1. multiplicative demand function of the form: Qd = aPb1Yb2Pob3 is estimated usi
ID: 1098923 • Letter: 1
Question
1. multiplicative demand function of the form: Qd = aPb1Yb2Pob3 is estimated using cross-sectional data and 224 observations. The regression results were as follows: Constant (a) Price Income Price of other good (Po) (P) (Y) Coefficient 0.02248 -0.2243 1.3458 0.1034 Standard Error 0.01885 0.0563 0.5012 0.8145
A. How should the coefficients be interpreted in this equation? Explain.
B. What is the quantity demanded if price is $10, income is $9000, and price of the other good is $15? Show your calculations.
C. Is demand elastic or inelastic? How can you tell? What impact would a price increase have on total revenue? on total profit? Explain.
D. How are these two goods related? Should the firm be concerned about a change in the price of the other good? Explain.
E. Is this product a luxury, necessity, or inferior good? Explain.
Explanation / Answer
a) t value of coefficients = coefficient value / standard error
t value
constant = 0.02248 / 0.01885 = 1.1925
price = -0.2243 / 0.0563 = 3.984
income = 1.3458 / 0.5012 = 2.685
price of other goods = 0.1034 / 0.8145 = 0.126
t value from table at 95 % confidence level is 2
since peice and income have values greater than 2 so they are significant others are not significant
Q = 0.02248 - 0.2243 * Price + 1.3458 * income + 0.1034 * price of other good
putting the values in the eq we get
Q = 12111.53
elasticity = (dQ/dp) * (P/Q) = ( -0.2243 ) * ( 10 / 12111.53) = 0 ( approx)
so it is elastic
it will decrease
D) because it is statically insignificant so firm should not worry about prices of other goods
E) necessay because elsticity is close to zero