A firm has estimated the following demand function for its product: Q = 100 - 5 P + 5 I + 15 A Where Q is quantity demanded per month in thousands, P is product price, I is an index of consumer income, and A is advertising expenditures per month in thousands

1. A firm has estimated the following demand function for its product:

Q = 100 - 5 P + 5 I + 15 A

Where Q is quantity demanded per month in thousands, P is product price, I is an index of consumer income, and A is advertising expenditures per month in thousands. Assume that P=$200, I=150, and A=30. Use the point formulas to complete the elasticity calculations indicated below.

(i) Calculate quantity demanded.
Q=100-5*200+5*150+15*30=300
Q=300,000 per month

(ii) Calculate the price elasticity for demand. Is demand elastic, inelastic, or unit elastic? (Hint: use equation (3-8), page 100, the price elasticity is
(-5)(200/300)= -3.33. The demand is elastic.
dQ/dP=-5
Price elasticity = dQ/dP*P/Q = -5*200/300=-3.33
Since absolute value of elasticity is >1.0, the demand is elastic.

(iii) Calculate the income elasticity of demand. Is the good normal or inferior? Is it a necessity or a luxury?
dQ/dI=15
Income elasticity = dQ/dI*I/Q = 15*150/300=7.5
Since the income elasticity is positive i.e. demand increases when income increases and decreases when income decreases, it is a normal good. The elasticity is greater than 1, so it is a luxury good.

2. A firm has kept track of the quantity demanded of its output, Good X, during three time periods. The price of X and the price of the other good, Good Y, were also recorded for each time period. The information is provided in the table that follows. Use it to calculate the own-price arc elasticity of demand and the cross-price elasticity of demand. Determine whether Good Y is a complement or a substitute for Good X.

Time Period 1 2 3
Quantity of X 220 80 250
Price of X 15 25 15
Price of Y 10 10 5
Own price elasticity of demand of X= % change in quantity of X / % change in price X
=(80-220)/(80+220)*(25+15)/(25-15)
=-1.86

Cross price elasticity of demand of X for Y= % change in quantity of X/ % change in price of Y
=(220-250)/(250+220)*(5+10)/(10-5)
=-0.19
Since the cross price elasticity is negative i.e. demand of X increase when price of Y decreases, the two products are complementary products.

3.. Just The Fax, Inc. (JTF) has hired you as a consultant to analyze the demand for its line of telecommunications devices in 35 different market areas. The available data set includes observations on the number of thousands of units sold by JTF per month (QX), the price per unit charged by JTF (PX), the average unit price of competing brands (PZ), monthly advertising expenditures by JTF (A), and average gross sales (in $1,000) of businesses in the market area (I). The results of a regression analysis (with standard errors in parenthesis) are given below.

Q X = 300 - 6 PX + 2 PZ + 0.04 A + 0.01 I
(200) (1.8) (0.8) (0.03) (0.004)

R2 = 0.91 S.E.E. = 3.6

Evaluate the statistical significance of each of its coefficients. (Hint: the t ratio for Px is -3.33 (=-6/1.8), and significant)
Assume significance level = 5%
The critical value of t is 1.85
t value for PZ=2/0.8=2.5 >1.85, hence PZ is significant.
t value for A=0.04/0.03=1.33 <1.85, hence A is not statistically significant.
t value for I=0.01/0.004=2.5 >1.85, hence I is significant.