day 7 part 2 Economics: Principles of Elasticity

In the field of economics, the term elasticity refers to the degree of responsiveness of one economic variable to changes in another variable.
Responsiveness vs. Unresponsiveness: - A highly responsive case is described as elastic. - An unresponsive case is described as inelastic.
Elasticity conceptually measures the sensitivity of a dependent variable (such as quantity demanded) to a change in an independent variable (such as price).

Economics commonly focuses on three specific responsiveness relationships involving quantity demanded:

Quantity Demanded and Own Price: This measures how the quantity demanded of a particular good responds to changes in its own price. This is the primary form of price elasticity of demand.
Quantity Demanded and Cross Price: This measures how the quantity demanded of a good responds to price changes in other related goods. It formalizes the relationships between: - Substitutes: Goods that can replace one another. - Complements: Goods that are used together.
Quantity Demanded and Income: This measures how quantity demanded responds to changes in consumer income. It differentiates between: - Normal Goods: Goods for which demand increases as income rises. - Inferior Goods: Goods for which demand decreases as income rises.

Price elasticity of demand answers the fundamental question: By how much does quantity demanded change when the price of the good changes?
Mathematical Formula: Price elasticity is defined as the percentage change in quantity demanded divided by the percentage change in price: $E_p = \frac{\% \Delta \text{Quantity Demanded}}{\% \Delta \text{Price}}$
The Arrow Concept: To simplify the mathematical formula, consider the relative sizes of the changes (referred to as "arrows"): - The numerator represents the size of the "q arrow" (the magnitude of quantity change). - The denominator represents the size of the "p arrow" (the magnitude of price change). - The formula essentially compares the magnitude of the q arrow against the p arrow.
Direction of Movement and Negativity: - Because of the Law of Demand, price and quantity demanded move in opposite directions (an increase in price leads to a decrease in quantity and vice versa). - Therefore, the raw calculation of price elasticity will almost always result in a negative value. - For ease of comparison, economists typically analyze the absolute value of this expression: $\lvert E_p \rvert$ .

Definition: A situation where quantity demanded is completely unresponsive to any changes in price.
Graphical Representation: A perfectly vertical demand line.
Elasticity Value: $E_p = 0$ .
Calculation Context: In this case, the numerator (percentage change in quantity) is zero because the quantity remains constant regardless of price fluctuations ( $q_0$ at price $p_0$ and price $p_1$ ). Dividing zero by any change in price results in zero.

Definition: An imaginary or theoretical extreme where consumers are infinitely responsive to price changes. It suggests producers can sell any amount at a specific price, but demand drops to zero if the price changes slightly.
Graphical Representation: A perfectly horizontal demand line.
Elasticity Value: $E_p = \infty$ .

The relationship between the slope of the demand curve and elasticity is nested between the two extremes (vertical and horizontal lines): - Flatter Demand Curves: Represent more elastic demand (higher responsiveness). - Steeper Demand Curves: Represent more inelastic demand (lower responsiveness).

occurs when the percentage change in quantity demanded is larger than the percentage change in price (q \text{ arrow} > p \text{ arrow}).
Result: \lvert E_p \rvert > 1.
Example: A $50\%$ discount (price decrease) leads to an $80\%$ increase in quantity demanded. $\lvert \frac{80\%}{-50\%} \rvert = 1.6$
Since 1.6 > 1, the demand is elastic.

occurs when the percentage change in quantity demanded is smaller than the percentage change in price (q \text{ arrow} < p \text{ arrow}).
Result: \lvert E_p \rvert < 1.
Example: A $50\%$ discount (price decrease) leads to only a $20\%$ increase in quantity demanded. $\lvert \frac{20\%}{-50\%} \rvert = 0.4$
Since 0.4 < 1, the demand is inelastic.

occurs when the percentage change in quantity demanded is exactly equal to the percentage change in price ( $q \text{ arrow} = p \text{ arrow}$ ).
Result: $\lvert E_p \rvert = 1$ .
Example: A $50\%$ discount (price decrease) leads to an exactly $50\%$ increase in quantity demanded. $\lvert \frac{50\%}{-50\%} \rvert = 1$

Understanding elasticity is critical for determining how to increase earnings/revenue (Total Revenue = $Price \times Quantity$ ).
Strategy for Inelastic Demand: - If a firm faces inelastic demand, consumers are not sensitive to price changes. - The optimal strategy to increase earnings is to increase prices. The decrease in quantity will be relatively smaller than the increase in price, pushing total earnings up.
Strategy for Elastic Demand: - If a firm faces elastic demand, consumers are highly sensitive to price changes. - The optimal strategy to increase earnings is to decrease prices (e.g., cutting a cover charge). The resulting increase in quantity demanded will be large enough to outweigh the lower price per unit, increasing total revenue.
Case Study: University Tuition: - Universities with a "cult following" or high loyalty have inelastic demand. These institutions can increase tuition to raise revenue because students are unlikely to leave despite higher costs. - Universities that are not well-known or lack a loyal following face elastic demand. For these institutions, it may be pragmatic to cut tuition to attract a significantly larger number of students and increase total earnings.