The demand for company X's product is given by Qx = 2 - 3Px + 4Py
Suppose good X sells for $2.00 per unit and good Y sells for $4 per unit.
a. Calculate the cross-price elasticity of demand between goods X and Y at the given prices.
b. Are goods X and Y substitutes or complements?
c. What is the own price elasticity of demand at these prices?
Please show work
a) Ans: The cross-price elasticity of demand between goods X and Y at the given prices is 1.33.
Explanation:
Qx = 2 - 3Px + 4Py
= 2 - 3(2) + 4(4) = 2 - 6 + 16 = 12
Cross-price elasticity of demand = ∆Qx /∆Py * Py / Qx
= 4* (4/12) = 4 * 0.3333 = 1.33
Where , ∆Qx /∆Py = 4, which is the price coefficient of good Y.
b) Ans: Goods X and Y are substitutes.
Explanation:
When cross elasticity of demand is positive , then the two goods are substitutes.
When cross elasticity of demand is negative , then the two goods are complements.
c) Ans: The own price elasticity of demand at these prices is -0.5.
Explanation:
Elasticity of demand = ∆Qx /∆Px * Px / Qx
= -3 * ( 2 /12 )
= -3 * 0.1667
= -0.5
Where , ∆Qx /∆Px = -3 , which is the price coefficient of good X.
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