Economics and business studies provide a wealth of empirical data. From the study of how markets, competitors and prices behave, a number of generally accepted models have emerged. These models are similar to the laws of natural science and provide a useful toolbox for the forecaster. Market behaviour models fall into the category of qualitative forecast methods. They also share similarities with time series and causal models, because they explain what happens over time and how different factors are related. For example, price elasticity is an observation that describes how demand reacts to price, and it may be possible to determine the price elasticity coefficient using regression analysis.
The product life cycle
It has been observed that markets for products grow in an s-shaped manner and
eventually decline to be replaced by new products. The product and industry life cycle and its use in strategic analysis are discussed in Chapters 7 and 8. For the purposes of market forecasting, the product life cycle is best analysed in five phases:
Introduction phase. Sales volumes are low and increase in a near linear fashion.
There are few competitors, the product may suffer from quality problems and there is little variety between different versions of the product. Unit costs and prices are high.
Accelerating growth phase. Buyer groups widen and sales increase rapidly. More suppliers enter the market and prices start to fall. A greater variety of product forms start to appear.
Decelerating growth phase. Penetration is still increasing, but at a declining rate. Prices are falling more quickly and become a significant issue. Variety increases further and there is an increased focus on product quality. Late adopters buy the product.
Maturity. Penetration is no longer increasing. There may be consolidation. Prices are declining further, but at a slower rate.
Declining phase. Prices are low, but no longer declining. Some competitors may exit the market.
Chart 12.12 Forecast using Pearl’s equation logistic curve
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 0 200 400 600 800 1,000 1,200 1,400 1,600 1,800
Installed base
Actual
Model
These observations provide inputs with regard to forecasting sales volumes, prices and market share: the essential elements of the demand forecast. This is extremely useful, because it means that by using an s-curve to forecast penetration, it is possible to forecast price. It may be argued that lower prices increase demand. Therefore you have to forecast price to establish demand. However, prices relate in some ways to costs, and costs are a function of volumes (see the experience effect below). Although in specific cases cause and effect can be clearly identified, medium- to long-term forecasts are subject to many
influences in a complex system. The product life cycle model encapsulates these effects and is therefore an appropriate model for medium- to long-term demand forecasts.
Diffusion of innovation
Everett Rogers1and Frank Bass2proposed models that describe how a new product or service is adopted by a population. Because of its better predictive power, the Bass model is commonly used. It is based on the observation that there are some innovators who adopt products early and imitators who adopt the products as a result of having seen other people using them. The Bass curve can be written as follows:
nt=nt–1+p (m – nt–1) +q (nt-1÷ m) (m – nt–1) Where:
nt = the number of users in year t
m = the maximum penetration or market potential, which is the total number of people who will eventually use the product or service
p = the coefficient of external influence or coefficient of innovation, which is the probability that an individual will start using the product or service because of advertising or other external factors
q = the coefficient of internal influence or imitation, which is the probability that individuals buy the product because of word-of-mouth or other influences from those who already have the product
Chart 12.13 The product life cycle curve
Introduction Accelerating growth phase Decelerating growth phase Maturity Decline
Time
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0 10 20 30 40 50 60 70 80 90 100
%
Market behaviour models 125
Estimates for p and q can be obtained by looking at similar products or through market research. An estimate for m, the maximum potential penetration, can also be obtained through market research. The Bass model explains well how innovation diffuses, but because of uncertainty in establishing the values for p and q, it does not solve the forecasting problem. Academic arguments aside, the Bass model is another useful way of producing and using an s-curve.
The experience curve
At the heart of the experience curve is the observation that unit costs decline in a predictable manner as the total quantity produced over time increases. Research carried out by the Boston Consulting Group showed that each time cumulative production volume doubled, unit costs declined by 20–30%. The experience curve can be written as follows:
Cn=C1× V–E Where:
Cn = price of the nth unit C1 = price of the first unit
V = cumulative production/sales volume
E = the experience effect, which is the % by which costs fall each time cumulative production volume doubles
Chart 12.14 Bass curves
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0 10 20 30 40 50 60 70 80 90 100
% penetration
p = 0.02, q = 0.60 p = 0.04, q = 0.30
years
The experience curve, which forecasts costs, can be used in the context of a demand forecast as an input into the price forecast. Although costs are only one aspect in pricing, it provides an indication of how far and how fast prices may decline. If a penetration forecast is made for a consumer durable product and replacement sales are calculated (see below), the cumulative production volume can be easily calculated.
Price elasticity of demand and other elasticities
Elasticities are a measure of how a change in a variable affects demand. There are many different types of elasticities, such as price elasticity of demand, cross-price elasticity of demand, elasticity to advertising expenditure, income elasticity, and so on. Elasticities occur where causal relationships exist. If elasticities are known and remain constant, forecasting becomes a mathematical exercise (see Regression analysis on page 119).
In practice, elasticities have to be estimated. Furthermore, they are generally not constant.
The law of diminishing returns applies. For example, if prices fall to zero demand would have to be infinite. Clearly this is not the case.
In the context of market forecasting, the most important elasticity is price elasticity of demand. The price elasticity coefficient is the ratio of percentage demand growth of a product to percentage drop in the unit price of the product. In other words, the price elasticity coefficient indicates the proportional effect of a change in price on demand. A price elasticity coefficient of –1 means demand is completely price elastic; that is, a percentage drop in price is offset by an equal percentage increase in demand, so that the market value is constant. 0 means demand is totally price inelastic; that is, it remains the same whatever you do to the price. If the price elasticity is greater than –1, price reductions yield revenue growth. In many cases, price elasticity coefficients are between 0 and –1.
This means as prices fall, revenue falls, but not as fast. The price elasticity of demand formula can be written as follows:
E =((Q2– Q1)÷ ((Q1 +Q2) ÷ 2))÷ ((P2– P1)÷ ((P1 +P2) ÷ 2)) Chart 12.15 Experience curves
1 2 4 8 16 32 64 128 256 512 1024
0 10 20 30 40 50 60 70 80 90 100
Unit cost
Cumulative production volume E = 0.2
E = 0.4
Market behaviour models 127
Where:
E = the price elasticity coefficient Q = the quantity demanded P = the price
Or:
Q2=(Q1× (1 +E× (P2–P1) ÷ (P1+P2))÷ (1 – (E× (P2–P1) ÷ (P1+P2))
Although the price elasticity coefficient may not be known, in any forecast an assumption should be made that a change in prices has some effect on demand. The forecast may simply assume that if prices drop by 10%, revenue will decline by 10%, that is, the quantity demanded remains constant and so the price elasticity coefficient is 0. It is much better to use price elasticity explicitly. Even if the price elasticity coefficient is not an explicit input, it should be calculated as an output.
In some cases, there are difficulties in establishing the quantities demanded. For example, in the case of a mobile phone, the monthly bill consists of the subscription or line rental charge (which may include some minutes of usage), the per minute charge for voice calls and an amount for data services. Different rates may apply for different types of minutes and data services. With a great deal of effort the elasticities for each could be established.
A way around this difficulty is to apply the price elasticity coefficient directly to the monthly bill:
B2=B1×( 1 +(P1– P2) ÷P1×( 1 – E )) Where:
B = the average monthly bill E = the price elasticity coefficient P = the price index
Chart 12.16 Price elasticity of demand
100 104 109 113 118 123 129 134 140 146
0 10 20 30 40 50 60 70 80 90 100
2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000
Unit price Revenue
Quantity Unit price
Revenue E = -0.4
This demonstrates that the general principle of price elasticity of demand and other elasticities can be used imaginatively to develop a forecast that is still based on accepted models of market behaviour.
Using price elasticity as an explanatory variable to forecast demand has limitations. As is apparent from diffusion of innovation theories, demand increases regardless of changes in price. However, a combination of different methods may yield appropriate results. The example below illustrates how the problem of forecasting revenue from mobile internet services can be tackled.
Empirical evidence shows that average monthly bills are decreasing (see Chart 12.17 on the next page). This is used as supporting evidence. On average, later adopters are willing to spend less than earlier adopters are.
Existing mobile phone users react to changes in tariffs in an elastic manner (see Chart 12.18 on the next page). As tariffs decrease, they spend less but also use the handset more. The increase in usage partially offsets the decrease in prices. Price elasticity coefficients can be used to forecast the average monthly bill for existing customers as a function of changes in tariffs.
Market research into how much potential users of mobile internet services are prepared to pay reveals a classic price elasticity of demand curve (see Chart 12.19 on page 131).
Based on market research, an s-shaped penetration curve is used to make a forecast for the penetration of mobile internet services among the population.
An assumption is made that prices for mobile internet services decrease following an s-shaped curve.
The average monthly spend for mobile internet services is calculated in two steps (see Chart 12.20 on page 131). First, the formula from the price elasticity chart is used to
calculate how much marginal users will spend per month, that is, what the monthly bill of marginal customers will be. Second, the average monthly bill is calculated as the sum of the marginal bills, adjusted by how existing users react to price decreases. In the example, a price elasticity coefficient of –0.3 is used in the formula that applies price elasticity directly to the monthly bill.
Market behaviour models 129
Source: Oftel Quarterly Data 1994-97
Chart 12.18 Empirical evidence of price elasticity of demand in the UK telephony market
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0 50 100 150 200 250 300 350 400 450
Average price per minute, £
Originated minutes per month
UK mobile and fixed spend per minute and usage per line 1994–7
Vodafone and Cellnet Orange
One2One BT fixed network
*Excluding long distance and roaming.
Source: CTIA
Chart 12.17 Empirical evidence of declining monthly bill in the US mobile telephony market
y = -26.239Ln(x) + 331.14 R2 = 0.9767
1988 1989
1990
1991 1992
1993 1994
1995 1996 1997
1998 1999
0
0 20 40 60 80 100 120 140 160
Av. monthly bill*, 1999, real terms US$
Subscribers, ’000
10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000
Repeat and replacement sales
In the case of non-durable products or services, the sales volume is a function of how many customers are using the product and how often they make a repeat purchase. For consumer durable products, sales volumes are a function of first-adoption and
replacement sales. In both cases, it is advisable first to forecast the number of first-time users (which can be done based on the diffusion of innovation theory) and second to make an assumption for the frequency of repeat sales. This two-step approach makes the forecasting process easier and also provides a breakdown of sales. In marketing terms, there is a big difference between the number of people using a product and repeat sales.
In the case of consumer durable goods, the annual sales volume is a function of the increase in the installed base, or first-time sales, and replacement sales to those who are
Source: Coleago Consulting Ltd
Chart 12.20 Average monthly bill forecast
1 2 3 4 5 6 7 8 9 10 11
0 5 10 15 20 25 30 35 40 45 50 55
Mobile internet monthly bill, £
Marginal bill
Average bill
Years from launch
Sample: 1,000, UK population 15+, March 2001.
Source: Coleago Consulting Ltd
Chart 12.19 Mobile internet demand survey
Y = -21.768Ln(x) + 2.3762 R2 = 0.9341
Willing to pay for mobile internet access
0 10 20 30 40 50 60 70 80 90 100
0 10 20 30 40 50 60 70 80 90 100
Average price per minute, £
Potential users, %
Market behaviour models 131
already using the product. Replacement sales are a function of product failure,
obsolescence, or upgrades. The average useful life of a product may change over time.
The calculation of replacement sales could be very complex. This is because, for every period, the number of replacement sales is not a function of the installed base, but a function of the number of new sales n years before the current year, where n is the average product life before replacement. Given that n is an estimated average and the precise age distribution of the existing base is normally not known, a simpler approach, such as expressing replacement sales as a percentage of the installed base at the end of the previous period, is just as good.
Combining market behaviour models to make a forecast
As indicated above, an s-shaped product life cycle in combination with the experience effect and a repeat or replacement sales calculation can be used to construct a forecast where all variables are dependent on the product life cycle curve. Chart 12.22 shows a simple sales projection for the total market. The market share assumption has to be added to this in order to calculate the firm’s sales.
The penetration of potential demand is forecast using the formula on page 123. Sales prices have been forecast using the observation of how prices decrease over the product life cycle. The assumption has been made that the decrease is inversely proportional to the rate of market growth. When the market grows fastest, prices are also falling rapidly.
Chart 12.21 Replacement sales forecast for a consumer durable
1 2 3 4 5 6 7 8 9 10 11 12 13
0 500 1,000 1,500 2,000 2,500
0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000
Annual sales Installed base
Replacements New installations
Installed base
Chart 12.23 Installed base, unit sales, costs, prices
1 2 3 4 5 6 7 8 9 10 11
0 100 200 300 400 500 600 700
0 200 400 600 800 1,000 1,200
Unit cost/prices Installed base/sales volume
Average unit cost
Sales price Installed base
Total unit sales
Chart 12.22 Marketing forecast model
Product life cycle model inputs Maximum potential penetration 10%
Years to maturity 10
PLC curve skew value a 99 Product launched in year 1
Experience factor 0.4
Cost of first unit 1,000 Sales price in year 1 600
Margin in year 10 60%
Replacement % 40%
Year 1 2 3 4 5 6 7 8 9 10 11
Population 10,000 10,030 10,060 10,090 10,121 10,151 10,181 10,212 10,243 10,273 10,304 Potential installed base ‘000 1,000 1,003 1,006 1,009 1,012 1,015 1,018 1,021 1,024 1,027 1,030
Value b 0.988842
Penetration of potential 1% 3% 7% 16% 35% 59% 79% 91% 96% 99% 100%
Years product on market 0 1 2 3 4 5 6 7 8 9 10
Installed base 10 27 68 166 349 595 807 930 988 1,014 1,025
New sales 10 17 42 97 184 246 211 124 58 25 12
Replacements 0 2 19 47 103 189 280 347 384 400 408
Total unit sales 10 19 61 144 287 435 492 471 442 426 419
Cumulative sales 10 29 89 233 520 955 1,447 1,918 2,360 2,785 3,205
Average unit cost 525 306 196 131 93 71 59 51 47 43 41
Sales price 600 587 566 518 428 308 205 146 119 108 102
Margin 12% 48% 65% 75% 78% 77% 71% 65% 61% 60% 60%
Implied price elasticity -26.9 -29.7 -9.2 -3.5 -1.3 -0.3 0.1 0.3 0.4 0.2
Market value 6,000 10,865 34,481 74,557 122,800 133,811 100,922 68,814 52,644 46,124 42,659 Costs 5,253 5,671 11,924 18,829 26,754 30,980 28,830 24,148 20,564 18,405 17,064 Profits 747 5,194 22,556 55,728 96,046 102,831 72,092 44,665 32,080 27,719 25,596
Market behaviour models 133