## Elasticity in Economics

### Meaning

The Law of demand shows only the direction of change in quantity demanded due to change in price but it fails to explain how much change does quantity demand realizes due to change in the price of a commodity. So, to fulfill this limitation of the law of demand, Prof. Dr. Alfred Marshall developed the concept of Elasticity of Demand.

It is the ratio of proportionate change in quantity demand to the proportionate change in determinants of demand. Determinants include income, price of a related product, tax policy, and so on.

It is the degree of responsiveness of a dependent variable towards the change in the independent variable. Similarly, the elasticity of demand shows the impact of change in the determinants of demand for a good on its demand. Accordingly, the elasticity of demand is the degree of sensitivity of demand to change in the determinants of demand.

### Types of Elasticity of Demand

There are three types of Elasticity of demand. They are Price, Income, and Cross Elasticity of Demand.

#### Price Elasticity of Demand

Price elasticity of demand is one of the important concepts in economics. it refers to the degree of responsiveness of quantity demanded a commodity due to change in its price. It is the ratio of proportionate change in quantity demanded to proportionate change in price. Moreover, it also refers to the percentage change in quantity demanded divided by the percentage change in price. Generally, it is negative because of the application of the 'Law of demand'. However, Giffen goods have a positive price elasticity of demand.

#### Income Elasticity of Demand

Income Elasticity of demand refers to the responsiveness of quantity demanded towards the change in the income of a consumer. It the percentage change in quantity demanded by the percentage change in income of the consumer. Moreover, it is the ratio of proportionate change in quantity demanded to proportionate change in the income of a consumer. It is positive for normal goods and negative for inferior goods.

#### Cross Elasticity of Demand

Cross elasticity of demand refers to the degree of responsiveness of quantity demand of X-commodity to the change in the price of Y-commodity. It is the ratio of the percentage change in demand for X goods to the percentage change in the price of Y-good. It is positive for substitute goods and negative for complementary goods.

## Slope

#### Meaning

The slope is the inclination of a curve. It shows the magnitude and degree of relationship between two variables. The slope measures the degree of flatness and steepness of the curve about the x-axis. We determine the slope of a curve using tan(Î¸), 'rise by run', the first derivative, point method, and so on.

Using the point method, [latex] boxed{Slope=frac {y_2-y_1} {x_2-x_1}}[/latex]

## Elasticity and Slope

Elasticity and Slope are different concepts. With a linear demand curve, the slope is constant throughout the demand curve, but the elasticities of demand is different in each point. They are not the same, but they affect each other. This concept can be easily understood through the figure.

### Calculating Slope

With reference to the figure, we can calculate the slope of the line using the two-point method.

Slope of inverse demand curve = [latex] dfrac {y_2-y_1} {x_2-x_1}[/latex] = [latex]dfrac {20-10} {100-200} [/latex] = -0.10

The slope of the demand curve is the reciprocal of the slope of the inverse demand curve, so slope of demand curve [latex] (dfrac {dQ} {dP}) [/latex] = [latex] - dfrac {1} {0.10} [/latex] = -10.

The slope is constant throughout the demand curve provided that the demand curve is linear.

### Calculating Price Elasticity (Pe)

We know,

Pe = [latex] dfrac {dQ} {dP} [/latex] [latex]times[/latex] [latex] dfrac {P} {Q} [/latex]

**Pe at Point A**

=-10 [latex]times[/latex] [latex] dfrac{20} {100} [/latex]

=-2

**Pe at Point B**

=(-10) [latex]times[/latex] [latex] dfrac {10} {200} [/latex]

=[latex]- dfrac {1} {2} [/latex]

So, the price elasticity at points A and B are different, while the slope of the demand curve is constant throughout the linear demand curve.

Similarly, if a good is perfectly elastic, then the slope of the demand curve for the good will be '0'. Accordingly, if a good is perfectly inelastic, then the slope of the demand curve for the good will be '∞'. Thus, we can conclude that higher the slope, lower the elasticity, and lower the slope, higher the elasticity.

# Conclusion

Lastly, the slope of a linear demand curve is constant throughout the demand curve, but the elasticity of demand is different at different points of the demand curve. However, the slope and the elasticity are interrelated. As the elasticity of demand increases, the slope of demand curve approaches to '0'. Necessarily, as the slope of demand curve approaches to '∞' as the elasticity of demand decreases.

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