Advertising elasticity of demand calculator

Plotting the demand curves. Calculating equilibrium price and quantity

The following relations describe demand and supply conditions in the lumber/forest products industry

QD = 80,000 - 20,000P (Demand)

QS = -20,000 + 20,000P (Supply)

where Q is quantity measured in thousands of board feet (one square foot of lumber, one inch thick)

and P is price in dollars.

A. Set up a spreadsheet to illustrate the effect of price (P), on the quantity supplied (QS), quantity

demanded (QD), and the resulting surplus (+) or shortage (-) as represented by the difference between

the quantity supplied and the quantity demanded at various price levels. Calculate the value for each

respective variable based on a range for P from $1.00 to $3.50 in increments of 104 (i.e., $1.00, $1.10,

$1.20, . . . $3.50).

B. Using price (P) on the vertical or y-axis and quantity (Q) on the horizontal or x-axis, plot the

demand and supply curves for the lumber/forest products industry over the range of prices indicated

previously. What is the equilibrium price and quantity?

SOLUTION

A. A table or spreadsheet that illustrates the effect of price (P), on the quantity supplied (QS),

quantity demanded (QD), and the resulting surplus (+) or shortage (-) as represented by the difference

between the quantity supplied and the quantity demanded at various price levels is as follows:

Lumber and Forest Industry Supply

and Demand Relationships

Price

Quantity

Demanded

Quantity

Supplied

Surplus (+) or

Shortage (-)

$1.00

60,000

0

-60,000

2

Lumber and Forest Industry Supply

and Demand Relationships

Price

Quantity

Demanded

Quantity

Supplied

Surplus (+) or

Shortage (-)

1.10 58,000 2,000 -56,000

1.20

56,000

4,000

-52,000

1.30

54,000

6,000

-48,000

1.40

52,000

8,000

-44,000

1.50

50,000

10,000

-40,000

1.60

48,000

12,000

-36,000

1.70

46,000

14,000

-32,000

1.80

44,000

16,000

-28,000

1.90

42,000

18,000

-24,000

2.00

40,000

20,000

-20,000

2.10

38,000

22,000

-16,000

2.20

36,000

24,000

-12,000

2.30

34,000

26,000

-8,000

2.40

32,000

28,000

-4,000

3

Lumber and Forest Industry Supply

and Demand Relationships

Price

Quantity

Demanded

Quantity

Supplied

Surplus (+) or

Shortage (-)

2.50

30,000

30,000

0

2.60

28,000

32,000

4,000

2.70

26,000

34,000

8,000

2.80

24,000

36,000

12,000

2.90

22,000

38,000

16,000

3.00

20,000

40,000

20,000

3.10

18,000

42,000

24,000

3.20

16,000

44,000

28,000

3.30

14,000

46,000

32,000

3.40

12,000

48,000

36,000

3.50

10,000

50,000

40,000

B. Using price (P) on the vertical Y axis and quantity (Q) on the horizontal X axis, a plot of the

demand and supply curves for the lumber/forest products industry is as follows:

4

2. Demand and Supply Curves. The following relations describe monthly demand and supply

relations for dry cleaning services in the metropolitan area:

QD = 500,000 - 50,000P (Demand)

QS = -100,000 + 100,000P (Supply)

where Q is quantity measured by the number of items dry cleaned per month and P is average

price in dollars.

A. At what average price level would demand equal zero?

B. At what average price level would supply equal zero?

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C. Calculate the equilibrium price/output combination.

2 SOLUTION

A. From the demand relation, note that demand equals zero when:

QD = 500,000 - 50,000P

0 = 500,000 - 50,000P

50,000P = 500,000

P = $10

B. From the supply relation, note that supply equals zero when:

QS = -100,000 + 100,000P

0 = -100,000 + 100,000P

100,000P = 100,000

P = $1

C. The equilibrium price/output relation is found by setting QD = QS and solving for P and Q:

QD = QS

6

500,000 - 50,000P = -100,000 + 100,000P

150,000P = 600,000

P = $4

Then,

QD = ? QS

500,000 - 50,000($4) = ? -100,000 + 100,000($4)

300,000 = _ 300,000

Elasticity of demand, its determinants, and its relationship to total revenue Determinants of Price Elasticity of Demand

A. Number of Substitute Goods

1. Demand is more inelastic when there are fewer substitutes available, all

else constant.

2. An example of inelastic demand is airline travel by business passengers

due to the lack of available substitute modes of transportation.

B. Percent of Consumer’s Income Spent on the Product

1. Demand is more inelastic when a smaller fraction of a consumer’s income

is spent on the product, all else constant.

2. An example of inelastic demand is the local newspaper because it makes

up a very tiny fraction of a consumer’s income.

C. Time Period

1. Demand is more inelastic when the time period under consideration is

short, all else constant.

2. It takes time for substitute products to be made available.

D. Durability of the Goods

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1. Demand is more inelastic for nondurable goods that are consumed immediately, all else

constant.

2. An example of inelastic demand is milk, which is nondurable. CALCULATING ELASTICITIES

An example of computing elasticity of demand using the formula above is shown

below. When the price decreases from $10 per unit to $8 per unit, the quantity sold increases

from 30 units to 50 units. The elasticity coefficient is 2.25.

Elasticity Example

P1 = $10 P2 = $8 Q1 = 30 Q2 = 50 (Q1 – Q2) / (Q1 + Q2) = (50 – 30) / (50 + 30) = 20 / 80 (P1 – P2) / (P1 + P2) ($10 - $8) / ($10 + $8) $2 / 18 1 / 4 = 1 x 9 = 9 = 2.25 1 / 9 4 x 1 4

Inelasticity Example

P1 = $12

P2 = $6

Q1 = 40

Q2 = 50

(Q1 – Q2) / (Q1 + Q2) = (50 – 40) / (50 + 40) = 10 / 90 (P1 – P2) / (P1 + P2) ($12 - $6) / ($12 + $6) $6 / $18 1 / 9 = 1 x 3 = 3 = .33 1 / 3 9 x 1 9

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 Relationship Between Elasticity and Total Revenue Demand is elastic for one good and inelastic for another good. Does it matter? As you just read, it can

matter to you as an individual, and it definitely matters to the sellers of goods. In particular, it matters

to a seller’s total revenue (money sellers receive for selling their goods). To see how elasticity of

demand relates to a business’s total revenue, let’s consider four cases in detail. The cases look at both

elastic and inelastic goods and what happens to each when the price rises, and when the price falls.

Elastic Demand and a Price Increase

Example 1

John currently sells 100 basketballs a week at a price of $20 each. His total revenue (price quantity)

per week is $2,000. Suppose Javier raises the price of his basketballs to $22 each, a 10 percent

increase in price. As a result, the quantity demanded falls from 100 to 75, a 25 percent reduction. The

demand is elastic because the change in quantity demanded (25%) is greater than the change in price

(10%).What happened to Javier’s total revenue at the new price and quantity demanded? It is $1,650:

the new price ($22) multiplied by the number of basketballs sold (75). Notice that if demand is

elastic, a price increase will lead to a decline in total revenue. Even though he raised the price,

Javier’s total revenue went down, from $2,000 to $1,650. An important lesson here is that an increase

in price does not always bring about an increase in total revenue. Elastic demand _ Price increase _ Total revenue decrease

Elastic Demand and a Price Decrease

Example 2

In example 2, as in example 1, demand is elastic. This time, however, John lowers the price of his

basketballs from $20 to $18, a 10 percent reduction in price. We know that if price falls, quantity

demanded will rise. Also, if demand is elastic, the percentage change in quantity demanded is

greater than the percentage change in price. Suppose quantity demanded rises from 100 to 130, a 30

percent increase. Total revenue at the new, lower price ($18) and higher quantity demanded (130) is

$2,340. Thus, if demand is elastic and price is decreased, total revenue will increase. Elastic demand _ Price decrease _Total revenue increase

Inelastic Demand and a Price Increase

Now let’s assume that the demand for basketballs is inelastic, rather than elastic, as it was in cases 1

and 2. Suppose John raises the price of his basketballs to $22 each, a 10 percent increase in price. If

demand is inelastic, the percentage change in quantity demanded must fall by less than the percentage

rise in price. Suppose the quantity demanded falls from 100 to 95, a 5 percent reduction. John’s total

revenue at the new price and quantity demanded is $2,090, (complete the

following…)…………………..

PROBLEM ILLUSTRATING ELASTICITY CALCULATIONS (including ARC elasticities)

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Enchantment Cosmetics, Inc., offers a line of cosmetic and perfume products marketed through

leading department stores. Product manager Erica Kane recently raised the suggested retail price on

a popular line of mascara products from $9 to $12 following increases in the costs of labor and

materials. Unfortunately, sales dropped sharply from 16,200 to 9,000 units per month. In an effort to

regain lost sales, Enchantment ran a coupon promotion featuring $5 off the new regular price. Coupon

printing and distribution costs totaled $500 per month and represented a substantial increase over the

typical advertising budget of $3,250 per month. Despite these added costs, the promotion was judged

to be a success, as it proved to be highly popular with consumers. In the period prior to expiration,

coupons were used on 40 percent of all purchases and monthly sales rose to 15,000 units.

A. Calculate the arc price elasticity implied by the initial response to the Enchantment price

increase.

B. Calculate the effective price reduction resulting from the coupon promotion.

C. In light of the price reduction associated with the coupon promotion and assuming no change

in the price elasticity of demand, calculate Enchantment's arc advertising elasticity.

D. Why might the true arc advertising elasticity differ from that calculated in part C?

P5.8 SOLUTION

A. EP = 2 1

2 1

Q + P P x

P + Q Q





= 9,000 - 16,200 $12 + $9

x $12 - $9 9,000 + 16,200

= -2

B. The effective price reduction is $2 since 40 percent of sales are accompanied by a coupon:

ΔP = -$5(0.4) or P2 = $12 - $5(0.4)

= -$2 = $10

ΔP = $10 - $12

= -$2

C. To calculate the arc advertising elasticity, the effect of the $2 price cut implicit in the coupon

promotion must first be reflected. With just a price cut, the quantity demanded would rise to 13,000,

because:

10

EP = 2 11

2 1 1

Q* - + Q P P x

- Q* + QP P

-2 = Q* - 9,000 $10 + $12

x $10 - $12 Q* + 9,000

-2 = -11(Q* - 9,000)

(Q* + 9,000)

-2(Q* + 9,000) = -11(Q* - 9,000)

-2Q* - 18,000 = -11Q* + 99,000

9Q* = 117,000

Q* = 13,000

Then, the arc advertising elasticity can be calculated as:

EA = 2 12

2 1 2

- Q* + Q A A x

- + Q*QA A

= 15,000 - 13,000 $3,750 + $3,250

x $3,750 - $3,250 15,000 + 13,000

= 1

D. It is important to recognize that a coupon promotion can involve more than just the

independent effects of a price cut plus an increase in advertising as is implied in Part C. Synergistic or

interactive effects may increase advertising effectiveness when the promotion is accompanied by a

price cut. Similarly, price reductions can have a much larger impact when advertised. In addition, a

coupon is a price cut for only the most price sensitive (coupon-using) customers, and may spur sales

by much more than a dollar equivalent across-the-board price cut.

Synergy between advertising and the implicit price reduction that accompanies a coupon promotion

can cause the estimate in Part C to overstate the true advertising elasticity. Similarly, this advertising

elasticity will be overstated to the extent that targeted price cuts have a bigger influence on the

quantity demanded than similar across-the-board price reductions, as seems likely.

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Demonstration of computation of elasticities from an

estimated demand equation The following questions refer to this regression equation. (Standard errors in parentheses.)

QD = 15,000 - 10 P + 1500 A + 4 PX + 2 I, (5,234) (2.29) (525) (1.75) (1.5)

R2 = 0.65

N = 120

F = 35.25

Standard error of Y estimate = 565

Q = Quantity demanded

P = Price = 7,000

A = Advertising expense, in thousands = 54

PX = price of competitor's product = 8,000

I = average monthly income = 4,000

1) Calculate the price elasticity for demand and briefly comment on what information this gives

you.

Answer: Based on the figures above, QD = 66,000 (by plugging in the values for the different

variables)

Price elasticity = -10(7,000/66,000) = -1.06. Demand is elastic (at this point).

2) Calculate the t-statistics for price and explain what this tells you.

Answer: Price: 10/2.29 = 4.37

This means that the variable is statistically significant . Thus we can conclude that price has an

impact on the quantity demanded of this product.