1. Suppose the demand curve for a product is given as Q = 10 – 2P + Po where P i
ID: 1199538 • Letter: 1
Question
1. Suppose the demand curve for a product is given as Q = 10 – 2P + Po where P is the price of the product, Po is the price of another good, and Q is the quantity demanded. Assume the price of the other good is $2.00. a. Suppose P = $1.00. What is the price elasticity of demand? What is the cross-price elasticity of demand? Is the other good a substitute or a complement of the product demanded? b. Suppose the price of the good (P) increases to $2.50. What are the values for the price elasticity of demand and the cross-price elasticity of demand now?
Explanation / Answer
(a) Demand function is as follows -
Q = 10-2P+Po
Price of other good (Po) = $2.00
Price of product (P) = $1.00
Calculate quantity demanded (Q) -
Q = 10 - 2P + Po = 10 - 2*1 + 2 = 10
The quantity demanded (Q) is 10 units.
Calculate the price elasticity of demand -
Price elasticity = (dQ/dP) * (P/Q)
= [d(10 - 2P + Po)/dP] * (1/10)
= -2 * (1/10)
= -0.20
The Price-elasticity of demand is -0.20.
Calculate the cross-price elasticity of demand -
Cross-price elasticity of demand = (dQ/dPo) * (Po/Q)
= [d(10 - 2P + Po)/dPo] * (2/10)
= 1 * (2/10)
= 0.20
The cross-price elasticity of demand is 0.20.
If the value of cross-price elasticity of demand is positive then two goods are substitutes.
If the value of cross-price elasticity of demand is negative then two goods are complements.
In given case, as calculated, the cross price elasticity of demand is positive.
Therefore, the other good is a substitute of the product demanded.
(b) Demand function is as follows -
Q = 10-2P+Po
Price of other good (Po) = $2.00
Price of product (P) = $2.50
Calculate quantity demanded (Q) -
Q = 10 - 2P + Po = 10 - 2*2.50 + 2 = 7
The quantity demanded (Q) is 7 units.
Calculate the price elasticity of demand -
Price elasticity = (dQ/dP) * (P/Q)
= [d(10 - 2P + Po)/dP] * (2.50/7)
= -2 * (2.50/7)
= -0.71
The Price-elasticity of demand is -0.71.
Calculate the cross-price elasticity of demand -
Cross-price elasticity of demand = (dQ/dPo) * (Po/Q)
= [d(10 - 2P + Po)/dPo] * (2/7)
= 1 * (2/7)
= 0.28
The cross-price elasticity of demand is 0.28.
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