Question

A study of the consumption of beverages in Mexico found that "overall, for soft drinks a \(10 \%\) price increase decreases the quantity consumed by \(10.6 \%\)." Given this information, calculate the price elasticity of demand for soda in Mexico. Is demand price elastic or price inelastic? Briefly explain. Source: M. A. Colchero, et al. "Price Elasticity of the Demand for Sugar Sweetened Beverages and Soft Drinks in Mexico," Economics and Human Biology," Vol. 19, December 2015, pp. \(129-137\).

Short answer

The price elasticity of demand for soda in Mexico is -1.06. This means that the demand is price elastic. An increase in price by 1% decreases the quantity demanded by approximately 1.06%.

Step-by-step solution

Understanding Price Elasticity of Demand

Price Elasticity of Demand (PED) measures the responsiveness of quantity demanded to a change in price. It is calculated by dividing the percentage change in quantity demanded by the percentage change in price. Mathematically, \(PED = \frac{% \Delta Qd}{% \Delta P}\), where %\(\Delta Qd\) is percentage change in quantity demanded and %\(\Delta P\) is percentage change in price.

Calculate the Price Elasticity of Demand

Given that the percentage change in price (%\(\Delta P\)) is 10% (increase is considered positive) and the percentage change in quantity demanded (%\(\Delta Qd\)) is -10.6% (decrease is considered negative), substitution these values into the PED formula gives \( PED = \frac{-10.6}{10} = -1.06 \). The PED is negative, as expected, because price and quantity demanded move in opposite directions (law of demand).

Interpret the Price Elasticity of Demand

The PED in absolute value is 1.06, which we can interpret as follows: a 1% increase in price causes quantity demanded to decrease by approximately 1.06%. If PED > 1 in absolute value, demand is price elastic, if PED < 1 in absolute value demand is price inelastic, and if PED = 1, then demand is unit elastic. Therefore, the demand for soda in Mexico is slightly elastic since |PED| = 1.06 > 1.

Key concepts

Elasticity of Demand

Elasticity of demand is a vital concept in understanding how small changes in the price of a good can significantly affect the quantity of that good which consumers are willing to buy. It's a measure of economic responsiveness, which in simple terms tells us how sensitive the demand for a product is to changes in its price. In a practical sense, if a good has a high price elasticity, a tiny price change can lead to a substantial change in the quantity demanded. This is crucial for businesses when they're making decisions about pricing strategies, and for governments that might consider the implications of taxes or subsidies on certain goods.

For example, luxury items typically have high elasticity because consumers will drastically reduce their purchases if prices go up. On the other hand, essentials like medication tend to have low elasticity because people need them regardless of price increases. The formula to calculate the elasticity of demand is given by dividing the percentage change in quantity demanded by the percentage change in price (PED = %ΔQd / %ΔP). This ratio gives us a numeric value, which determines if the demand is elastic (PED > 1), inelastic (PED < 1), or unitary elastic (PED = 1).

Quantity Demanded

Quantity demanded refers to the exact amount of a good or service consumers are willing to purchase at a specific price. Unlike 'demand,' which refers to the overall desire or need for a product, quantity demanded is directly connected to and changes with the price level. It is depicted as a single point on the demand curve; as the price of a good changes, the quantity demanded will move along the curve to a new point which reflects the new price level. The key to understanding this concept is recognizing that quantity demanded is not static.

Based on the law of demand in economics, there's an inverse relationship between price and quantity demanded. This means that, typically, when price increases, the quantity demanded decreases, and vice versa. This relationship is graphically represented on a demand curve, which usually slopes downwards from left to right. It's important to note that changes in other factors aside from price – like consumer income or tastes – can shift the entire demand curve rather than just result in a movement along it.

Economic Responsiveness

Economic responsiveness, in the context of demand, is essentially how consumers alter their purchasing behavior in response to changes in market conditions, such as price changes, income levels, or shifts in preferences. It's an aggregate measure of change — if the change is large in relation to the price movement, the demand is said to be more 'responsive'.

When it comes to price elasticity, if the demand is responsive, it means that consumers are quick to adjust their buying habits with fluctuating prices, indicating elastic demand. Conversely, if consumers change their buying habits very little despite significant changes in price, the demand is considered inelastic. Understanding economic responsiveness is vital for businesses planning their product pricing, sales forecasting, and for policymakers who need to predict how changes in taxes or subsidies will affect consumer behavior.