key variables can be embedded in the software to minimize or eliminate the adverse effects of extreme changes in the value of key variables. Although an explora- tion of these issues might be fascinating, it is not the pur- pose of this paper. So, with the possible exception of the work of Murff, Teach and Schwartz, (2006) it is fair to say that ABSEL literature has added very little to understanding the model- ing of the demand functions since Gold and Pray's work in 1983. In one respect, the Gold/Pray algorithm has been accepted as the standard for modeling demand in simula- tions. In 2010, Goosen presented a paper at the annual AB- SEL conference which called into question the validity and robustness of the Gold/Pray demand model. This paper is written as a response to the arguments advanced by Goosen. Goosen (2010) has raised five problems with the Gold/Pray (1983) model. The paper will proceed by listing and then replying to each of these alleged problems. Impact of Exponential Smoothing on Marketing Expenditures Table 1 Period Marketing (Mn) Exponentially Smoothed Marketing (M) b = 0.4 b = 0.6 b = 0.8 1 $1,000 $1,000.00 $1,000.00 $1,000.00 2 $0 $700.00 $500.00 $200.00 3 $0 $490.00 $250.00 $40.00 4 $0 $343.00 $125.00 $8.00 5 $0 $240.10 $62.50 $1.60 6 $0 $168.07 $31.25 $0.32 7 $0 $117.65 $15.63 $0.06 8 $0 $82.35 $7.81 $0.01 9 $0 $57.65 $3.91 $0.003 10 $0 $40.35 $1.95 $0.001 Page 30 - Developments in Business Simulation and Experiential Learning, Volume 38, 2011 FIRST PROBLEM: DOES THE GOLD/ PRAY MODEL ALLOW ADVERTISING OR R & D TO BE ZERO? Goosen (2010) states “The first problem concerns the effect of marketing (e.g., advertising) on demand. If adver- tising and R& D in the G/P model are zero, then demand is zero. There is no demand when price stands alone without advertising and R & D.” There are two reasons why this is not true. First the Gold/Pray model distinguishes between firm level demand and market level demand. With respect to firm level de- mand, the Gold/Pray model uses a weighting function which determines the firm’s market share and its demand. In this weighting function there is a constant term added to each of the demand variables including price, advertising, and R & D. The equation is given as number 6 in Gold and Pray (1983) and is shown below as equation 1 of this paper: (1) Wi = [Pi + k1]-(k2 + k3Pi) [Mi + k4]+(k5 – k6Mi) [Ri + k7]+ (k8 – k9Ri) where: Wi = weight of firm i Pi = price of firm i Mi = marketing expenditures of firm i Ri = research and development expenditures of firm i ki = parameters or constants i = 1 to 9 Referring to equation 1, the value for the firm’s weight (Wi) determines the firm level demand. The con- stant terms associated with the demand variables of price (k1), marketing (k4), and research and development (k7) prevent the firm demand from going to zero, even if the demand variables are zero. But what about the market level demand? Can the market level demand go to zero if all firms in the market charge a price of zero, and spend nothing on marketing and R & D? First, in the market demand equation “average” Demand at three different levels of Marketing Expenditures Table 2 $50,000 $75,000 $100,000 Price Demand-50 Demand-75 Demand-100 $180 1 3 5 $160 2 5 9 $140 3 9 17 $130 4 12 23 $120 5 16 30 $110 7 21 40 $100 9 28 54 $90 12 37 71 $80 16 48 93 $70 20 63 122 $60 26 82 158 $50 34 105 203 $40 43 134 259 $30 55 169 326 $20 68 209 404 $10 82 254 490 Page 31 - Developments in Business Simulation and Experiential Learning, Volume 38, 2011 marketing expenditures and “average” R & D for the entire market is used. It is highly unlikely that all firms would decide not to advertise or do any R & D. Second, and more importantly, even if average values for marketing and R & D were zero in a period of the game, the market demand would not go to zero in the Gold/Pray model because the market level demand is a function of “exponentially smoothed” values for both market and firm price, market- ing expenditures, and research and development expendi- tures. Equations 2, 3 and 4 in the Gold & Pray (1983) pa- per specify exponential smoothing for all demand variables and are shown below: (2) P = aPn + (1-a)P0 ; where 0