A multiplicative demand function of the form: Qd = a*P^b1*Y^b2*Po^b3 is estimated using cross-sectional data and 224 observations. The regression results were as follows:
Constant (a) Price(P) Income(Y) Price of other good (Po)
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?
b. What is the quantity demanded if price is $10, income is $9000, and price of the other good is $15?
c. Is demand elastic or inelastic? How can you tell? What impact would a price increase have on total revenue and on total profit?
d. How are these two goods related? Should the firm be concerned about a change in the price of the other good?
e. Is this product a luxury, necessity, or inferior good?
a. In case of multiplicative demand function, coefficients represent the percent change in demand due to 1% change in value of independent variable.
In the given model, the coefficient of P is -0.2243. Negative value of coefficient indicates that price and quantity demanded have inverse relationship. It means that, keeping the other factors unchanged, a 1% increase in price would cause 0.2243% decrease in quantity demanded and 1% fall in price would cause 0.2243% increase in quantity demanded .
In the given model, the coefficient of Y is 1.3458. The positive value of the coefficient indicates that income and demand have a direct relationship. It means that, keeping the other factors unchanged, a 1% increase in income would cause a 1.3458% increase in demand and a 1% fall in income would cause a 0.2243% fall in demand.
In the given model, the coefficient of Po is 0.1304. A positive ...
Solution analyzes the given regression results. It discusses about the price elasticity of demand, relationship between the two goods in consideration and nature of given good based upon the information provided.