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Price Elasticity of Demand Sample Problems

Price Elasticity of Demand Sample Problem #1:

When Hank’s Hamburger Stand priced its signature burger at $7, they sold 500 burgers per week. When they raised the price to $8, they sold 450 burgers per week. Based on this information, calculate the price elasticity of demand for hamburgers.

The price elasticity of demand = percentage change in quantity demanded / percentage change in price

Start by calculating the % change in quantity demanded = change in quantity / (sum of quantities / 2), and then multiply 100 to put in % form

% change in quantity demanded = (500 – 450) / ((500 + 450) /2) = 50 / (950 / 2) = 50 / 475 = .1053

.1053 X 100 = 10.53% is the change in quantity demanded

Next calculate the percentage change in price = change in price / (sum of prices / 2), then multiply by 100 to put it in % form

(7 – 8) / ((7 + 8)/2) = -1 / (15/2) = -1/7.5 = -.1333

-.1333 X 100 = -13.33% is the change in price

Finally, calculate the elasticity of demand.

The price elasticity of demand = percentage change in quantity demanded / percentage change in price

Price elasticity of demand for burgers = 10.53% / -13.33% =-.79

Note that when we discuss price elasticity of demand, we take the absolute value of these calculations (meaning, the number will always be positive).

Price elasticity of demand for burgers = .79

Demand is considered to be elastic if the price elasticity of demand is greater than 1.

Demand is considered to be inelastic if the price elasticity of demand is less than 1.

That makes the demand for Hank’s signature burger inelastic.

PED Sample Problem #2:

When the price of hamburgers is $2, 200 are demanded. When the price is $3, 150 are demanded.

The price elasticity of demand = percentage change in quantity demanded / percentage change in price

Start by calculating the % change in quantity demanded = change in quantity / (sum of quantities / 2)

(200-150) / ((200+150)/2) = .29

Next calculate the percentage change in price = change in price / (sum of prices / 2)

(3-2) / ((3+2)/2) = .4

Then calculate the price elasticity of demand = .29 / .4 = .71

Demand is inelastic.

PED Sample Problem #3:

When the price of a treat is $2, 250 are demanded. When the price is $3, 200 are demanded.

The price elasticity of demand = percentage change in quantity demanded / percentage change in price

Start by calculating the % change in quantity demanded = change in quantity / (sum of quantities / 2)

(250-200) / ((200+250)/2) = .22

Next calculate the percentage change in price = change in price / (sum of prices / 2)

(3-2) / ((3+2)/2) = .4

Then calculate the price elasticity of demand = .22/ .4 = .56

Demand is inelastic.

PED Sample Problem #4:

When the price of coffee is $1, 150 are demanded. When the price is $2, 100 are demanded.

The price elasticity of demand = percentage change in quantity demanded / percentage change in price

Start by calculating the % change in quantity demanded = change in quantity / (sum of quantities / 2)

(150-100) / ((100+150)/2) = .4

Next calculate the percentage change in price = change in price / (sum of prices / 2)

(2-1) / ((1+2)/2) = .67

Then calculate the price elasticity of demand = .4 / .67 = .6

Demand is inelastic.

Sample Problem #5:

When the price of tickets is $9, 250 are demanded. When the price is $8, 300 are demanded.

The price elasticity of demand = percentage change in quantity demanded / percentage change in price

Start by calculating the % change in quantity demanded = change in quantity / (sum of quantities / 2)

(300-250) / ((300+250)/2) = .18

Next calculate the percentage change in price = change in price / (sum of prices / 2)

(9-8) / ((9+8)/2) = .12

Then calculate the price elasticity of demand = .18 / .12 = 1.55

Demand is elastic.

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