Question

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

Option 2
Note: 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

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

Q          =          Quantity demanded of 3-pack units
P (in cents)       =          Price of the product = 200 cents per 3-pack unit
PX (in cents)     =          Price of leading competitor’s product = 300 cents per 3-pack unit
I (in dollars)       =          Per capita income of the standard metropolitan statistical area
(SMSA) in which the supermarkets are located = $5,000
A (in dollars)     =          Monthly advertising expenditures = $640

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

Answer 1

We have the equation for demand

QD = -2,000 - 100P + 15A + 25PX + 10I

Here, we have

Q = Quantity demanded of 3-pack units
P (in cents)       =          Price of the product (This value is currently 200 cents per 3-pack unit)
PX (in cents)     =          Price of leading competitor’s product (This value is currently 300 cents per 3-pack unit)
I (in dollars)       =          Per capita income (This value is currently $5,000)
A (in dollars)     =          Monthly advertising expenditures (This value is currently $640)

Using the current values, we find that demand is

Q = -2,000 – 100P + 15A + 25PX + 10I

Q = -2000-100*2 + 15*640 + 25*3 + 10*5000 = 57475

Now we have four elasticities to compute in this case.

Price elasticity of demand: This measures the effect of change in price of own good which is P on the quantity demanded of the product. Hence, elasticity is given by ed = coefficient of P in demand function x (current P/Current Q)

ed = -100*2/57475 = -0.003

Income elasticity of demand: This measures the effect of change in income of the consumer on the quantity demanded of the product. It is given by em = coefficient of I in demand function x (current I/current Q)

em = 10*5000/57475 = 0.870

Cross price elasticity of demand. This measures the effect of change in the price of rival good on the quantity demanded of the product. This is given by ec = coefficient of PX in demand function x (current PX/current Q)

ec = 25*3/57475 = 0.001

Advertising elasticity of demand. It measures the effect of the change in the advertising expenditure on the quantity demanded. This is given by eA = coefficient of A in demand function x (current A/current Q)

eA = 15*640/57475 = 0.167