# Calculating price and income elasticity of demand

1. Demand Analysis.

Aspen, Colorado is engaging in a bumper-sticker advertising campaign. Monthly sales data from ski shops selling the "Don't Worry-Be Happy (in Aspen)" bumper-stickers indicate that:

Q = 6,000 - 2,000P

where Q is bumper-sticker sales and P is price.

A. How many bumper-stickers could Aspen sell at $2 each?

B. What price would Aspen have to charge to sell 5,000 bumper-stickers?

C. At what price would bumper-sticker sales equal zero?

D. How many bumper-stickers could be given away?

E. Calculate the point price elasticity of demand at a price of $1.

2. Optimal Price.

Last week, Wally's Burgers, Inc. reduced the average price on the half-pound Papa burger by 1%. In response, sales jumped by 2%.

A. Calculate the point price elasticity of demand for Papa burgers.

B. Calculate the optimal price for Papa burgers if marginal cost is $1 per unit.

3. Arc Price Elasticity.

Assume that amazon.com cut the price on a 1.10ct Princess Cut Diamond Solitaire engagement ring from $4,500 to $2,500, and sales rose from 50 to 75 units per week.

A. Calculate the implied arc price elasticity of demand.

B. Is a further price decrease warranted? Why or why not?

4. Income Elasticity.

The Electronics Warehouse, Inc. is a leading retailer of home theater systems. Demand for home theater systems is sensitive to changes in national income. Electronics retailing is highly competitive, so retail demand for home theater systems is also very price-sensitive. During the past year, the Electronics Warehouse sold 550,000 home theater systems at an average retail price of $4,000 per unit. This year, GDP per household is expected to fall from $58,800 to $53,200 as the nation enters a steep recession. Without any price change, the Electronics Warehouse expects current-year sales to fall to 450,000 units.

A. Calculate the implied arc income elasticity of demand.

B. Given the projected fall in income, the sales manager believes that current volume of 550,000 units could only be maintained with a price cut of $500 per unit. On this basis, calculate the implied arc price elasticity of demand.

C. Holding all else equal, would a further increase in price result in higher or lower total revenue?

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#### Solution Preview

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1. Demand Analysis.

Aspen, Colorado is engaging in a bumper-sticker advertising campaign. Monthly sales data from ski shops selling the "Don't Worry-Be Happy (in Aspen)" bumper-stickers indicate that:

Q = 6,000 - 2,000P

where Q is bumper-sticker sales and P is price.

A. How many bumper-stickers could Aspen sell at $2 each?

Q = 6,000 - 2,000P

Put P=$2

Q=6000-2000*2=2000

B. What price would Aspen have to charge to sell 5,000 bumper-stickers?

Q = 6,000 - 2,000P

Put Q=5000

5000=6000-2000P

2000P=1000

P=$0.5

C. At what price would bumper-sticker sales equal zero?

Q = 6,000 - 2,000P

Put Q=0

0=6000-2000P

2000P=6000

P=$3

D. How many bumper-stickers could be given away?

Q = 6,000 - ...

#### Solution Summary

There are four problems. Solutions to these problems explain methodology to calculate price and income elasticity of demand.

Elasticity of demand

Using the "arc formula" and the data from the table below, compute where possible the own- price and income elasticities of demand. (remember that these elasticities are computed holding all other variables constant).

Price quantity price of related goods income

$10 600 $20 $ 16,000

$10 600 $30 $22,000

$12 500 $30 $22,000

$10 500 $20 $22,000

A. Compute owner price elasticity of demand?

B. Demand is -------- (elastic, inelastic, Unitary elastic)?

C. The cross price elasticity of demand= ------- ?

d. The related good is a------- ?

E. The income elasticity =------- /

F. The good is a ...... good?

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