elasticity – summary information - net

Dr. Gary Stone, Winthrop University

Elasticity – Summary Information

Name of Elasticity

Ratio

Categories

Value

price‐elasticity of demand

Ed = %'QdX %'PX

Demand for Good X is elastic

over this price range.

|Ed| > 1.0

Demand for Good X is unitary elastic over this price range.

|Ed| = 1.0

Demand for Good X is

inelastic over this price range.

|Ed| < 1.0

cross‐price elasticity of demand

ECP = %'DX %'PW

X and W are substitutes

ECP > 0.0

X and W are complements

ECP < 0.0

X and W are unrelated goods

ECP = 0.0

income‐elasticity of demand

EI = %'DX %',

X is a normal, luxury good

EI > 1.0

X is a normal, necessity good

0 < EI < 1.0

X is an inferior good

EI < 0.0

price‐elasticity

of supply

Es = %'QsX %'PX

Supply of Good X is elastic


Es > 1.0

Supply of Good X is unitary elastic over this price range.

Es = 1.0

Supply of Good X is inelastic


Es < 1.0

Ed and total revenue: 1. If demand is elastic, price and total revenue move in opposite directions. 2. If demand is inelastic, price and total revenue move in the same direction. 3. If demand is unitary elastic, total revenue is unaffected by a change in price.

A Basic Primer on the Concept of Price-Elasticity of Demand

The law of demand states if the price of a good rises (falls), consumers will want to buy less (more) of the good, other things being constant. The concept of price-elasticity of demand goes beyond this to give information on how strongly consumers respond to the price change. Another way of looking at these two concepts is to say when the price of a good changes, the law of demand tells you the direction of the consumers’ response (whether they buy more or less) and the price-elasticity of demand tells you the strength of that response. Definition: The price-elasticity of demand (Ed) for a product is a number that indicates the degree of consumer response to a change in the price of that product. Ed is the ratio of the percentage change in quantity demanded divided by the percentage change in price. Example #1 A firm lowers the price of its good by 8% and consumers increase their quantity demanded by 4%. Find the value of Ed over this price range. Ed = +4% = -0.5

-8% Example #2 A firm lowers the price of its good by 5% and consumers increase their quantity demanded by 10%. Find the value of Ed over this price range. Ed = +10% = -2.0

-5% Example #3 A firm lowers the price of its good by 7% and consumers increase their quantity demanded by 7%. Find the value of Ed over this price range. Ed = +7% = -1.0

-7% Since the law of demand states price and quantity demanded move in opposite directions, Ed will be a negative number. When interpreting Ed, economists consider its absolute value. Thus, Ed = -0.5 is regarded as Ed = +0.5 for purposes of interpretation. This chart shows you how to interpret the value of Ed.

If the absolute value of Ed is: Over this price range demand is:

greater than 1.0 elastic equal to 1.0 unitary elastic less than 1.0 inelastic

Note: The same approach is used if the firm increases its price and consumers decrease the quantity demanded of the good. If price is increased by 8% and the quantity demanded falls by 4%, Ed = -4% = - 0.5. +8%

DIFFERENT VIEWS OF AN EXAMPLE OF PRICE-ELASTICITY OF DEMAND

There are different ways of looking at the concept of price-elasticity of demand. These descriptions all refer to the same example. [Note: In calculating percentage changes in price and quantity demanded, use the average value of P or Q as your base.] View 1. A firm increases the price of its product from $48 to $52. As a result the number of units of its product demanded by consumers falls from 824 per week to 776. The percentage change in price is ______ while the percentage change in quantity demanded is _______. The value of the price-elastically of demand is _______. View 2. As a result of raising its price by 8.0%, a firm finds that the number of units it sells per week falls by 6.0%. This indicates that over this price range the demand for the good is (elastic, inelastic). View 3. Use the graph below to calculate the price-elasticity of demand for the range of the demand curve between points A and B. Ed = _______. [You will get the same answer whether you assume the price changes from $48 to $52 as you will if you assume the price changes from $52 to $48.] View 4. P__ _Qd_ Total Revenue $48 824 $_________ $52 776 $_________ The fact that TR increases when P rises means over this price range demand is (elastic, inelastic). View 5. Suppose a firm knows that over a certain price range the price-elasticity of demand for its product is -0.75. This means that if its raises its price by 8.0%, the quantity of its product demanded will (rise, fall) by ______ %. View 6. The price-elastically of demand for a firm's product is estimated to be -0.75 over a certain price range. If the firm wants to increase the number of units it sells by 6.0%, it must (increase, decrease) its price by _______ %.

PRICE-ELASTICITY OF DEMAND, MARGINAL REVENUE, AND TOTAL REVENUE

1. The typical downward-sloping demand curve illustrates all three ranges of elasticity as indicated in the top graph. 2. As seen in the top graph, this firm faces a downward-sloping demand curve which means it must lower its price to sell additional units of output. Here is what happens as the price is lowered: (a) As the firm lowers its price from Po (where 0 units are demanded), the number of units demanded will increase. Initially output increases through the elastic range of the demand function. As price is reduced in the elastic range to sell these extra units the firm’s total revenue will increase. [The “total revenue test” says that if price is lowered when demand is elastic, total revenue will rise.] Because total revenue increases with each extra unit we know the marginal revenue of these units is positive. Hence, in the elastic range of the demand curve marginal revenue is positive. [Marginal revenue declines as more output is sold because of the need to lower price to sell extra output.] (b) As price is lowered to sell more output, the firm eventually will reach output level Q1 where demand is unitary elastic. At Q1 total revenue will be maximized and marginal revenue is zero. [The total revenue test shows that if price is lowered when demand is unitary elastic there will be no change in total revenue.] (c) If the firm reduces price to levels that will make consumers want to buy more than Q1 units, it has moved into the inelastic range of the demand curve. A price reduction in this range causes total revenue to fall which means the marginal revenue from extra output units in this range is negative. 3. It is a fact that for a straight-line, downward-sloping demand curve, the demand curve will hit the horizontal (quantity) axis at twice the output level at which the marginal revenue curve hits that axis which means Q2 is twice as great as Q1. In this case the marginal revenue function is twice as steep as the demand function. 4. The relationship between price-elasticity of demand (Ed) and marginal revenue is shown by the following equation. When using this equation, use the actual (negative) value of Ed rather than the absolute value of Ed. For example, if Ed = -1.2 and P = $40, then MR = (40)[1 + (1/-1.2)] = (40)[1 – 0.833] = (40)(0.167) = $6.68.

Connecting Demand, Ed and Total Revenue

Here is an activity that will show why total revenue rises and then falls when a firm must lower its price to sell more output.

1. Draw a linear downward‐sloping demand curve which hits the vertical P axis at $30 and the horizontal Q axis at 60 units. (The equation of this demand function is Q = 60 – 2P.) The graph should contain these seven combinations of P and Q. (Leave the total revenue data out of the chart initially.)

Point

Price (P)

Quantity Demanded (Q)

Total Revenue (TR)

A $30 0 B $25 10 C $20 20 D $15 30 E $10 40 F $ 5 50 G $ 0 60

2. Now draw another graph directly below the demand graph. Label the vertical axis as “TR” and the horizontal axis as “Q”. Have the same Q values on the horizontal axis of each graph.

3. The negative slope of the demand curve reflects the Law of Demand (when P rises, Qd falls). The demand curve has a constant slope because each time P falls by $5, Q rises by 10 units. The slope equals (change in P)/(change in Q) = (‐$5)/(+10 units) = ‐0.5.

4. Complete the “TR” column in the chart and place dots on the lower graph for each combination of Q and TR in the chart. Draw a smooth curve which connects those dots. This is the TR curve which begins at the origin, rises until it peaks at Q = 30, then declines until TR = $0 at Q = 60. On the vertical axis write the dollar values of TR for each level of output.

5. Here are some facts about your two graphs.. (a) If a firm faces a downward‐sloping demand curve, it must lower its price to sell more output. (b) The upper half of the demand curve is the “elastic” range. When price is lowered here, the firm’s total revenue will increase as it sells more units of output. (c) The demand for the good is “unitary elastic” at the mid‐point of the demand curve. Here, total revenue is maximized. (d) The lower half of the demand curve is the “inelastic” range. When price is lowered here, the firm’s total revenue will decrease as it sells more units of output.

Why Ed Has a Different Value at Each Point on a

Linear, Downward‐sloping Demand Curve

The graph below shows a linear, downward‐sloping demand curve. “Linear” means it is a straight line with constant slope all along its length. “Downward‐sloping” means that as the price decreases, the quantity demanded increases. In the case of this particular graph, each time the price falls by $1, the quantity demanded increases by 2 units. (The equation of this demand curve is Qd = 200 – 2P.)

slope = rise = change in P = 'P = ‐$1 = ‐0.5 run change in Qd 'Qd +2 units

price‐elasticity of demand = Ed = % change in Qd = %'Qd % change in P %'P

This chart shows the effect of reducing price by $4 in three different ranges of the demand curve. The “B to C” shift is in the top half of the demand curve. The “H to J” shift is centered at the mid‐point of the demand curve. The “V to W’ shift is in the bottom half of the demand curve. In each range, the $4 drop in price results in an 8 unit increase in quantity demanded. This reflects the constant slope of the demand curve all along its length.

actual average actual average change P1 P2 'P P Q1 Q2 'Qd Qd %'P %'Q Ed B to C $70 $66 ‐$4 $68 60 68 +8 64 ‐5.9% +12.5% ‐2.12 H to J $52 $48 ‐$4 $50 96 104 +8 100 ‐8.0% +8.0% ‐1.00 V to W $31 $27 ‐$4 $29 138 146 +8 142 ‐13.8% +5.6% ‐0.41

Note, however, that the average values of P and Qd are different at each point on the demand curve. Thus, the percentage changes in P and Qd will be different at each point as well. A $4 price change is a smaller percentage change in the “B to C” range than in the “V to W” range because the average value of P is larger in the “B to C” range than in the “V to W” range. Similarly, an 8 unit change in Qd is a smaller percentage change in the “V to W” range than in the “B to C” range because the average value of Q is larger in the “V to W” range than in the “B to C” range. As a result, the value of Ed is different at every point on the demand curve. Rules for a linear, downward‐sloping demand curve: 1. Demand is elastic in the upper half of the demand curve. 2. Demand is unitary elastic at the mid‐point of the demand curve. 3. Demand is inelastic in the lower half of the demand curve. In the upper half of the demand curve (e.g., B to C), the $4 drop in price produces a %'Qd which is larger than the %'P. As a result, the absolute value of Ed is greater than one (elastic). In the lower half of the demand curve (e.g., V to W), the $4 drop in price produces a %'Qd which is smaller than the %'P. As a result, the absolute value of Ed is less than one (inelastic). In the middle of the demand curve (e.g., H to J), the $4 drop in price produces a %'Qd which is equal to the %'P. As a result, the absolute value of Ed is equal to one (unitary elastic). _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Unique Demand Curves Where Ed is Constant All Along the Curve: 1. If the demand curve is vertical, there is no change in Qd when the P changes. Thus, the value of Ed = 0 at every point on the curve. This means demand is “perfectly inelastic” at every point. 2. If the demand curve is horizontal, there is an infinite response in Qd to even a very small change in P. Thus, the value of Ed = infinity at every point on the curve. This means demand is “perfectly elastic” at every point. 3. If the demand curve is a rectangular hyperbola, the %'Qd is equal to the %'P all along the curve. In this unique situation, the value of Ed = ‐1.0 at every point on the curve. This means demand is “unitary elastic” at every point.

I. Income elasticity of demand (EI) is a measure of how responsive the demand for a particular good is to a change in the income of consumers. For a typical good an increase in income leads to an increase in its demand. Such a good is called a "normal good" or a "superior good." In the case of an "inferior good" an increase in income leads to a fall in the demand for the good. EI indicates the strength of the demand change resulting from an income change. It is the ratio of the percentage change in demand divided by the percentage change in income. As an example, suppose that as a result of consumer income increasing by 5%, the demand for Country Valley Bicycles increases by 8%. The value of EI is found using the following ratio: EI = % change in demand = + 8% = + 1.60 % change in income + 5% The EI value of +1.60 means that for each 1% increase in income there was a 1.6% increase in demand. Note that the "sign" of EI tells you what type of good it is (normal or inferior) while the "size" of EI indicates the strength of the response in demand to the income change. Use the following table to interpret values of EI: Value of EI Type of Good Under Consideration 1. EI > 0.0 1. The good is a normal (superior) good. (a) 0.0 < EI < 1.0 (a) The good is a necessity. (b) EI > 1.0 (b) The good is a luxury. 2. EI < 0.0 2. The good is an inferior good. II. Cross-price elasticity of demand (Ecp) is a measure of how strongly the demand for one good responds to a change in the price of another good. It is useful in determining if two goods are substitutes or complements and the strength of the relationship between the two goods. (Are they close substitutes such as Pepsi and Coke?) Assume the price of a Rocky Road Bicycle increases by 9.5% while the price of a Country Valley Bicycle is unchanged. This means that consumers will want to buy more CVBs than they did before. [It does not mean that they will want to buy more CVBs than RRBs; we would need to see the demand schedule for RRBs to know that.] Assume the demand for CVBs increases by 11.8%. The value of Ecp is found using the following ratio: Ecp = % change in demand for CVBs = + 11.8% = +1.24 % change in price of RRBs + 9.5% Refer to this table to interpret the value of Ecp: Value of Ecp Relationship Between the Two Goods 1. Ecp > 0.0 1. The goods are substitutes. 2. Ecp < 0.0 2. The goods are complements. 3. Ecp = 0.0 3. The goods are unrelated. The "sign" of Ecp tells us the nature of the relationship that exists between the two goods while the "size" of Ecp indicates the strength of that relationship. In our example we're not surprised to find Ecp is a positive number since we know these two kinds of bicycles are substitutes for each other. Since skateboards and bicycles are weaker substitutes than are our two types of bicycles, we would expect the cross-price elasticity of demand between CVBs and skateboards to be positive, but smaller than the value 1.24.

INCOME ELASTICITY OF DEMAND AND CROSS-PRICE ELASTICITY OF DEMAND

Es = (% change in Qs) / (% change in P) Expect Es to be a positive number because of the Law of Supply (if P rises, then Qs rises). For interpretation purposes, look at Es’s actual value. Actual Value of Es Interpretation > 1.0 Supply over this price range is elastic < 1.0 Supply over this price range is inelastic = 1.0 Supply over this price range is unitary elastic There is no relationship between TR and Es since TR = P x Qd and thus is based on how many units consumers buy rather than how many units producers put on the market for sale. Other things equal (ceteris paribus), the flatter a Supply curve is, the relatively more elastic it is. See Graph #3.

(a) S1 is a perfectly elastic S curve all along its length since it is horizontal. (b) S2 is a perfectly inelastic S curve all along its length since it is vertical. (c) S3 is unitary elastic all along its length since it is a straight line intersecting

the origin. The value of Es will be 1.0 all along the length of S3. (d) S4 is elastic all along its length since it is a straight line intersecting the

vertical axis. The value of Es varies all along the length of S4. (e) S5 is inelastic all along its length since it is a straight line intersecting the

horizontal axis. The value of Es varies all along the length of S5.

Price-elasticity of supply - measures the strength of producers’ response to a price change

Price Elasticity of Supply

1. When the Breazeale Company changed the price of its landscaping service from $97 to $103, the quantity demanded of its service changed from 84 jobs to 76 jobs per week. (Show your work.)

(a) The percentage change in price is ______. (b) The percentage change in quantity demanded is ______. (c) The numerical value of the price-elasticity of demand is ______.

2. When income rises by 4.5%, the demand for Good X falls by 3.1%.

(a) The numerical value of the income-elasticity of demand for Good X is ________. (b) Based on your answer to (a), an economist would say Good X is a(n): (1) normal, necessity good (2) normal, luxury good (3) inferior good 3. When the price of Good A falls by 5.3%, the demand for Good B rises by 4.1%.

(a) The numerical value of the cross-price elasticity of demand between A and B is ______. (b) Based on your answer to (a), an economist would say A and B are: (1) substitute goods (2) complementary goods (3) unrelated goods 4. You are given the demand curve facing a monopoly selling Good X. In the top graph add the marginal revenue curve. In the bottom graph add the total revenue curve. Be accurate.

Elasticity Practice Set 1

When the Anchors Away Boat Company changes the price of its Carolina Breeze sailboat from $14,500 to $15,500, the number of boats it sells changes from 88 boats per year to 76 boats.

1. The percentage change in the price of the Carolina Breeze sailboat is ( +, ‐ ) ________% Show your work: 2. The percentage change in the quantity demanded of the sailboat is ( +, ‐ ) ________% Show your work: 3. The value of the price‐elasticity of demand over this price range is ( +, ‐ ) _________. Show your work: 4. The total revenue of the company changes from $_______________ to $______________. Show your work: 5. Demand over this price range is ( elastic, unitary elastic, inelastic ).

Price‐Elasticity of Demand Practice Set 2

1. When the price of Good W falls by 8%, the quantity demanded of Good W rises by 3%.

(a) The demand for Good W over this price range is (elastic, unitary elastic, inelastic).

(b) The calculated value of Ed over this price range = ‐ ________. Show your work:

(c) Total revenue to sellers of Good W will (increase, not change, decrease). 2. When the price of Good B rises by 5%, the quantity demanded of Good B falls by 12%.

(a) The demand for Good B over this price range is (elastic, unitary elastic, inelastic).

(b) The calculated value of Ed over this price range = ‐ ________. Show your work:

(c) Total revenue to sellers of Good W will (increase, not change, decrease). 3. When the price of Good J changes from $57 to $63, the quantity demanded of Good J changes from 2,040 units to 1,960 units per week.

(a) The percentage change in the price of Good J is + / ‐ _______%. Show your work:

(b) The percentage change in the quantity demanded of Good J is + / ‐ ________%. Show your work:

(c) Total revenue from the sale of Good J changed from $____________ to $__________. Show your work:

(d) Demand for Good J over this price range is (elastic, unitary elastic, inelastic).

(e) The calculated value of Ed over this price range = ‐ ________. Show your work:

(f) The absolute value of Ed over this price range = _________.

Price‐Elasticity of Demand Practice Set 3

1. When the price of airplane tickets from Charlotte to St. Louis changes from $365 to $405, the number of tickets demanded changes from 770 to 740 per month.

(a) The percentage change in price is: + / ‐ __________% Show your work:

(b) The percentage change in quantity demanded is: + / ‐ __________% Show your work: (c) The value of the price‐elasticity of demand over this price range is: Ed = _________. 2. By reducing its price by 5%, the Winthrop Company sees its total revenue increase. From this information, we know the quantity demanded of Winthrop’s product (increased, decreased) by (more, less) than 5% as a result of the price change.

3. When the price of Good A fell by 3%, the demand for Good B rose by 2%, the demand for Good C fell by 6%, the demand for Good D rose by 5%, and the demand for Good E fell by 1%. (a) Which goods are substitutes for Good A? B C D E (b) Which goods are complements to Good A? B C D E

4. When consumer income increased by 5.2%, the demand for Good W rose by 2.3%, the demand for Good X fell by 4.0%, and the demand for Good Y rose by 7.1%. (a) Which goods are normal goods? W X Y (b) Which goods are inferior goods? W X Y (c) Which goods are necessity goods? W X Y (d) Which goods are luxury goods? W X Y

5. When the Homer Diamond Company lowers its price from $28.50 to $28.00, the number of units it sells increases from 49 to 50 units per day. (a) The marginal revenue of the 50th unit is $________. Show your work: (b) In which range of its demand curve is the firm operating? Explain how you know.

Price Elasticity of Demand Practice Set 4

1. When the price of the Waffle House All‐Star Special meal changes from $6.40 to $6.00, the number of meals demanded per day changes from 230 to 250.

(a) The percentage change in price is: + / ‐ __________% Show your work:

(b) The percentage change in quantity demanded is: + / ‐ __________% Show your work:

(c) The value of the price‐elasticity of demand over this price range is: Ed = _________.

2. By reducing its price by 4%, the Kinard Company sees its total revenue decrease. From this information, we know the quantity demanded of Winthrop’s product (increased, decreased) by (more, less) than 4% as a result of the price change.

3. When the price of Good A rose by 7%, the demand for Good B fell by 10%, the demand for Good C fell by 3%, the demand for Good D rose by 9%, and the demand for Good E rose by 4%. (a) Which goods are substitutes for Good A? B C D E (b) Which goods are complements to Good A? B C D E

4. When consumer income decreased by 3.7%, the demand for Good W fell by 4.2%, the demand for Good X fell by 2.8%, and the demand for Good Y rose by 1.6%. (a) Which goods are normal goods? W X Y (b) Which goods are inferior goods? W X Y (c) Which goods are necessity goods? W X Y (d) Which goods are luxury goods? W X Y

5. When the Catawba Cake Company lowers its price from $16.00 to $15.60, the number of cakes it sells increases from 60 to 61 units per day.

(a) The marginal revenue of the 61st unit is $________. Show your work: (b) In which range of its demand curve is the firm operating? Explain how you know.


When the price of Good X changes from $87 to $81, the quantity demanded of Good X changes from 775 to 865.

1. Total revenue changes from $____________ to $____________ as a result of this change in the price of Good X. Show your work: 2. Based on the results of part (a), an economist would conclude that the percentage change in the quantity demanded was (greater than, equal to, less than) the percentage change in the price.

3. This means that the demand for Good X over this price range is (elastic, unitary elastic, inelastic).

4. Let’s check out our answers to #2 and #3.

(a) The percentage change in P is: + / ‐ _________% Show your work:

(b) The percentage change in Qd is: + / ‐ _________% Show your work:

(c) The value of the price‐elasticity of demand (Ed) is: + / ‐ ________ Show your work: (d) The absolute value of Ed is: + / ‐ ___________. (e) Based on the answer to (d4), an economist would say the demand for Good X over this

price range is (elastic, unitary elastic, inelastic).


Elasticity Practice Review 1. When the price of Good A falls by 4%, the quantity demanded rises by 6%. Demand over this price range is (elastic, unitary elastic, inelastic). 2. The price-elasticity of demand for Papa John’s Pizza is -1.25. If Papa John’s decreases its price by 5%, the quantity demanded would increase by ________%. 3. When consumers’ income increases by 3.5%, the demand for Good A increases by 2.1%, the demand for Good B increases by 3.9%, and the demand for Good C decreases by 1.2%. (a) Good A is a(n) (normal necessity good, normal luxury good, inferior good). (b) Good B is a(n) (normal necessity good, normal luxury good, inferior good). (c) Good C is a(n) (normal necessity good, normal luxury good, inferior good). 4. As a result of the price of Good W decreasing by 6.2%, the demand for Good X increases by 3.4% and the demand for Good Y decreases by 2.1%. (a) Goods W and X are (substitute, complementary) goods. (b) Goods W and Y are (substitute, complementary) goods. 5. When the Ajax Company decreases the price of its product, its total revenue increases. Demand for its product is (elastic, unitary elastic, inelastic) over this price range. 6. The Crockett Company sells 2,000 units of its product each week at a price of $15. If the firm is operating in the inelastic range of its demand curve, what should it do with its price to increase its total revenue? It should (increase, not change, decrease) its price.

Dr. Gary Stone, Winthrop University

Ed Quick Check

1. When the price of Good M decreases by $20, the quantity demanded increases by 100 units. What does this tell us about the price-elasticity of demand for Good M over this price range? (a) Demand is elastic. (b) Demand is inelastic. (c) Demand is unitary elastic. (d) We cannot tell.

2. When a firm increases its price, its total revenue also increases. What does this tell us about the price-elasticity of demand for the firm’s product over this price range? (a) Demand is elastic. (b) Demand is inelastic. (c) Demand is unitary elastic. (d) We cannot tell.

3. The quantity demanded of Good W falls by 4% when the price of Good W rises by 7%. What does this tell us about the price-elasticity of demand for Good W over this price range? (a) Demand is elastic. (b) Demand is inelastic. (c) Demand is unitary elastic. (d) We cannot tell.

4. Which of the following ranges of the absolute value of Ed would tell us the demand for a product is elastic over a given price range? (a) greater than 0.0 (b) less than 0.0 (c) greater than 1.0 (d) less than 1.0

5. The price-elasticity of demand for Good Y good over a given price range equals -0.8 (Ed = -0.8). What does this tell us about the price-elasticity of demand for Good Y over this price range? (a) Demand is elastic. (b) Demand is inelastic. (c) Demand is unitary elastic. (d) We cannot tell.

elasticity – summary information - net

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