RA-inst-U1-2

READING ASSIGNMENTS

Unit 1 --- Second Reading Assignment ---

The second reading assignment in Unit 1 is pp. 509-532. The topic is elasticity.

Price elasticity of demand is a measure of the responsive of quantity demanded to a price change. It is a way of measuring the strength of the law of demand, that is, the inverse relationship between price and the sales level. Remember that the law of demand applies as you study elasticity. For example, the fact that the sales level drops in response to a price increase does not necessarily mean demand is elastic. Elasticity depends on the result of a comparison between the percentage change in quantity demanded and the percentage change in price.

In most cases, demand will be either elastic or inelastic, although there are some special cases that will be discussed later. If the price of a gallon of milk rises from $2.00 to $2.20 (a ten percent increase) and the quantity demanded falls from 100 gallons per day to 75 per day (a twenty-five percent decrease), then demand is quite responsive or elastic. Alternatively, if the sales level only falls from 100 to 95, then the demand is relatively unresponsive and is said to be inelastic. These are the two usual results. A third outcome is for the quantity to drop from 100 to 90 (a ten percent decrease). Here, since the percentage increase in price (10%) and the percentage decrease in quantity demanded (10%) exactly cancel each other, demand is said to be unit elastic (or of unitary elasticity). Note that in this third case, the percentage change in quantity demanded divided by the percentage change in price yield a result of -1. However, because of the inverse relationship between price and quantity demanded, price elasticity of demand results are always negative. In order to eliminate the redundant negative sign, the absolute value is taken, yielding a result of +1.

In the first case above, the % change in quantity demanded divided by the % change in price yields a result of 2.5 ( 25 divided by 10). This is an example of relatively responsive or elastic demand. Results that are greater than 1 are classified as elastic.

In the second case, we have five divided by ten or .5 as the elasticity result. Demand is relatively unresponsive or inelastic. Results between 0 and 1.00 are classified as inelastic. Remember to take the absolute value before classifying the result as elastic or inelastic.

The General Formula for Price Elasticity of Demand is:

% Change in Quantity Demanded divided by % Change in Price

In the example about milk prices, it makes a difference whether you start at a price of $2.00 and raise it to $2.20, a 10% price increase, or start at $2.20 and drop it to $2.00, a 9% price decrease. The elasticity result should be the same for this price range. The result should not vary depending on whether your start with the old or new price. The same issue arises with the quantity changes. To resolve this discrepancy, an averaging formula known as the midpoint formula is used. It provides a method of comparing percentage changes in quantity so as to obtain consistent results for a given price range. The midpoint formula is as follows:

(Q1 - Q2)/(Q1 + Q2) divided by (P1 - P2)/(P1 + P2), where:

Q1 = the "old" quantity, Q2 = the "new" quantity, P1 = the "old" price, and P2 = the "new" price.

In the first milk example above, the old quantity = 100, the new quantity = 75, the old price = $2.00, and the new price = $2.20. If you substitute into the midpoint formula and then reduce the fraction, you should obtain an elasticity result of 3. Remember that the law of demand says there is an inverse relationship between price and quantity demanded. Therefore, price elasticity results are always negative. Since the negative sign is redundant, economists take the absolute value and the answer = 3.00. Since the answer is greater than one, it is classified as elastic demand.

When you work with the midpoint formula, it is recommended that you keep your work in fractional form until the very last step. At that point, you should convert to decimal form. Doing this will avoid certain rounding discrepancies. By convention, elasticity results are given two places to the right of the decimal point.

In the second example of milk elasticity, the price change is the same but the quantity drops from 100 to just 95. If you substitute into the midpoint formula, then the old quantity = 100, the new quantity = 95, the old price = $2.00, and the new price = $2.20. Your elasticity result using the midpoints formula should be .54, which is inelastic. You may have noticed some discrepancies between the results using the general formula and the results obtained using the midpoint formula. This is normal. When specific price and quantity data are available for a particular price range, then the midpoint formula is the preferred method. Alternatively, if all you are given is percentage changes (e.g., the price of milk increases by 10% and the quantity demanded drops by 15%), then you should use the general formula. Here, the elasticity would be 1.5, which is elastic.

Two extreme cases of elasticity are as follows:

The price increases from $2.00 to $2.20 but the quantity demanded remains the same at 100. This is the limiting case of perfectly inelastic demand and seems to contradict the law of demand. In practice, products whose demand might approach perfect inelasticity could include medical prescriptions or medical devices with life or death consequences for a patient. We would not expect to find a perfectly inelastic result over a wide price range, nor would we expect such a result for a large market, such as medical patients who use a certain type of blood pressure medicine. If the price range is narrow (e.g., $2.00 to $2.20) and the market is narrowly defined (e.g., your individual household demand), then such a result is possible.
The price rises from $2.00 to $2.20 and the quantity demanded drops all the way from 100 to 0. This is the largest possible quantity demanded response and is known as perfectly elastic demand. The elasticity result would be very large. The concept is similar to a soybean farmer raising his price from $5.00 to $5.10 per bushel and finding that his sales drop to zero, since no one will buy from him at an above market price of $5.10. He operates in a purely competitive market structure (more about that later) and is a pure price taker at the market determined price. Such a farmer faces a demand curve that is horizontal, or perfectly elastic. In other words, the farmer can sell any quantity he chooses at the market determined price. This type of demand curve is as responsive as it can possibly be to a price increase because sales would fall to zero. Note that the farmer would not consider lowering his price because the conditions in a perfectly competitive market are such that any quantity may be sold at the market determined price, so it would be irrational to sell below the market price.

On pp. 518-519, note the author's presentation of the determinants of elasticity. Based on these factors, how would you classify your own demand for the economics text you are using in this course? You probably answered inelastic because it is necessary for the course and there are no good substitutes for it.

Note the discussion of elasticity and total revenue on pp. 520-521. An easy way to remember the total revenue test for elasticity is: if price and total revenue (not quantity) move in the same direction, demand is inelastic. If they move in opposite directions, demand is elastic. If total revenue remains the same in response to a price change, demand is unit elastic. If you have two different price-quantity combinations, just multiply the first combination to find the starting total revenue amount; then multiply the second combination and find the new total revenue number. If price increased and total revenue increased, demand is inelastic, or if price decreased and total revenue decreased, demand is inelastic. But if price increased and total revenue fell, demand is elastic or, if price decreased and total revenue increased, demand is elastic.

Although price elasticity is the major elasticity type, there are others. These are presented on pp. 523-526. One of these other elasticity types is known as cross-price elasticity of demand. A price change for one product leads to a quantity demanded change for another, related product, either a substitute or a complement. Suppose the price of Pepsi goes up 10% and the sales level for Coke increases 20%. The elasticity result = 20/10 = + 2. Note that the positive or negative sign is retained when figuring cross elasticity. The plus sign indicates that the goods are substitutes. The value 2 says that the result is elastic, meaning that the two products are close substitutes. Alternatively, if the price of coffee increased 10% and the quantity demanded of tea went up 2%, then the cross-price elasticity would be 2/10 = +.2, which would be an inelastic result. This indicates that these two products are weak substitutes.

Now suppose we have two products that are often used or consumed together, sometimes referred to as complements. The price of jelly rises by 10% and the quantity demanded of peanut butter drops by 6%. The cross-price elasticity would be -6/10 = -.6, which is inelastic. The negative sign indicates the products are complements and the .6 value says that while the two goods are related, the responsiveness is limited. If, in response to the 10% increase in the price of jelly, the quantity demanded for peanut butter had dropped by 18%, then the elasticity result would = -18/10 = -1.8, which is elastic. Again, the minus sign signifies complements and the value greater than one shows relative responsiveness to the price change.

Another elasticity type is income elasticity. Again, the positive or negative sign is retained. Suppose household income increases by 10% and the quantity demanded of pizza increases by 15%. Income elasticity = 15/10 = + 1.5, which is positive and elastic. The plus sign means the good is normal (i.e., more income leads to more demand; less income leads to less demand) and the value greater than one indicates relative responsiveness, or an elastic result. On the other hand, if your income went up 10% and the quantity demanded for pizza increased by 5%, then income elasticity = 5/10 = .5, which is an inelastic result.

Now suppose your income increased 10% and your quantity demanded for macaroni and cheese declined 16%. The income elasticity result = -16/10 = -1.6, which means the good is inferior (i.e., more income results in less demand; less income leads to more demand). The result is elastic because the value exceeds 1. The minus sign signifies inferior goods. If, in response to the 10% increase in income, your quantity demanded for macaroni and cheese had dropped by 7%, then the income elasticity = -7/10 = -.7, which indicates inferior goods with an inelastic response.

For both cross elasticity and income elasticity the sign is retained in order to classify the result as substitutes/complements or normal/inferior. After doing this, take the absolute value of the numerical result, just as you would for the standard price elasticity, to determine whether the result is elastic or inelastic.

Look at the presentation on elasticity and taxes on pp. 529-532. When it comes to taxes on cigarettes, liquor, and other excise taxes , government will tend to tax products that are associated with inelastic demand. Based on your understanding of the explanations given above, you should understand why government does this. Let me know if you are not sure.

Study the chapter summary on page 532.

You have now completed your second reading assignment.

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