L04 - Elasticity

Total Revenue

Price x Quantity

Calculate the Price elasticity of demand, for the following examples: a) Demand is given by Q = 50 - P at the price of $10. b) Demand is given by Q = 100 - P, at the price of $50. c) Demand is given by Q = 25 - .25P, at the price of $40. d) Demand is given by Q = 20 - .1P, at the price of $80. e) Demand is given by Q = 60 - 1/3P, at the price of $60.

a) -.25 b) -1 c) -.667 d) -.667 e) -.5

If we have a linear demand curve, the price elasticity of demand --- as you move along a linear demand curve

changes

why can't one just use slope of a demand curve to determine the elasticity

the slope is sensitive to units of measurement (imagine using quarts vs. galloons) so instead of using changes in slope, we use percentage changes. When using percentages changes, the units do not matter.

if demand is of unitary elasticity

total revenue is unchanged when price changes. This occurs because the percentage change in quantity is exactly equal to the percentage change in price, and since they move in opposite directions, they exactly offset one another in the determination of total revenue.

The price elasticity of demand will always be - positive or negative

negative because price and demand are inversely related.

Elasticity

make sure you understand all three definitions/concepts provided below a set of measures of responsiveness of one variable to changes in another variable Elasticity is a concept in economics that deals with responsiveness - typically, the responsiveness of the quantity demanded or supplied to a change in price or income. Elasticity quantifies the response of one variable to changes in another variable. More formally, the elasticity of X with respect to Y equals the percentage change in X that results from a given percentage change in Y

perfectly inelastic demand

the case where the quantity demanded is completely unresponsive to price and the price elasticity of demand equals zero An extreme case where there is no responsiveness of quantity demanded to changes in price - that is, there is zero change in quantity demanded when price changes. This would occur with a demand curve that is vertical. Elasticity is thus equal to zero.

perfectly elastic demand

the case where the quantity demanded is infinitely responsive to price and the price elasticity of demand equals infinity An extreme case where quantity demanded would decline to zero (a 100 percent decline) with the slightest increase in price. This would occur with a horizontal demand curve. It entails a very high elasticity (minus infinity, at the limit)

total revenue is maximized when the absolute value of the elasticity of demand equals

1

Determinants of the Price Elasticity of Demand What factors result in demand being elastic or inelastic? There are three key factors that are relevant.

1. the availability of substitutes 2. the share of expenditures on the product as a fraction of the consumer's total expenditures 3. the time consumers have to react to a price change

Inelastic demand

A situation in which an increase or a decrease in price will not significantly affect demand for the product occurs when the absolute value of the percentage change in quantity demanded is smaller than the absolute value of the percentage change in price. The responsiveness of quantity demanded to changes in price is comparatively small, and the calculated elasticity will be between zero and -1. For example, if a 10 percent increase in price resulted in a 5 percent decline in the quantity demanded, this would entail an elasticity of -0.5.

Unitary elasticity of demand

The absolute value of the price elasticity of demand is equal to 1. The percentage change in quantity demanded is just equal to the percentage change in price. refers to a demand relationship in which the percentage change in quantity demanded is exactly equal in absolute value to the percentage change in price. This entails greater responsiveness of quantity demanded to changes in price, and the calculated elasticity is -1.

Marginal Revenue (MR)

the change in revenue total revenue that occurs when we change output (Q) by one unit

If demand is elastic then total revenue will change in the same direction as the change in quantity and in the direction opposite to the change in price; while if demand is inelastic then total revenue will change in the same direction as the change in price and in the direction opposite to the change in quantity.

If demand is elastic then total revenue will change in the same direction as the change in quantity and in the direction opposite to the change in price; while if demand is inelastic then total revenue will change in the same direction as the change in price and in the direction opposite to the change in quantity.

share of expenditures on the product as a fraction of the consumer's total expenditures

If expenditures on a product are only a small portion of a consumer's total expenditures, demand will be inelastic, while if expenditures are substantial, demand will be more elastic. A good example here is salt - it's something almost all of us buy, but it costs so little that we can easily absorb a substantial percentage increase in price.

elasticity of demand and total revenue

One of the reasons why elasticity of demand is an important concept in economics is that it helps us understand the different possible consequences for the total revenue of producers when price changes. Total revenue equals the price received times the quantity sold - i.e., a producer who sells 50 units of a product for $12 per unit earns a total revenue of $600. We can express this as TR = P x Q. But what happens to his total revenue if he raises his price to $13 per unit, or if he lowers his price to $11 per unit? Many people intuitively think that raising price will also raise total revenue, but this will only be true when demand is inelastic (i.e., when the percentage change in quantity demanded is smaller than the percentage change in price). If demand is elastic, the percentage change in quantity demanded is bigger (in absolute value) than the percentage change in price, so a price increase will in fact result in lower total revenues. Likewise, a decline in price will result in an increase in quantity demanded, but the impact on total revenue will depend on the elasticity of demand. If demand is elastic, a price decline will increase total revenue, while if demand is inelastic, a price decline will reduce total revenue.

availability of substitutes

The greater the availability of close substitutes for a good or service, the more elastic will be the demand (if a product increases in price, the availability of substitutes will lead to a greater decrease in the original product quantity demanded (= greater elasticity with the availability of substitutes) than if there are no substitutes available). Conversely, a product or service for which there are no close substitutes will likely confront a fairly inelastic demand. When price increases, the consumer has an incentive to substitute away from the good in question, but her ability to do so (and hence reduce her quantity demanded) will depend on the availability of substitutes.

cross-price elasticity of demand

This measures the responsiveness of the quantity demanded of one good to changes in the price of another good. More formally, the cross-price elasticity of demand for Y with respect to X is the percentage change in the quantity of Y demanded in response to a given percentage change in the price of X. The cross-price elasticity of demand, like the income elasticity of demand, may be either positive or negative. When X and Y are substitutes, their cross-price elasticity of demand will be positive, since an increase in the price of X will increase demand for Y and ultimately the quantity demanded of Y. Conversely, if X and Y are complements, the cross-elasticity of demand will be negative, since an increase in the price of X will reduce demand for Y and ultimately reduce quantity demanded of Y.

For a demand curve, at a particular price, you determine the price elasticity of demand to be -2/3. What does this mean?

When the price changes by 1%, the quantity demanded will change by 2/3 of a percent (and that too in the opposite direction). So, if the price increases by 1%, demand will decrease by 2/3 of a percent. If the price decreases by 1%, the quantity demanded will increase by 2/3 of a percent. This should make sense because the slope of a demand curve is negative (= inverse relationship between price and demand).

Use the midpoint formula to calculate the price elasticity of demand for each of the following: a) Demand is given by P = 20 - QD, between the prices of $5 and $6. b) Demand is given by P = 10 - .2QD, between the prices of $1 and $2. c) Demand is given by P = 20-.2QD, between the prices of $12 and $13. d) Demand is given by P = 50 - QD, between the prices of $10 and $11. e) Demand is given by P = 150 - 7.5QD, between the prices of $30 and $45.

a) -.379 b) -.176 c) -1.67 d) -.266 e) -.333

law of supply

supply curves slope upward - an increase in price will draw forth an increase in quantity supplied (but by how much - elasticity will answer this question)

When the price of bagels is $.50, the quantity demanded is 4300. When the price rises to $1.50, the quantity demanded is 3600. What is the price elasticity of demand?

0.177 The price elasticity of demand is calculated as the percent change in quantity demanded divided by the percent change in price.

Assume that the absolute value of the price elasticity of demand for a slice of pizza is 4. If price decreases by 3%, by how much does quantity demanded increase?

12% If price decreases by 3%, and the price elasticity of demand is 4, then the quantity demanded increases by 4*3% = 12%.

For a demand curve, as P (price) increases, Q (quantity demanded) decreases. What does this mean for elasticity?

At higher values of P, as we move to higher prices, demand becomes more elastic (quantity demanded decreases by a greater percentage than at lower values of P)

Suppose the demand for crossing the Harbor Tunnel in Baltimore is given by:Qd=10,000-1000*P. a. If the toll (price) is $2, how much total revenue is collected? b. Using the mid-point formula discussed in class and the book, calculate the price elasticity of demand between the prices of $2 and $3. c. Given your answer to b, is the demand for crossing the bridge elastic, inelastic, or unitary elastic? d. If the bridge authorities want to increase their total revenue, should they increase or decrease the price from $2? e. Suppose a ferry service begins operation, offering a different way to cross the water. Carefully explain what effect this is likely to have on the price elasticity of demand for crossing the bridge. f. Use the point slope formula to calculate the Price Elasticity of Demand when Price = $2. Hint: it will be useful to use the inverse demand function. The demand curve above can be written as P = 10 - .001Qd g. Use the point slope formula to calculate the Price Elasticity of Demand when Price = $5.

a) Qd = 10,000-1000P. If P = $2, then Quantity = 8000. Therefore total revenue = P*Q = $2*8000 = $16,000. b) When P = $2, Qd = 8000. When P = $3, Qd = 7000. Using the midpoint formula, the % change in Qd = (7000-8000)/7500. The % change in Price = (3-2)/2.5. The % change in Qd divided by the % change in Price = PED = -1/3. c) Inelastic d) Since Price Elasticity of Demand is inelastic, total revenue will increase if the price increases. e) The availability of more substitutes will tend to make demand MORE ELASTIC. f) -.25 g) -1

Suppose the demand for the Notre Dame-Penn State football game is given by:Qd = 200,000-2000*P. a) If the ticket price is $60, how much total revenue is collected? b) What is the price elasticity of demand when the price is $60? c) If Penn State wants to increase their total revenue, should they increase or decrease the price from $60? d) What price should Penn State charge if they want to maximize their revenue? (Hint: remember that revenue is maximized when ε = -1). e) Over what price range is demand inelastic?

a) TR = $4,800,000 b) -3/2 or -1.5 c) Decrease d) P = $50 e) $0 < P < $50

The price elasticity of demand measures the responsiveness of quantity demanded to a change in a) a good's own price b) consumer income c) consumer tastes d) the price of a competing product

a) a good's own price The price elasticity of demand measures the magnitude of the change in quantity demanded resulting from a change in price.

Demand tends to be relatively inelastic a) in more broadly defined markets b) in the long run c) when there are many substitutes available d) when the good is a luxury

a) in more broadly defined markets

A 10% rise consumer income results in a 4% decrease in the quantity demanded for pasta. The income elasticity of demand for pasta is a) negative, so pasta is an inferior good b) positive, so pasta is an inferior good c) negative so pasta is a normal good d) positive so pasta is a normal good

a) negative, so pasta is an inferior good When an increase in income leads to a reduction in the quantity consumed, the good is described as inferior.

Suppose you are a producer that sells products to two groups of buyers. These groups of buyers have no contact with one another. Group 1 has a relatively elastic demand curve and group 2 has a relatively inelastic demand curve. If your goal is to maximize total revenue you should a) charge both groups the same price b) charge group 1 a lower price than group 2 c) charge group 2 a lower price than group 1 d) increase the price to both groups

b) charge group 1 a lower price than group 2 When demand is elastic, a decrease in price will increase total revenue.

The flatter (more horizontal) a supply curve is, the more _____ the supply curve is. a) inelastic b) elastic c) unit elastic d) perfectly inelastic

b) elastic

You are hired as an economic consultant for an online store that sells music downloads. Currently each download costs $.98. Your assignment is to increase the firm's total revenue. Your research indicates that the industry wide price elasticity of demand for music downloads is equal to 2.6 in absolute value. You recommend that the firm change the price per download to a) $.95 since demand is inelastic b) $1.05 since demand is elastic c) $.95 since demand is elastic d) $1.05 since demand is inelastic

c) $.95 since demand is elastic When the price elasticity of demand is greater than one in absolute value, the demand is elastic.

On a downward sloping demand curve, total revenue is at its maximum a) on the upper portion of the demand curve b) on the lower portion of the demand curve c) at the midpoint of the demand curve d) when price is highest

c) at the midpoint of the demand curve (where we have unitary elastic demand)

You own a bagel shop on College Ave. You hear a news report that says that consumer income has risen by 10%. After this report you notice that the amount of bagels you sell has decreased by 5%. In this case the income elasticity of demand is a) greater than one in absolute value, so the demand for bagels is income inelastic b) less than one in absolute value, so the demand for bagels is income elastic c) less than one in absolute value, so the demand for bagels is income inelastic d) greater than one in absolute value, so the demand for bagels is income elastic

c) less than one in absolute value, so the demand for bagels is income inelastic The income elasticity of demand is calculated as the percent change in quantity demanded divided by the percent change in income.

When the percent change in price is equal to the percent change in quantity demanded, we say that the demand is a) elastic b) inelastic c) unit elastic d) perfectly inelastic

c) unit elastic When the percent change in price is equal to the percent change in quantity demanded, the demand curve can be described as unit elastic.

You own a bagel shop on College Avenue. Currently you charge $.50 per bagel and total revenue is $300. You decide to increase your per bagel price to $.75. You notice however that total revenue stays at $300. This information suggests that your bagel shop faces a _______ demand. a) inelastic b) elastic c) unitary elastic d) perfectly elastic

c) unitary elastic When price changes and total revenue remains unchanged, demand is unit elastic.

Demand tends to be more elastic a) in more broadly defined markets b) in the short run c) when there are many substitutes available d) when the good is a necessity

c) when there are many substitutes available Goods that have many available substitutes have relatively elastic demands.

When the price elasticity of demand is larger than 1 in absolute value, demand is a) unit elastic b) perfectly elastic c) inelastic d) elastic

d) elastic

law of demand

demand curves slope downward - i.e., a decrease in price will result in an increase in quantity demanded (but by how much - elasticity will answer this question)

Elastic demand

demand in which changes in price have large effects on the amount demanded exists when the responsiveness of quantity demanded to changes in price is comparatively large - i.e., when the absolute value of the percentage change in quantity demanded exceeds the absolute value of the percentage change in price. For example, if a 10 percent increase in price resulted in a 20 percent decline in quantity demanded, the calculated elasticity would be -2. More generally, elastic demand corresponds to calculated elasticity where the absolute value exceeds 1.

Income elasticity of demand

measures the responsiveness of quantity demanded to changes in income. More specifically, it measures the percentage change in quantity demanded of a good associated with a given percentage change in income. Ordinarily, we expect that increases in income will lead to increases in the quantity demanded of a good or service (this is what economists refer to as a normal good), so the income elasticity of demand will ordinarily be positive. However, it is possible that increases in income are associated with a decline in quantity demanded; this would entail a negative income elasticity of demand, and this is called an inferior good.

price elasticity of supply

measures the responsiveness of quantity supplied to changes in price. This is defined in a corresponding manner to the price elasticity of demand, being equal to the percentage change in quantity supplied divided by the percentage change in price, either along some span of a supply curve or at a point on the curve. According to the Law of Supply, we expect supply elasticity for production of goods and services to be positive.

time consumers have to react to a price change

the longer the time frame under consideration, the greater the ability of consumers to adjust to price changes, and hence the more elastic will be demand. For example, if the price of gasoline doubles today, quantity demanded in the next week or month will decline somewhat, as more drivers opt to walk instead of drive when they can do so, or to take mass transportation. But in the next year, some consumers are likely to respond to the sharp increase in the price of gasoline by purchasing more fuel-efficient vehicles, thereby reducing their quantity of gasoline demanded even more than in the short term.

price elasticity of demand

the percentage change in quantity demanded in response to a given percentage change in price