Thus whether we move from M to P or P to M on the arc PM of the DD curve, the formula for arc elasticity of demand gives the same numerical value. The closer the two points P and M are, the more accurate is the measure of elasticity on the basis of this formula. On the basis of this formula, we can measure arc elasticity of demand when there is a movement either from point P to M or from M to P. (iii) Suppose the price of commodity X falls from Rs. 3 per kg to Re.lper kg. (i) Suppose the price of commodity X falls from Rs. 5 per kg. As a result, the quantity demanded increases from 18 to 20 units.

At the midpoint of a linear demand curve, demand is unit price elastic. Another argument for considering only small changes in computing price elasticities of demand will become evident in the next section. We will investigate what happens to price elasticities as we move from one point to another along a linear demand curve. This measure of elasticity, which arc method of elasticity of demand is based on percentage changes relative to the average value of each variable between two points, is called arc elasticity. The arc elasticity method has the advantage that it yields the same elasticity whether we go from point A to point B or from point B to point A. The demand curve shows how changes in price lead to changes in the quantity demanded.

Arc elasticity of demand uses a midpoint between the two points. The movement from point B to point C shows unitary elastic demand as total expenditure has remained unchanged with the change in price. Similarly, the movement from point C to point D shows inelastic demand as total expenditure as well as price has decreased.

## Calculating Arc Elasticity Coefficient

With a downward-sloping demand curve, price and quantity demanded move in opposite directions, so the price elasticity of demand is always negative. A positive percentage change in price implies a negative percentage change in quantity demanded, and vice versa. Sometimes you will see the absolute value of the price elasticity measure reported. In essence, the minus sign is ignored because it is expected that there will be a negative (inverse) relationship between quantity demanded and price. In this text, however, we will retain the minus sign in reporting price elasticity of demand and will say “the absolute value of the price elasticity of demand” when that is what we are describing.

What happens to the price elasticity of demand when we travel along the demand curve? On a linear demand curve, such as the one in Figure 5.2 “Price Elasticities of Demand for a Linear Demand Curve”, elasticity becomes smaller (in absolute value) as we travel downward and to the right. To calculate arc elasticity of demand we first take the midpoint in between.

## Why the arc elasticity matters

Saying that the price elasticity of demand is infinite requires that we say the denominator “approaches” zero. 1Notice that since the number of units sold of a good is the same as the number of units bought, the definition for total revenue could also be used to define total spending. If we are trying to determine what happens to revenues of sellers, then we are asking about total revenue. If we are trying to determine how much consumers spend, then we are asking about total spending. For most countries, price elasticity of demand for crude oil tends to be greater (in absolute value) in the long run than in the short run.

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By doing so, we will get the same answer (in absolute terms) by choosing $9 as old and $10 as new, as we would choosing $10 as old and $9 as new. When we use arc elasticities we do not need to worry about which point is the starting point and which point is the ending point. This benefit comes at the cost of a more difficult calculation. In 1998, 2,000 people in the United States died as a result of drivers running red lights at intersections. In an effort to reduce the number of drivers who make such choices, many areas have installed cameras at intersections.

## Using Arc elasticity of demand

In the figure, we can see that AB is an arc on the demand curve DD, and point C is the mid-point on AB. If we followed point method to measure PED at points A and B in the curve DD, we get different coefficients as a result of using different bases. To avoid this discrepancy, elasticity is measured by taking mean values of price and quantity demanded in arc method. Again, assume that the price and quantity demanded revert to their prior levels, determine the arc elasticity coefficient again and see the result. Under the total outlay method, the measurement of elasticity only lets us know whether it is unitary, greater, or less than unitary.

The answer depends in large part on how much time we allow for a response. If we are interested in the reduction in quantity demanded by tomorrow afternoon, we can expect that the response will be very small. But if we give consumers a year to respond to the price change, we can expect the response to be much greater. We expect that the absolute value of the price elasticity of demand will be greater when more time is allowed for consumer responses. The greater the absolute value of the price elasticity of demand, the greater the responsiveness of quantity demanded to a price change. What determines whether demand is more or less price elastic?

## Price elasticity on a non-linear income demand curve

The elasticity of demand that is obtained in the case of this price change is called the arc-elasticity of demand—here over the arc R1R2 of the demand curve. But if the change in price is not infinitesimally small, if the change is by a considerable amount, then move to another point on the demand curve which is somewhat away from the initial point. In this case, the elasticity of demand that is obtained over the arc of the demand curve between the two points is called the arc-elasticity of demand. On the other hand, you can measure the arc elasticity directly and do not need such a mathematical function. To do this, you need two observation points for the price and quantity demanded.

- Consumer’s income is one of the major factors that determine demand of a product.
- This means, higher the price, lower will be the demand, and lower the price, higher be the demand of the commodity.
- Total outlay method of measuring price elasticity of demand does not provide us exact numerical measurement of elasticity of demand but only indicates if the demand is elastic, inelastic or unitary in nature.
- In the second, a price increase left total revenue unchanged.

The thing with a straight line is that the elasticity varies. At the top left, quantity is showing a big % increase, compared to price. Among the most common applications of price elasticity is to determine prices that maximize revenue or profit. You should notice that this is the same if we are to find the average of the prices and quantities. Hence, we can say that by finding the midpoints, we are actually finding the average price and average quantity.

Quantity demanded falls by the same percentage by which price increases. Finding the price elasticity of demand requires that we first compute percentage changes in price and in quantity demanded. We calculate those changes between two points on a demand curve. There are two possible ways of calculating elasticity—price (or point) elasticity of demand and arc elasticity of demand. Price elasticity of demand measures the responsiveness of quantity demanded to a price. It takes the elasticity of demand at a particular point on the demand curve, or between two points on the curve.

This method produces a consistent elasticity value, regardless of whether the price is rising or falling. That’s because we are using the average as the denominator for both the price and the quantity demanded. Arc elasticity of demand is more useful than price elasticity of demand when there is a considerable change in price.

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With percentage changes in price and quantity demanded obtained, we can now determine the elasticity coefficient. Use the arc elasticity method to determine the price elasticity of demand if a decrease in the price to \$35 leads to an increase in quantity demanded to 250 units. So, when total expenditure moves in the opposite direction to the change in price, the elasticity of demand is greater than unitary. Following schedule and graph help to understand the nature of elastic demand.

There is; the effect depends on the price elasticity of demand. According to this method, elasticity of demand will be different on each point of a demand curve. Thus, this method is applied when there is small change in price and quantity demanded of the commodity. As demonstrated, arc or midpoint elasticity method uses average price and average quantity points to determine elasticity coefficients. This solves the annoyance with point elasticity method in which a different result is obtained when price and quantity revert back to their initial state.

When total expenditure decreases with fall in price and increases with rise in price, the value of PED will be less than 1. Here, price of commodity and total outlay move in same direction. When total expenditure increases with fall in price and decreases with rise in price, the value of PED will be greater than 1. Here, rise in price and total outlay or expenditure move in opposite direction. Income elasticity of demand is the measure of degree of change in quantity demanded for a commodity in response to the change in income of the consumers demanding the commodity.