Question

After a careful statistical analysis, the Chidester Company concludes the

demand function for its product is Q = 500 - 3P + 2Pr + 0.1/

where Q is the quantity demanded of its product, P is the price of its product,

P, is the price of its rival’s product, and I is per capita disposable income (in

dollars). At present, P = $10, Pr = $20 and I = $6,000.

a. What is the price elasticity of demand for the firm’s product?

b. What is the income elasticity of demand for the firm’s product?

c. What is the cross-price elasticity of demand between its product and its

rival’s product?

d. What is the implicit assumption regarding the population in the market?

Answer 1

The Chidester Company concludes the demand function for its product;

Q = 500 - 3P + 2Pr + 0.1I

where Q = quantity demanded of its product
P = price of its product,
Pr = the price of its rival’s product
I = per capita disposable income

Given;

P = $10
Pr = $20
I = $6,000

Q = 500 - 3(10) + 2(20) + 0.1(6000)
= 500 - 30 + 40 + 600
Q = 1110

a) Price elasticity of demand : It is the ratio of percenatge change in quantity demanded and the percentage change in price.

E =

= d/dP (500 - 3P + 2Pr + 0.1I) * 10 / 1110

= 0 - 3 + 0 + 0 * 10 / 1110

= -3 * 10 / 1110
E_P = (-) 0.027

b) Income elasticity of demand : It is the ratio of percenatge change in quantity demanded and the percentage change in income.

E_I =

= d/dI (500 - 3P + 2Pr + 0.1I) * 6000 / 1110

= 0 - 0 + 0 + 0.1 * 6000 / 1110

= 0.1 * 6000 / 1110
E_I = 0.54

c) Cross price elasticity of demand :

It is the ratio of percenatge change in quantity demanded and the percentage change in price of another good.

E_Pr =

= d/d_Pr (500 - 3P + 2Pr + 0.1I) * 20 / 1110

= 0 - 0 + 2 + 0 * 20 / 1110

= 2 * 20 / 1110
E_Pr = 0.036

d) As we can see, price elasticity of demand is 0.027 = 2.7%, which means when price increases by $1, quantity demanded will decrease by 2.7 units.

Income elasticity of demand is 0.54 = 54%, which means when income increases by $1, quantity demanded will increase by 54 units.

Cross price elasticity of demand is 0.036 = 3.6%, which means when price of another good increases by $1, quantity demanded of the good will increase by 3.6 units. As, when price of other good increases, the quantity demand of the good increases, this means that the goods are perfect substitutes because elasticity is positive.