DEMAND AND SUPPLY ESTIMATION

Demand and Supply Estimation


Imagine that you work for the maker of a leading brand of low-calorie, frozen microwavable food that estimates the following demand equation for their product using data from 26 supermarkets around the country for the month of April.

Option 1:


Note: The following is a regression equation. Standard errors are in parenthesis for the demand of widgets.

QD= - 5200 - 42P + 20Px + 5.2I + 0.20A + 0.25M

(2.002) (17.5) (6.2) (2.5) (0.09) (0.21)

R2= 0.55, N = 26 F= 4.88

Your supervisor has asked you to compute the elasticity for each independent variable. Assume the following values for the independent variables:



Q D = Quantity demanded

P (in cents) per case = Price of the product = 500 cents

PX (in cents) = Price of leading competitor’s product = 600 cents

I (in dollars) = Per capita income of the standard metropolitan statistical area (SMSA) where the supermarkets are located = 5500

A (in dollars) = Monthly advertising expenditures = $10,000



1. Compute the elasticity for each independent variable. Note: Write down all of your calculations.

When P= 500, C=600, I=5,500, A=10,000, and M=5000, using the regression equation,

QD= - 5200 – 42(500) + 20(600) + 5.2(5500) + 0.20(10000) + 0.25(5000)= 17,650

Price Elasticity = (P/Q) (∆Q/∆P)

From the regression equation, ∆Q/∆P = -42.

So, Price Elasticity (Ep) = (P/Q) (-42) (500/17650) = -1.19, Likewise,

Ec = 20(600/17560) = 0.68



EA= (P/Q) (0.20) (10000/17650) = 0.11

EI = (P/Q) (5.2) (5500/17650) = 1.62

EM = (P/Q) (0.25) (5000/17650) = 0.07



2. Determine the implications for each of the computed elasticity for the business in terms of short-term and long-term pricing strategies. Provide a rationale in which you cite your results.



Price Elasticity is – 1.19. That is a 1% increase in price of the product will make quantity demanded to drop by 1.19%. Thus, the demand for this product is somewhat elastic. Consequently, increase in income may drive consumers away.



Cross- price elasticity is 0.68 that is if the price of the competitor’s product goes up by 1%, then quantity demanded of this product with increase by 0.68%. This product is fairly inelastic to a competitor’s price and there exists no need to be concerned about the competitor since their pricing won’t affect sales.



Income-elasticity is 1.62. This indicates that a 1% rise in the average area income will boost the quantity demanded by 1.62%. In this aspect, the product is elastic and the company can make the decision to raise the price if the average income rises.



Advertisement-elasticity is 0.11, which means that A 1% increase in advertising expense will raise the quantity demanded by 0.11%. Therefore, demand is rather inelastic to advertising. For that reason, more advertisement doesn’t automatically means a company can raise the price because that still could drive consumers away.



With respect to microwave ovens in the area, elasticity is 0.07, which shows an elevation of 1% in the number of ovens in the area increasing the quantity demanded by a mere 0.07%. Therefore, in this aspect, demand is inelastic and the pricing strategy can simply skip this element.



3. Recommend whether you believe that this firm should or should not cut its price to increase its market share. Provide support for your recommendation.



Since the price elasticity is greater than one in absolute value, a decrease in price will lead to an even greater increase in quantity demanded (in % terms), leading to an increase in market shares. Yes, cutting the price will lead to an increase in the company share as the PED is bigger than (1.19).



4. Assume that all the factors affecting demand in this model remain the same, but that the price has changed. Further assume that the price changes are 100, 200, 300, 400, 500, 600 cents.

i) Plot the demand curve for the firm.

ii) Plot the corresponding supply curve on the same graph using the supply function Q = 5200 + 45P (Q= -7909.89+79.0989P) with the same prices.

iii) Determine the equilibrium price and quantity

iv) Outline the significant factors that could cause changes in supply and demand for the product. Determine the primary manner in which both the short-term and the long-term changes in market conditions could impact the demand for, and the supply, of the product.





Solutions:

With all others factors remaining constants, the demand equation is as follows:

Q = -5200 - 42(P) + 20(600) +5.2(5500) +0.2(10,000) +0.25(5000)

Q = 38,650 – 42P

P = 38,650/42-Q/42

Q = 5200 =45P

P = - 5200/45 + Q/45

Thus, solving the demand and supply curves concurrently,

38,650 - 42P = 5200 + 45P

87P = 33,450

P = 384.48 AND

Q = 5200 + 45(384.48)

Q = 22,501.6



Therefore, the equilibrium price is 384 cents and the equilibrium quantity is 22,501 units. Additionally, the equilibrium price and the quantity can be seen on the graph indicated at the point where the supply and demand meet or intercept.

As is pointed out in the demand equation, demand of the low-calorie food can change if there is a change in consumer income, the pricing of a competitor product, and the price of correlating goods (microwave ovens). This change can also happen as the result of change in consumer preference (e.g. consciousness towards low-calorie food). Supply of the product can change if there is a change in the number of product suppliers, production technological advances in additional to the other elements like labor and raw materials availability change, which directly affect production costs.



5. Indicate the crucial factors that could cause rightward shifts and leftward shifts of the demand and supply curves.



An increase in consumer income, a price cut in the price of complementary product (e.g. microwave ovens) could cause a right ward shift of demand curve for the product; as well

as a population increase or increased preference for the product (e.g. awareness towards low-calorie food). A decrease in consumer income or a recession (like the U.S have been experiencing) can cause a left ward shift of the demand curve; additionally, an increase in a price of a complementary product (microwave ovens etc) could cause a leftward shift of the demand curve.



Technology advances in food processing, increased availability of cheap labor and raw materials, increased tax-cuts and government subsidies (among other things) can cause a right-ward shift of supply curve. A leftward shift can be caused by a decrease in availability or an increase in price of labor and raw materials, increased taxes, etc.