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## Note on Income and Cross Elasticity of Demand

• Note
• Things to remember

### INCOME ELASTICITY OF DEMAND (Ey)

The proportionate change in quantity demanded for a goods due to the proportionate change in consumer's income is called income elasticity of demand. Income elasticity is usually symbolized by 'Ey' and written as:

Ey = $$\frac{\%\:of\:change\:in\:demand}{\%\:of\:change\:in\:income}$$

Ey =$$\frac{\frac{\Delta Q}{Q}\:X\:100 \%}{\frac{\Delta y}{y}\:X\:100\%}$$

 i.e. Ey=$$\frac{ΔQ}{Δy}$$ X $$\frac{y}{Q}$$

Where,

Ey = Income elasticity demand

Δ = Small Change

Q = Quantity

y = Income

DEGREE / TYPES OF INCOME ELASTICITY OF DEMAND

There are three types of income elasticity of demand. They are as follow:

1) Positive Income Elasticity (Ey>0)

If the quantity demand for a commodity increases with the increase in consumer's income and decreases with the decrease in income of the consumer is known as positive income elasticity. Hence, there is a positive relation between income and demand. In that case, the value of elasticity remains greater than zero.

Under positive income elasticity of demand, there are three types of demand. They are:

i) Income Elasticity of Demand is greater than unity (Ey>1)

If the proportionate change in quantity demanded is more than the proportionate change in the consumer's income, then it is called income elasticity greater than unity.

Fig: Income Elasticity of Demand is greater than unity.

ii) Income Elasticity of Demand is equal to unity (Ey=1)

If the proportionate change in quantity demanded is equal to the proportionate change in the consumer's income, then it is called income elasticity equal to unity.

iii) Income Elasticity of Demand is less than unity (Ey<1)

If the proportionate change in quantity demanded is less than the proportionate change in the consumer's income, then it is called income elasticity less than unity.

2) Negative Income Elasticity (Ey<0)

If the quantity demand for a goods increase with the decrease in consumer's income & vice versa, then it is called negative income elasticity.

Fig: Negative income elasticity demand

In the given figure, quantity demanded is measured along OX-axis & consumer's income is measured along OY-axis. D1D is the demand curve which is negatively sloped. Here, when the consumer's income increases from OY to OY1, demand for goods decreases from OQ to OQ1.

3) Zero Income Elasticity of Demand (Ey=0)

If the quantity demanded for a goods does not change with the change in consumer's income, then it is called zero income elasticity of demand.

Fig: Zero income elasticity demand

In the given figure, quantity demanded is measured along OX-axis & consumer's income is measured along OY-axis. D1D is the demand curve which is perfectly inelastic. Here, whatever be the consumer's income be i.e. OY, OY1 or OY2 quantity demanded is same as OQ.

### CROSS ELASTICITY OF DEMAND (Exy)

If the proportionate change in quantity demanded of goods due to the proportionate change in the price of a related good (i.e. substitute goods or complementary goods), is called cross elasticity of demand. Cross elasticity of demand is symbolized by 'Exy' and written as:

Exy = $$\frac{\%\:of\:change\:in\:quantity\:demand\:for\:'x'\:goods}{\%\:of\:change\:in\:price\:of\:'y'\:goods}$$

Exy =$$\frac{\frac{\Delta Qx}{Qx}\:X\:100 \%}{\frac{\Delta Py}{Py}\:X\:100\%}$$

 i.e. Exy=$$\frac{ΔQx}{ΔPy}$$ X $$\frac{Py}{Qx}$$

Where,

Exy = cross elasticity demand between X and Y

Δ = Small Chnage

Qx = Quantity demand of Y goods

Py = Price of Y goods

DEGREE / TYPES OF CROSS ELASTICITY OF DEMAND

There are two types of cross elasticity of demand described below:

i) Positive cross elasticity (Exy>0)

Positive cross elasticity of demand is only applied in the case of substitute goods like coffee and tea. If the increase in price of another substitute goods and vice versa, then it is called positive cross elasticity of demand. Hence, the increases in the price of a commodity result to the rise in a quantity demand of a substitute good.

Fig: Positive cross elasticity demand

In the given figure, quantity demand of coffee is measured along OX-axis and price of tea is measured along OY-axis. When the price of tea increases from OP to OP1, the quantity demand for coffee also increases from OQ to OQ1. Hence, the DD1 is the positive cross demand curve sloping upward to the right.

ii) Negative cross elasticity (Exy<0)

Negative cross elasticity of demand is only applied in the case of complementary goods like petrol & car. If the quantity demanded for a goods increase with the decrease in price of other complementary goods and vice versa,  then it is called negative cross elasticity of demand. Hence, the rise in the price of commodity results to decreases in quantity demands of complementary goods.

Fig: Negative cross elasticity demand

In the given figure, quantity demand of pen is measured along OX-axis and price of ink is measured along OY-axis. When the price of ink increases from OP to OP1, the quantity demand of a pen decreases from OQ to OQ1. Hence, DD1 is the negative cross elasticity demand curve sloping downward to the right.

Zero Cross Elasticity of Demand:

Zero cross-elasticity of demand can be defined as change in price of 'Y' does not affect to quantity demanded for 'X'.

In the above figure,  quantity demanded for goods X is measured along ox-axis & price of goods y is measured along oy-axis. when price of y changes quantity demanded for y remains constant. Hence, in case of zere cross elasticity of demand, deamnd curve becomes vertocal straight line parallel to oy-axis.

(Karna, Khanal, and Chaulagain)(Khanal, Khatiwada, and Thapa)(Jha, Bhusal and Bista)

Bibliography

Jha, P.K., et al. Economics II. Kalimati, Kathmandu: Dreamland Publication, 2011.

Karna, Dr.Surendra Labh, Bhawani Prasad Khanal and Neelam Prasad Chaulagain. Economics. Kathmandu: Jupiter Publisher and Distributors Pvt. Ltd, 2070.

Khanal, Dr. Rajesh Keshar, et al. Economics II. Kathmandu: Januka Publication Pvt. Ltd., 2013.

Income elasticity of demand

• Zero Income Elasticity of Demand (Ey=0)
• Positive Income Elasticity (Ey>0)
• Negative Income Elasticity (Ey<0)

Cross elasticity of demand

• Positive Income Elasticity (Exy>0)
• Negative Income Elasticity (Exy<0)

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