Question

Option 1

Note: The following is a regression equation. Standard errors are in parentheses for the demand for 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 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 = 500 cents per 3-pack unit
PX (in cents)     =          Price of leading competitor’s product = 600 cents per 3-pack unit
I (in dollars)       =          Per capita income of the standard metropolitan statistical area
(SMSA) in which the supermarkets are located = $5,500
A (in dollars)     =          Monthly advertising expenditures = $10,000
M                     =          Number of microwave ovens sold in the SMSA in which the
supermarkets are located = 5,000

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

Answer 1

Elasticities of independent variables are computed as follows.

Plugging in all values,

QD = - 5,200 - (42 x 500) + (20 x 600) + (5.2 x 5,500) + (0.2 x 10,000) + (0.25 x 5,000)

QD = - 5,200 - 21,000 + 12,000 + 28,600 + 2,000 + 1,250

QD = 17,650

(a) Own price elasticity = (QD/P) x (P/QD) = - 42 x (500/17,650) = - 1.19

(b) Cross price elasticity = (QD/PX) x (PX/QD) = 20 x (600/17,650) = 0.68

(c) Income elasticity = (QD/Y) x (Y/QD) = 5.2 x (5,500/17,650) = 1.59

(d) Advertising elasticity = (QD/A) x (A/QD) = 0.2 x (10,000/17,650) = 0.11

(e) Elasticity with respect to M = (QD/M) x (M/QD) = 0.25 x (5,000/17,650) = 0.07