Demand Elasticity: Price Elasticity, Income Elasticity & Cross Elasticity

Demand elasticity could be measured in three forms:

Price Elasticity of Demand

Price elasticity of demand is defined as the percentage change in the quantity demanded divided by the percentage change in the price of the commodity. Algebraically:

E_d = Percentage change in quantity demanded/Percentage change in price

Price elasticity also shows the degree of responsiveness to the change in the quantity demanded of a product due to the change in its price.

The above equation can be written as:

E_d = (∆Q/Q*100)/(∆P/P*100)

E_d = (∆Q/Q)/(∆P/P)

E_d = (∆Q/∆P) * (P/Q) ………………………………………….. (1)

Now since there exists inverse relation between the price and quantity of a product, therefore, as the price increases, the quantity demanded falls. Therefore, the value of price elasticity will always be negative. In order to overcome this, we add minus sign in the above equation (1) itself so as to get positive elasticity (because it is easier to apply further applications on positive numbers).

Hence the new and final elasticity formula becomes:

E_d = (- ∆Q/∆P) * (P/Q) ………………………………………….. (2)

According to Lipsey and Crystal, ‘Demand elasticity is measured by a ratio: the percentage change in quantity demanded divided by the percentage change in price that bought it about. For normal, negatively sloped demand curves, elasticity is negative, but the relative size of the two elasticities is usually assessed by comparing their absolute values’.

The larger value of elasticity indicates that the quantity demanded is highly responsive to a little change in the price, i.e. quantity demanded changes more than as compared to the change in the price. On the other hand, the smaller elasticity indicates that the quantity demanded is relatively unresponsive to a change in the price, i.e. the quantity demanded has little change as compared to a change in the price.

The value of price elasticity of demand varies from zero to infinity. According to Lipsey and Crystal, ‘Elasticity depends on the slope of the demand curve and the point at which the measurement is made. Starting at point A and moving to point B, the ratio ∆p/∆q is the slope of the line, while its reciprocal ∆q/∆p is the first term in the percentage definition of the elasticity. The second term is p/q, which is the ratio of the coordinates of point A. since the slope ∆p/∆q is constant, it is clear that the elasticity along the demand curve varies with the ratio p/q, which is zero where the curve intersects the quantity axis and infinity where it intersects the price axis’.

Zero elasticity implies that the quantity demanded does not change with a change in the price, i.e. quantity demanded is completely unresponsive to a change in the price of the commodity. In such a case, the demand curve is said to be perfectly inelastic.

Infinite elasticity implies that the quantity demanded is highly responsive to a change in the price, i.e. even with a very little price change, the change in quantity demanded is huge. In such a case, the demand curve is said to be perfectly elastic.

If the value of elasticity is one, then it represents that the quantity demanded is equally responsive to a change in its price, i.e. quantity demanded changes in the same proportion in which price changes. In such a case, the demand curve is said to be unit elastic.

However, if the value of elasticity is greater than one, then it is known as more than unit elastic and represents that the change in the quantity demanded is greater relative to a change in the price. In such a case, the demand curve will be downward-sloping but flatter in shape.

On the other hand, if the elasticity is less than one, then this is known as less than unit elastic. In such a case, the demand curve would be steeper and downward sloping as it represents a lesser change in the quantity demanded relative to a change in the price.

When the price elasticity is measured between any two points, then it is known as arc elasticity. When the elasticity is measured for a point on the demand curve, then it is known as point elasticity.

The arc elasticity is measured by the following formula:

E_d = (∆Q/∆P) * (P₀) + (P₁/Q₀) + Q₁

For instance, the elasticity between points J and K for the following figure is:

E_d = (∆Q/∆P) * (P₀) + (P₁/Q₀) + Q₁

E_d = (20/10) * (15+25)/(30+50) = 1

The point elasticity is measured by the following formula:

E_d = (∆Q/∆P) * (P/Q)

Or

E_d = lower segment/upper segment

For instance, the point elasticity at point P could be calculated as:

E_d = lower segment/upper segment

E_d = PN/PM Or QN/OQ

Elasticity and Total Spending:

The total spending of the product’s buyer is always equal to the money received by the product’s sellers plus the taxes levied by the government. For simplicity, let’s ignore the taxes and just take the total spending of buyers to be equal to the money which sellers receive.

Moving on, we know that a change in the total spending brought by a change in the price of the product is directly related to its elasticity of demand. If the elasticity is less than unit elastic, then the percentage change in the price will exceed the percentage change in the quantity, and this price change is so influential that this will lead to a change in the total spending of the buyers in the same direction as the price changes.

However, if the elasticity would be more than unit elastic, then the percentage change in quantity will exceed the percentage change in the price, and this change in quantity will be so influential so as to change the total spending in the same direction as it changes (opposite direction to the change in price). Hence based on this thing, we can draw the following outcomes:

When the elasticity of demand is less than unit elastic, a fall in price reduces the total spending on the product, and a rise in price increases it.

When the elasticity of demand is more than unit elastic, a fall in price will increase the total spending on the product and vice versa.

When the elasticity of demand is unity, then a rise or fall in price leaves the total spending on the product unaffected, i.e. total spending does not change.

Income Elasticity of Demand

Income elasticity of demand is defined as the percentage change in the quantity demanded divided by the percentage change in the income of the consumer.

Algebraically:

E_m = Percentage change in quantity demanded/Percentage change in money income

Income elasticity also shows the responsiveness of the change in the quantity demanded of a product due to the change in the income of the consumer (M).

The above equation can be written as:

E_m = (∆Q/Q*100)/(∆M/M*100)

E_m = (∆Q/Q)/(∆M/M)

E_m = (∆Q/∆M) * (M/Q) ………………………………………….. (1)

Now, since there exists a direct relation between the income and quantity of a normal good, therefore, as the income of the consumer increases, the quantity demanded also increases. Therefore, the value of income elasticity will always be positive for a normal good.

However, since there exists an inverse relationship between the income of the consumer and the demand for the inferior good therefore, as the income of the consumer increases, the demand for inferior goods reduces, and hence the income elasticity will be negative for inferior goods.

Cross Elasticity of Demand

Cross elasticity of demand is defined as the percentage change in the quantity demanded of one commodity divided by the percentage change in the price of the other commodity.

Algebraically:

E_c = (Percentage change in quantity demanded of X)/(Percentage change in price of commodity Y)

Cross elasticity also shows the responsiveness of the change in the quantity demanded of a product due to the change in the price of the other product.

The above equation can be written as:

E_c = (∆Qx/Qx * 100)/(∆Py/Py * 100)

E_c =  (∆Qx/Qx)/(∆Py/Py)

E_c = (∆Qx/∆Py) * (Py/Qx) ………………………………………….. (1)

Since there are different goods available in the market, therefore, the cross elasticity would depend on the nature of the goods.

In the case of substitute goods, if the price of one good increases, people shift their demand from that commodity to its substitute commodity. Thus, the demand for the other commodity increases due to an increase in the price of the first commodity. Hence, cross elasticity in the case of substitute goods would be positive.

In the case of complementary goods, when the price of one good increases, the demand for its complement reduces (because they can be used in fixed proportions). Hence in the case of complementary goods, the cross-elasticity of demand will be negative.

In the case of unrelated goods, even if the price of one good increases or decreases, it leads to no effect on the demand for the other good. Hence in such a case, the cross elasticity of demand for unrelated goods would be zero.

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