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The elasticity of demand and the slope of the demand curve are two basic concepts in economics. The notion of elasticity refers to the relationship between two economic parameters ; it is a measure of the impact of the variation of one of them on the variation of the other. The slope of the demand curve, the relationship between the quantity of product demanded and its price , is the trend that demand takes when the price changes. Although the elasticity of demand and the slope of the demand curve are different concepts, they are related; We see below how this relationship is.
the demand curve
Demand is the amount of goods and services that are purchased by consumers in a certain market and during a certain period of time. The incidence of different factors in demand is usually summarized in the price, that is, the amount of money that people are willing to pay for a good or service. In a basic economic analysis, the price at which a good or service is demanded is related to the quantity demanded through the demand curve, which is the graphical expression of the relationship between the price and the quantity of products demanded in a market (see figure below). The demand curve is also often represented with a mathematical function.
The claim is governed by a basic principle; when the price falls, the quantity of product demanded increases, and vice versa, when the price increases, the demand decreases. Therefore the demand curve is always decreasing. The combination between this curve and the supply curve, that is, the amount of products that are produced or offered based on price (the S curve in the previous figure), determines the amount of product that will be sold in a given market. as well as its price. The only exception that is postulated to the behavior of the law of demand, this is an increasing demand curve, translated into an increase in prices as the quantity of product demanded increases, is what is known as the Giffen good.
The slope of the demand curve m d expresses whether the curve is rising or falling and how strong that trend is. If the law of demand is fulfilled, the slope of the demand curve will always be negative, and its absolute value quantitatively expresses the variation in demand when the price changes. If the demand curve is expressed as a function, the slope at each point will be given by the derivative function; In a graphical representation, it can be visualized as the steepness or slope of the tangent line to the curve at each point. Its approximate value is the quotient between the price variation P , D P , and the product variation Q , D Q ; D P / D Q, when the incremental values are very small.
The slope of the demand curve can be thought of as the answer to the question, how much must the price of a product change in order for one more unit to be demanded?
The elasticity of demand
The elasticity of demand is an economic parameter that quantifies the response of the quantity of product demanded to a change in price. Changes in other parameters associated with demand such as income, which modify the demand curve (from D1 to D2 in the previous graph, for example), are also considered.
The elasticity of demand answers the question, to what extent does the quantity demanded of a product change when there is a change in price? The following figure shows three situations that allow a better understanding of the concept. When the quantity of product demanded does not change if the price changes, it is said that the demand is perfectly inelastic, and we have case (b) in the figure. An addiction, such as cigarette smoking, is a product that approximates this situation. On the contrary, when the price does not change when the quantity demanded changes, it is said that the demand is perfectly elastic, and we have case (c) in the figure. The consumption of basic goods or services, such as drinking water, approximates this situation. An intermediate situation is presented by case (a), in which the elasticity is 1.
The calculation of the elasticity e p establishes the relationship between the variation in the quantity of product demanded D Q before a variation in the price D P , both parameters expressed in relative terms. This is the quotient between the change in the quantity of product demanded divided by the quantity of product D Q / Q , and the change in price divided by the price D P / P .
e p = (DQ / Q ) / (D P / P )
It must be clarified that the absolute value of the previous calculation is taken, since as mentioned, if the demand law is fulfilled, the demand curve is decreasing and in that case there would be a negative variation in the quantity of product offered with the price variation. .
This arithmetic formula can be expressed as the ratio between the change in the quantity demanded and the change in the price multiplied by the ratio between the price and the quantity demanded.
e p = (D Q /D P ) × ( P / Q )
The first factor in this expression, D Q /D P , is the inverse value of the slope of the demand curve, D P /D Q , taken in absolute value, so that the elasticity of demand is the inverse function of the slope of the demand curve multiplied by the relationship between the price and the quantity of the product demanded.
e p = (1/ m d ) × ( P / Q )
The formula makes explicit the dependence of the elasticity of demand on the price and quantity of the product even in the case in which the slope of the demand curve were constant, in which the demand curve would be a straight line. Conversely, if the elasticity of demand is constant, as in case (a) of the previous figure, the slope of the demand curve varies with the quantity of product.
Elasticity of Supply and the Slope of the Supply Curve
If similar reasoning is made, the elasticity of supply will have the same relationship to the supply curve. The concept of elasticity is general and is not restricted to the relationship of demand and supply with price. One could consider the elasticity of income, in which case the relationship between the price of a product and the income of consumers should be studied, plotted on the vertical and horizontal axis respectively. The slope of this curve and the income elasticity would also have the same relationship as that obtained for the demand curve.
Sources
Mankiw, N. Gregory. Principles of economics . Second edition. mcgrawhill
Puig, Martha. Introduction to microeconomics. University of Barcelona, Spain, 2006.
