# Elasticity in Economics

## Definition of Elasticity

What does elasticity in economics mean? Elasticity describes the percentage change of a factor of interest if another impacting factor changes by one percentage point. For example, in their research, economists must discuss the price elasticity of demand in household theory. This kind of elasticity, therefore, describes the price sensitivity of demand. And also answers the question; of how demand for goods changes in percentage if the price increases by one percentage point. Three outcomes are consequently possible; the demand is inelastic (0 to 0,9

\varepsilon_{x,y}=\frac{(\frac{\Delta X}{X})}{(\frac{\Delta Y}{Y})}=\frac{\Delta X}{\Delta Y} \cdot \frac{Y}{X}= X'(Y) \cdot \frac{Y}{X}

## Elasticity in Household Theory

In household theory, the lecturer will first confront you with the previous example of price elasticity of demand after deriving the optimal decision-making of households. The lecturer might also consider discussing the Engel Curve using the income elasticity of demand and deriving different categories of goods (normal and inferior goods). Furthermore, the lecturer will use cross-price elasticity to categorize goods complements and substitute groups.

### How to derive the Direct Price Elasticity of Demand

Here is a mathematical description of how to derive the direct price elasticity of demand, which explains the sensitivity of demand to its price changes. The starting point is the demand equation $x(p)$ depending on the price of the good, which can take any functional form, depending on the case being analyzed.

\varepsilon_{x, p}=\frac{(\frac{\Delta x(p)}{x})}{(\frac{\Delta p}{p})}=\frac{\Delta x(p)}{\Delta p} \cdot \frac{p}{x(p)}= x'(p) \cdot \frac{p}{x(p)}

### Direct Price Elasticity of Demand using Linear Equation

Assuming linear demand equation $x(p)=b-a \cdot p$ leads to the following outcomes for the direct price elasticity of demand:

\varepsilon_{x, p}=\frac{(\frac{\Delta x(p)}{x})}{(\frac{\Delta p}{p})}= x'(p) \cdot \frac{p}{x(p)}=\frac{-ap}{b-ap}  \text{where the first derivative of demand is} \ x'(p)=-a

### Indirect Price Elasticity of Demand

The indirect price elasticity of demand measures how sensitive the demand for a product will react when prices of other related goods increase or decrease. Consequently, it allows for the measurement of indifference, substitution, and complementary effect of the demand for a good towards other commodities that a household would demand.

## Elasticity in Theory of the Firm

In the theory of the firm, an economist is interested in explaining the price sensitivity of input demand, input sensitivity of production levels, and the price elasticity of the firm’s supply. Each of the elasticities delivers essential information for business management.

The price elasticity of input demand helps the economist analyze the flexibility of the production technology and cost structure (complement inputs and substitutional inputs). Such information allows businesses to efficiently coordinate their resource acquisition, storage, maintenance, and production plans. The second one, input elasticity of production levels, reflects the firm’s capabilities to utilize its inputs and turn them to output efficiently. The third one, price elasticity of supply, reveals the firm’s competitiveness in the markets for the firm’s outcomes.

## Elasticity in Market Theory

In the theory of markets, economists explain how the price elasticities of demand and supply shape market competition. When describing how taxation affects the consumer and producer surpluses, economists quantify the share of the burden between buyers and sellers by relating the outcomes with the price elasticity of demand and supply. If the market demand is more sensitive than the supply, the suppliers will carry more tax burden than demand. Such a statement will force the student to figure out how to compare the elasticities.

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