A multiplicative demand function of the form: Qd = aPb1Yb2Pob3 is estimated usin

Question

A 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(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? 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

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