Introduction
The managerial team of a firm has the important task of taking policy decision for the firm in the present and make planning for the future. The managers have be well informed about the market trends. All the information about demand, market structure, strategies taken by the competitors as well as production related information technological innovations, the firm’s own production technique help the managers to decide upon the profit maximizing level of output and price. The policies adopted by the government also affect the firms and the firm has to adjust its operations accordingly. The firm also has to decide on the sales promotion techniques to be adopted depending on the degree of competition existing in the market and consumer’s choice and preferences.
Estimation of Demand
We can well understand how important it is for the managerial team to collect information and analyze to frame the best strategies that increase the firms market share and profit. In this analysis we present a simple case where a firm utilizes the result of a market survey on the demand for its goods, to frame its pricing and supply strategies. The firm that we are considering here produces and markets low-calories frozen food. We have the result of a market survey conducted at 26 supermarkets. The survey has been presented in two regression equations. Our first step would b to decide which regression result we are going to use in our study. The two results are presented below as option 1 and option 2.
Option 1Note: The following is a regression equation. Standard errors are in parentheses for the demand for widgets.QD = - 5200 - 42P + 20PX + 5.2I + .20A + .25M(2.002) (17.5) (6.2) (2.5) (0.09) (0.21)R2 = 0.55 n = 26 F = 4.88
Q = Quantity demanded of 3-pack unitsP (in cents) = Price of the product = 500 cents per 3-pack unitPX (in cents) = Price of leading competitor’s product = 600 cents per 3-pack unitI (in dollars) = Per capita income of the standard metropolitan statistical area(SMSA) in which the supermarkets are located = $5,500A (in dollars) = Monthly advertising expenditures = $10,000M = Number of microwave ovens sold in the SMSA in which thesupermarkets are located = 5,000
Option 2Note: The following is a regression equation. Standard errors are in parentheses for the demand for widgets.
QD = -2,000 - 100P + 15A + 25PX + 10I(5,234) (2.29) (525) (1.75) (1.5)R2 = 0.85 n = 120 F = 35.25
Q = Quantity demanded of 3-pack unitsP (in cents) = Price of the product = 200 cents per 3-pack unitPX (in cents) = Price of leading competitor’s product = 300 cents per 3-pack unitI (in dollars) = Per capita income of the standard metropolitan statistical area(SMSA) in which the supermarkets are located = $5,000A (in dollars) = Monthly advertising expenditures = $640
For option 1 we find that the value of R2 is 0.55 but for option 2 this value is 0.85. So option 1 has 55% predictability while the regression equation in option 2 has 85% predictability . Now let us compare the F values. We see that the F value for Option 1 is 4.88 while the F value for option 2 is 35.25. Thus the coefficients have greater significance for option 2 . Finally, we see that option 1 has only 26 observations while option 2 has 120 observations. So we conclude that regression equation in option 2 is more reliable in predicting demand existing in the market.
Computation of elasticities
Let us find the elasticity of demand with respect to each independent variable given in the regression equation. Substituting the values of the independent variables in the equation we get the demand for the good .
QD = -2000 -100*200 + 15*640 + 25*300 + 10*5000 = 45100
Elasticity of demand with respect to Price
Ep = dq/dp*p/q = -100*200/45100 = 0.44
Elasticity of demand with respect to Advertisement expenditure
Ea = dq/dA*A/q = 15*640/45100 = 0.21
Elasticity of demand with respect to Price of the close substitute
Epx = dq/dPX*PX/q = 25*300/45100 = 0.17
Elasticity of demand with respect to Income of the consumers
EY = dq/dY*Y/q = 10*5000/45100 = 1.11
Interpretation of Elasticities
We have obtained the elasticity of demand with respect to the four independent variables. Now we are going to present the interpretation of the values of the elasticities. We can see that the price elasticity of demand is 0.44 which is less than one. That is the demand for the good is price inelastic. The change in price affects the demand to a small extent.
The elasticity with respect to advertisement expenditure –which is 0.21 is quite low indicating little or no effect of advertisement expenditure on the demand for the good. Either advertisements are mis-targeted or the consumers rely more on the inherent qualities of the food item produced by the firm. The firm should not spend much on advertisements as that will have little impact on the firm’s earnings.
The elasticity with respect to the competitor’s price is 0.17. This low value implies that the price charged by the close competitor has little effect on the demand for the good of our firm. The low-calorie frozen food seems to possess some distinct characteristics that attracts the consumers irrespective of its own price and the price of the closest substitute.
Finally, we can see that the good is income elastic. This is suggested by the value of the income elasticity 1.11 which is greater than 1. As the income level rises the demand increases.
The Issue of Price Cut
We have already discussed the implications of the inelastic demand for the good. Now let us analyze how this inelasticity helps in deciding on the pricing policy. With an inelastic demand a price cut will lead to a fall in the revenue for the firm as the demand will not rise to any significant extent owing to the cut. So the market share cannot be increase by reducing the price of the product. So price undercutting is not a prudent strategy to be followed by the firm in this situation.
Derivation of the Equilibrium Price and Quantity
In this step we are going to find the equilibrium price and quantity. For this we need to plot the demand and the supply curve. Let us first derive the demand function from the regression equation and the values of the variables provided to us.
QD = -2000 -100P+ 15*640 + 25*300 + 10*5000 = 65100-100P
The demand can be expressed as a function if price as follows:
QD = 65100 -100P
We can find the demand for the good at different prices 100, 200, 300, 400, 500 and 600 cents. Plotting the quantity demanded for each prices we get the demand curve as shown below:
Now let us turn to the supply function. The supply function provided to us is:
Q = -7909.89 + 79.0989P
We put the same values of prices, that is, 100, 200, 300, 400, 500 and 600 cents, as we have done for the demand function in the above supply function to obtain the supply curve shown below:
The intersection of the demand and the supply curve gives us the equilibrium price and quantity. This is shown in the figure below:
The diagram shows that the equilibrium price is close to $400. The equilibrium quantity is above 20000 and below 30000. We can derive the equilibrium mathematically as well by equating the demand and supply functions as shown below:
65100 -100P = -7909.89 + 79.0989P
Price =$ 407.65
Quantity = 24335 units
The mathematical result confirms the result obtained graphically. We can see that the equilibrium price is $407.65 which we can find in the graph. The equilibrium quantity is 24335 units which lies between 200000 and 30000 as shown in the graph.
Conclusion
The regression equation has included four independent variables. Except the price of the product, the increase in the other three variables, income, advertisement expenditure and price of the substitute lead to a rightward shift in the demand curve. Similarly a fall in these variables will lead to a leftward shift in the demand curve. A change in the price will produce a movement along the demand curve. Apart from these three there are other factors that can lead to a shift in the demand curve. Increase in health awareness will increase the demand for the product as it is low-calorie food product. A faster lifestyle will necessitate a higher consumption of this product as it requires little cooking time. But a shift in preference towards fresh food or a doubt into the nutritional quality of frozen food will lead to leftward shift in the demand curve.
The shift in the supply curve depends on the price and supply of raw materials. This is a frozen food item so it requires agricultural raw materials. Rise in price of such raw materials will shift the supply curve leftwards and vice-versa. Preparation of food items involves labor intensive technique. So the wage rate will have a bearing on the supply of the product. Increase in wage rate will lead to increase in cost thereby shifting the supply curve leftwards. Fall in the wage rate will lead to a rightward shift in the supply curve indicating increase in supply.
References
Henderson, J. M., & Quandt, R. E. (1980). Microeconomic Theory: A Mathematical Approach. McGraw Hill.
Koutsoyiannis, A. (2003). Microeconomics. Pulgrave Macmillan.
Maddala, G. S., & Lahiri, K. (2009). Introduction to Econometrics. Wiley.
Pindyck, R., & Rubinfield, D. (2009). Microeconomics (7th ed.). Prentice Hall.
Woolridge, J. M. (2009). Econometrics. Cengage Learning.
