Suppose the demand curve for a product is given by Q = 10 − 2P + PS, where P is the price of the product and PS is the price of a substitute good. The price of the substitute good is $2.00.
Suppose P = $1.00. What is the price elasticity of demand? What is the cross-price elasticity of demand?
Suppose the price of the good, P, goes to $2.00. Now, what is the price elasticity of demand? What is the cross-price elasticity of demand?
Answers
To calculate the price elasticity of demand at a given price, we need to calculate the percentage change in quantity demanded for a given percentage change in price. We can do this using the following formula:
Price elasticity of demand = (% change in quantity demanded) / (% change in price)
To calculate the cross-price elasticity of demand, we need to calculate the percentage change in quantity demanded for a given percentage change in the price of the substitute good. We can do this using the following formula:
Cross-price elasticity of demand = (% change in quantity demanded) / (% change in price of substitute good)
Using this information, we can calculate the price elasticity of demand and the cross-price elasticity of demand for the given demand curve at the two different prices:
At P = $1.00:
Q = 10 - 2P + PS
= 10 - 2(1) + (2)
= 8
Price elasticity of demand = (% change in quantity demanded) / (% change in price)
= (8 - 10) / (-2 - 1)
= -2 / -3
= 2/3
Cross-price elasticity of demand = (% change in quantity demanded) / (% change in price of substitute good)
= (8 - 10) / (2 - 2)
= -2 / 0
= undefined
At P = $2.00:
Q = 10 - 2P + PS
= 10 - 2(2) + (2)
= 6
Price elasticity of demand = (% change in quantity demanded) / (% change in price)
= (6 - 8) / (-2 - 1)
= -2 / -3
= 2/3
Cross-price elasticity of demand = (% change in quantity demanded) / (% change in price of substitute good)
= (6 - 8) / (2 - 2)
= -2 / 0
= undefined
Therefore, at both prices, the price elasticity of demand is 2/3, and the cross-price elasticity of demand is undefined.
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