Question

The estimated market demand for good X is

Q=8,000-25P-0.12M-30Pg

where is the estimated number of units of good X demanded, P is the price of the good, M is income, and is the price of related good G. (All parameter estimates are statistically significant at the 1 percent level of significance.)

a.         Good X is a(n) ______________ good and goods X and G are _________________.

b.         At P = $12, M = $30,000, and = $50, the predicted quantity demanded is _________ units of good X.

c.         At the values in part b, calculate estimates of the following elasticities:

(1)        Price elasticity: E = _________.

(2)        Cross-price elasticity: Exg = __________.

(3)        Income elasticity: Em = __________.

Answer 1

The estimated market demand for good X is

Q=8,000-25P-0.12M-30Pg

where is the estimated number of units of good X demanded, P is the price of the good, M is income, and is the price of related good G. (All parameter estimates are statistically significant at the 1 percent level of significance.)

Answer A:- Good X is an inferior or griffin good as with the increase in income, the demand of the product is decreasing. This is reflected as the part of the equation containing the income i.e. -0.12M- has a negative value indicating the negative income effect.

Gods X and G both are complementary goods as with the increase of G goods, the demand of product X decreases.

Answer B:-        At P = $12, M = $30,000, and = $50, the predicted quantity demanded is _________ units of good X.

Q=8,000-25P-0.12M-30Pg

Putting P = $12, M = $30,000, and Pg = $50, in above equation:-

Q=8000-25*12-0.12*30000-30*50

Quantity demanded Q=2600

Answer:- Price Elasticity of Z with respect to Y = (dZ / dY)*(Y/Z)

Price elasticity of X =(d/dp)( 8,000-25P-0.12M-30Pg) *(P/Q)

(d/dp)( 8,000-25P-0.12M-30Pg)=-25

Price elasticity of X =(-25)*12/(8000-25*12-0.12*30000-30*50 )= -0.12

Cross-price elasticity=(d/dPg)( 8,000-25P-0.12M-30Pg) *(P/Q)

(d/dPg)( 8,000-25P-0.12M-30Pg)=-30

Cross-price elasticity=-30*50/2600=-0.58