where Qx = quantity demanded of commodity X; Px = unit price of commodity X; Y = consumer’s income; Ps = price of substitute good; A = advertisement expenditure; α is a constant (or the demand intercept), and b, c, d, and j are the parameters (or regression coefficients) expressing the relationship between demand and Px, Y, Ps, and A, respectively.
In linear demand functions, quantity demanded is assumed to change with changes in independent variables at a constant rate. The parameters are estimated by using the least- squares method. Having estimated the parameters, the demand can be easily forecast if data on the independent variables for the reference period are available.
2. The Power Function. In the linear functions of demand, the marginal effects on demand of independent variables are assumed to be constant and independent of changes in other variables. It is assumed, for instance, that the marginal effect of a change in own price is independent of change in income or other independent variables. There may, however, be cases in which it is intuitively or theoretically found that the marginal effect of the independent variables on demand is neither constant nor independent of the values of all other variables included in the demand function. For example, the effect of an increase in the price of sugar on demand may be neutralised by a rise in consumer’s income. In such cases, a multiplicative or ‘power’ form of the demand function, considered to be the most logical form, is used for estimating the demand of a commodity. The power form of the demand function is given by:
Qx = αP x bYcP s dAj (3.1.8)
The algebraic form of multiplicative demand function can be transformed into a log- linear form for simplicity in estimation as follows:
Log Qx = log α – b log Px + c log Y + d log Ps + j log A (3.1.9)
This can be estimated using the least-squares regression technique. The estimated function can easily be used in forecasting the future demand for the given commodity.
The first step is to develop a complete model and specify the behavioural assumptions regarding the variables included in the model. The variables included in the model are referred to as (i) endogenous variables, and (ii) exogenous variables.
The endogenous variables are variables whose values are determined within the model.
Endogenous variables are included in the model as dependent variables or variables to be explained by the model. These variables are often referred to in econometrics as
‘controlled’ variables. Note that the number of equations in the model must equal the number of endogenous variables.
Exogenous variables are those whose values are determined outside the model. They are referred to as inputs of the model. The purpose of a given model will determine whether a variable is endogenous or exogenous. Exogenous variables are also looked at as
‘uncontrolled variables.
The second step is to collect the necessary data on both endogenous and exogenous variables. If you find that data is not available, they can be generated from available primary or secondary sources.
Having developed the model, and the necessary data collected, the third step is to
estimate the model using the appropriate method, and the two-stage least-squares method to predict the values of the exogenous variables.
Finally, the model is solved for each endogenous variable in terms of exogenous variables. By plugging the values of exogenous variables into the equations, the objective value can be calculated and prediction made.
The simultaneous equation method is theoretically superior to the simple regression method. The main advantage of the method is that it is capable of capturing the influence of dependency of the variables. The major limitation is non-availability of adequate data.
The following example illustrates the simultaneous equation method. A simple macroeconomic model is given below:
Yt = Ct + It + Gt + Xt (3.1.10)
where,
Yt = Gross National Product (GNP) Ct = Total consumption expenditure It = Gross Private Investment
Gt = Government expenditure
Xt = Net Export (X – M), where X represents Export, and M, Import.
Subscript t represents a given time unit.
Equation (3.3.20) is an identity that can be explained with a system of simultaneous equations, such as:
Ct = a + bYt (3.1.11)
It = 20 (3.1.12)
Gt = 10 (3.1.13)
Xt = 5 (3.1.14)
In the above system of equations, Yt and Ct are the endogenous variables, and It, Gt, and Xt, are exogenous variables. Equation (3.1.11) is a regression equation that needs to be estimated. Equations (3.1.12) to (3.1.1) show the values of exogenous variables
determined outside the model.
Suppose you want to predict the values of Yt and Ct simultaneously, and that when you estimated equation (3.1.11) you get:
Ct = 100 + 0.75Yt (3.1.15)
Using this equation, the value of Yt can be determined as:
Yt = Ct + It + Gt + Xt
= 100 + 0.75Yt + 20 + 10 + 5 = 0.75Yt + 135 Yt – 0.75Yt = 135
0.25Yt = 135
Yt = 135/0.25 = 540.
Using this value of Yt, you can evaluate the value of Ct as follows:
Ct = 100 + 0.75Yt
= 100 + 0.75(540) = 100 + 405 = 505.
It follows that the predicted values will be:
Yt = 540 Ct = 505
Yt = 505 + 20 +10 + 5 = 540.
Note that the above example of econometric model is an extremely simplified model. In actual practice, the econometric models are generally very complex.
3.2 Self-Assessment Exercise
Discuss the necessary steps in the application of the simultaneous equation method of forecasting
4.0 Conclusion
You must have learned some useful forecasting techniques from this unit. You also learned that the term demand forecasting simply means predicting the future demand for a product. Information regarding future demand is essential for scheduling and planning production, acquisition of raw materials, acquisition of finance, and advertising.
Forecasting is most useful where large-scale production is involved and production requires long gestation period.
5.0 Summary
Among the numerous techniques employed in demand forecasting, the most important of them are the Survey and Statistical techniques. The survey techniques are used where the purpose is to make short-run demand forecasts. This technique uses consumer surveys to collect information about their intentions and future purchase plans. It involves:
(i) survey of potential consumers to elicit information on their intentions and plans; and, (ii) opinion polling of experts, that is, opinion survey of market experts and sales
representatives.
The statistical techniques use historical (or time-series), and cross-section data for estimating long-term demand for a product. The techniques are found more reliable than those of the survey techniques. They include: (i) the Trend Projection techniques; (ii) the Barometric techniques; and, (iii) the Econometric techniques. Our discussions, however, concentrated on the Econometric techniques as these are more superior and reliable than the Trend Projection and Barometric techniques.
6.0 Tutor-Marked Assignment
An Economic Research Centre has published data on the Gross Domestic Product (GDP) and the Demand for refrigerators as presented below:
Year: 2000 2001 2002 2003 2004 2005 2006 GDP
(N’ billions):
Refrigerators
20 22 25 27 30 33 35
(millions): 5 6 8 8 9 10 12
(a) Estimate the regression equation, R = a + bY
where R = refrigerators (in millions), and Y = GDP (in N’billions)
(b) Forecast the demand for refrigerators for the years 2007, 2008, and 2009, if the Research Centre projected the GDP for 2007, 2008, and 2009 to be N40 billion, N52 billion, and N65 billion, respectively
7.0 References
1. Dwivedi, D. N. (2002) Managerial Economics, sixth edition (New Delhi: Vikas Publishing House Ltd).
2. Haessuler, E. F. and Paul, R. S. (1976), Introductory Mathematical Analysis for Students of Business and Economics, 2nd edition (Reston Virginia: Reston Publishing Company)
UNIT 13: THE THEORY OF PRODUCTION