Answer to Question #242649 in Microeconomics for Mendie

Question

Suppose the demand for commodity X is estimated as follows:
X=68-1.6Px + 0.6Py + 0.08M

Where:
X=quantity of commodity X
Px=N20 is the price of X
Py= N40 is the price of Y
M=N10,000 is the income of the consumer

Calculate:
1. The price elasticity of X
2. The cross-price elasticity of demand for X with respect to the change in the price of Y
3. The income elasticity of demand X .
Also interpret your result is in 1,2, and 3

Answer 1

Solution:

1.). The price elasticity of X:

The price elasticity of demand (PEd) = $=\frac{\%\;change\; in\; quantity\; demanded}{\%\; change\; in\; price}$

PEd using point formula= $\frac{\triangle X}{\triangle P}\times \frac{P }{X}$

First derive quantity from the X demand function:

X=68-1.6Px + 0.6Py + 0.08M

Given:

Px=20, Py=40, M=1000

X = 68 – 1.6(20) + 0.6(40) + 0.08(10,000) = 68 – 32 + 24 + 800 = 860 units

X = 860

$\frac{\triangle X}{\triangle P} = -1.6$

PEd = $-1.6\times \frac{20}{860} = -0.04$

The price elasticity of X = 0.04

PEd = 0.04 < 1, therefore, the price elasticity of demand for commodity X is price inelastic. Demand is not sensitive to price changes.

 

2.). The cross-price elasticity of demand for X with respect to the change in the price of Y:

Cross elasticity of demand (XEd) = $\frac{\triangle X}{\triangle Py}\times \frac{Py }{X}$

$\frac{\triangle X}{\triangle Py} = 0.6$

XEd = $0.6\times \frac{40}{860} = 0.03$

The cross-price elasticity of demand for X with respect to the change in the price of Y = 0.03

XEd = 0.03 > 0, therefore, the cross elasticity of demand for X with respect to the change in the price for Y is greater than zero, which means that the two commodities are substitutes.

 

3.). The income elasticity of demand for X:

Income elasticity of demand (YEd) = $\frac{\triangle X}{\triangle I}\times \frac{I }{X}$

$\frac{\triangle X}{\triangle I} = 0.08$

YEd = $0.08 \times \frac{10,000}{860} = 0.93$

The income elasticity of demand for X = 0.93

YEd = 0.93 is positive and falls between 0 and 1, therefore the demand is income inelastic and the commodity is a normal good.