Question

The estimated demand function for commodity X is described by the following equation:

Qd = 50 – 2Px + 1.5 In - 0.75 Py

where Px = Price of commodity X

In = Consumer Income

Py = Price of commodity Y

(a)Does the behavior of the consumer of this product follow the law of demand? Explain

(b)Is commodity X a normal good or an inferior good? How did you know?

(c)Comment on the relationship between commodity X and commodity Y.

(d)Find price elasticity of demand, income elasticity of demand and cross price elasticity of demand given that the price of commodity X is $5 per unit, consumer’s income is $100 and commodity Y sells for $10 per unit.

Answer 1

Qd = 50 – 2Px + 1.5 In - 0.75 Py

a) As Px have negative sign as a coefficient, it shows that there exist negative relationship between Qdx and Price of x which explains the law of demand.

b) Normal goods are those goods whose demand increases when income increases while inferior goods are those goods whose demand decreases when income increases. Positive sign in front of Income (In) shows that there exist positive relationship between Qd and Income.

c) There is negative sign in front of Py which means that when price of good Y increases, Quantity demanded of X falls which shows that good X and Y complement to each other.

d) Price elasticity of demand: (dQ / dP) * (P / Q)

(dQ / dP) = -2

At a price of 5, Qd = 182.5

Price elasticity of demand: -2 * (5 / 182.5) = -0.05

Income elasticity of demand: (dQ / dIn) * (In / Q)

dIn / dP = 1.5

Income elasticity of demand: 1.5 * (100 / 182.5) = 0.82

Income elasticity of demand: (dQ / dPy) * (Py / Q)

dIn / dP = -0.75

Income elasticity of demand: -0.75 * (10 / 182.5) = -0.04