Sandra purchases 5 pounds of coffee and 10 gallons of milk per month when the price of coffee is $10 per pound. She purchases 6 pounds of coffee and 12 gallons of milk per month when the price of coffee is $8 per pound. Sandra’s cross-price elasticity of demand for coffee and milk is
A. 0.82, and they are substitutes.
B. -0.82, and they are complements.
C. 1.22, and they are substitutes.
D. -1.22, and they are complements.
B
Cross-price elasticity of demand =
Percentage change in quantity demanded of good 1 / Percentage change in the price of good 2
I did the work and that's what I got.
-0.82, and they are complements.
To calculate the cross-price elasticity of demand, we need to use the following formula:
Cross-price elasticity of demand = (Percent change in quantity demanded of coffee) / (Percent change in price of milk)
First, let's calculate the percentage change in quantity demanded of coffee:
Change in quantity demanded of coffee = (6 pounds - 5 pounds) = 1 pound
Percentage change in quantity demanded of coffee = (Change in quantity demanded of coffee / Initial quantity demanded of coffee) x 100%
Percentage change in quantity demanded of coffee = (1 pound / 5 pounds) x 100%
Percentage change in quantity demanded of coffee = 20%
Now, let's calculate the percentage change in price of milk:
Change in price of milk = ($8 per gallon - $10 per gallon) = -$2 per gallon
Percentage change in price of milk = (Change in price of milk / Initial price of milk) x 100%
Percentage change in price of milk = (-$2 per gallon / $10 per gallon) x 100%
Percentage change in price of milk = -20%
Finally, let's calculate the cross-price elasticity of demand:
Cross-price elasticity of demand = (Percentage change in quantity demanded of coffee) / (Percentage change in price of milk)
Cross-price elasticity of demand = 20% / -20%
Cross-price elasticity of demand = -1
The negative sign in the cross-price elasticity indicates that coffee and milk are complements.
Therefore, the correct answer is D. -1.22, and they are complements.
To find Sandra’s cross-price elasticity of demand for coffee and milk, we need to calculate the percentage change in the quantity of coffee demanded when the price of milk changes.
Step 1: Calculate the change in quantity of coffee demanded.
Change in quantity of coffee demanded = (6 pounds - 5 pounds) = 1 pound
Step 2: Calculate the percentage change in the quantity of coffee demanded.
Percentage change in quantity of coffee demanded = (Change in quantity of coffee demanded / Initial quantity of coffee demanded) * 100
Percentage change in quantity of coffee demanded = (1 pound / 5 pounds) * 100 = 20%
Step 3: Calculate the percentage change in the price of milk.
Percentage change in the price of milk = (Price of milk after change - Price of milk before change) / Price of milk before change * 100
Percentage change in the price of milk = ($8 - $10) / $10 * 100 = -20%
Step 4: Calculate the cross-price elasticity of demand for coffee and milk.
Cross-price elasticity of demand = (Percentage change in quantity of coffee demanded / Percentage change in the price of milk)
Cross-price elasticity of demand = 20% / -20% = -1
Now we need to determine the correct answer choice based on the calculated cross-price elasticity of demand.
Since the cross-price elasticity of demand is negative (-1) , it indicates that coffee and milk are complements (meaning they are consumed together). Looking at the answer choices, the correct answer is:
D. -1.22, and they are complements.