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4.2: Price elasticities and public policy

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    In Chapter 3 we explored the implications of putting price floors and supply quotas in place. We saw that price floors can lead to excess supply. An important public policy question therefore is why these policies actually exist. It turns out that we can understand why with the help of elasticity concepts.

    Price elasticity and expenditure

    Let us return to Table 4.1 and explore what happens to total expenditure/revenue as the price varies. Since total revenue is simply the product of price times quantity it can be computed from the first two columns. The result is given in the final column. We see immediately that total expenditure on the good is highest at the midpoint of the demand curve corresponding to these data. At a price of $5 expenditure is $25. No other price yields more expenditure or revenue. Obviously the value $5 is midway between the zero value and the price or quantity intercept of the demand curve in Figure 4.1. This is a general result for linear demand curves: Expenditure is greatest at the midpoint, and the mid-price corresponds to the mid-quantity on the horizontal axis.

    Geometrically this can be seen from Figure 4.1. Since expenditure is the product of price and quantity, in geometric terms it is the area of the rectangle mapped out by any price-quantity combination. For example, at img80.png total expenditure is $16 – the area of the rectangle bounded by these price and quantity values. Following this line of reasoning, if we were to compute the area bounded by a price of $7 and a corresponding quantity of 3 units we get a larger rectangle – a value of $21. This example indicates that the largest rectangle occurs at the midpoint of the demand curve. As a general geometric rule this is always the case. Hence we can conclude that the price that generates the greatest expenditure is the midpoint of a linear demand curve.

    Let us now apply this rule to pricing in the market place. If our existing price is high and our goal is to generate more revenue, then we should reduce the price. Conversely, if our price is low and our goal is again to increase revenue we should raise the price. Starting from a high price let us see why this is so. By lowering the price we induce an increase in quantity demanded. Of course the lower price reduces the revenue obtained on the units already being sold at the initial high price. But since total expenditure increases at the new lower price, it must be the case that the additional sales caused by the lower price more than compensate for this loss on the units being sold at the initial high price. But there comes a point when this process ceases. Eventually the loss in revenue on the units being sold at the higher price is not offset by the revenue from additional quantity. We lose a margin on so many existing units that the additional sales cannot compensate. Accordingly revenue falls.

    Note next that the top part of the demand curve is elastic and the lower part is inelastic. So, as a general rule we can state that:

    A price decline (quantity increase) on an elastic segment of a demand curve necessarily increases revenue, and a price increase (quantity decline) on an inelastic segment also increases revenue.

    The result is mapped in Figure 4.4, which plots total revenue as a function of the quantity demanded – columns 2 and 4 from Table 4.1. At low quantity values the price is high and the demand is elastic; at high quantity values the price is low and the demand is inelastic. The revenue maximizing point is the midpoint of the demand curve.

    Figure 4.4 Total revenue and elasticity
    img81.png
    Based upon the data in Table 4.1, revenue increases with quantity sold up to sales of 5 units. Beyond this output, the decline in price that must accompany additional sales causes revenue to decline.

    We now have a general conclusion: In order to maximize the possible revenue from the sale of a good or service, it should be priced where the demand elasticity is unity.

    Does this conclusion mean that every entrepreneur tries to find this magic region of the demand curve in pricing her product? Not necessarily: Most businesses seek to maximize their profit rather than their revenue, and so they have to focus on cost in addition to sales. We will examine this interaction in later chapters. Secondly, not every firm has control over the price they charge; the price corresponding to the unit elasticity may be too high relative to their competitors' price choices. Nonetheless, many firms, especially in the early phase of their life-cycle, focus on revenue growth rather than profit, and so, if they have any power over their price, the choice of the unit-elastic price may be appropriate.

    The agriculture problem

    We are now in a position to address the question we posed above: Why are price floors frequently found in agricultural markets? The answer is that governments believe that the pressures of competition would force farm/food prices so low that many farmers would not be able to earn a reasonable income from farming. Accordingly, governments impose price floors. Keep in mind that price floors are prices above the market equilibrium and therefore lead to excess supply.

    Since the demand for foodstuffs is inelastic we know that a higher price will induce more revenue, even with a lower quantity being sold. The government can force this outcome on the market by a policy of supply management. It can force farmers in the aggregate to bring only a specific amount of product to the market, and thus ensure that the price floor does not lead to excess supply. This is the system of supply management we observe in dairy markets in Canada, for example, and that we examined in the case of maple syrup in Chapter 3. Its supporters praise it because it helps farmers, its critics point out that higher food prices hurt lower-income households more than high-income households, and therefore it is not a good policy.

    Elasticity values are frequently more informative than diagrams and figures. Our natural inclination is to view demand curves with a somewhat vertical profile as being inelastic, and demand curves with a flatter profile as elastic. But we must keep in mind that, as explained in Chapter 2, the vertical and horizontal axis of any diagram can be scaled in such a way as to change the visual impact of the data underlying the curves. But a numerical elasticity value will never deceive in this way. If its value is less than unity it is inelastic, regardless of the visual aspect of the demand curve.

    At the same time, if we have two demand curves intersecting at a particular price-quantity combination, we can say that the curve with the more vertical profile is relatively more elastic, or less inelastic. This is illustrated in Figure 4.5. It is clear that, at the price-quantity combination where they intersect, the demand curve img78.png will yield a greater (percentage) quantity change than the demand curve D, for a given (percentage) price change. Hence, on the basis of diagrams, we can compare demand elasticities in relative terms at a point where the two intersect.

    Figure 4.5 The impact of elasticity on quantity fluctuations
    img82.png
    In the lower part of the demand curve D, demand is inelastic: At the point A, a shift in supply from S1 to S2 induces a large percentage increase in price, and a small percentage decrease in quantity demanded. In contrast, for the demand curve img83.png that goes through the original equilibrium, the region A is now an elastic region, and the impact of the supply shift is contrary: The %img84.png is smaller and the %img85.png is larger.

    This page titled 4.2: Price elasticities and public policy is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Douglas Curtis and Ian Irvine (Lyryx) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.