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Homework answers / question archive / Suppose the own price elasticity of demand for good X is -5, its income elasticity is 2, its advertising elasticity is 3, and the cross-price elasticity of demand between it and good Y is 6
Suppose the own price elasticity of demand for good X is -5, its income elasticity is 2, its advertising elasticity is 3, and the cross-price elasticity of demand between it and good Y is 6. Determine how much the consumption of this good will change if:(a.) the price of good X decreases by 4 percent; (b.) the price of good Y increases by 7 percent; (c.) advertising decreases by 3 percent; and (d.) income increases by 2 percent. Instructions: enter your answers as percentages; include a minus sign (-) for all negative answers.
(a.) The price elasticity of demand for a commodity (E) is given by the following formula:
Ep = (percentage change in the quantity demanded of the good)/(percentage change in price).
If the price of the commodity decreases by 4 percent and E=-5, then from the formula:
-5 = (percentage change in the quantity demanded of the good)/-4%
percentage change in the quantity demanded of the good = (-5)(-4%) = 20%.
So, quantity demanded of the good increases by 20%.
(b.) The cross-price elasticity of demand between a good X and good Y (Exy) is given by the following formula:
Exy = (percentage change in the quantity demanded of good X)/(percentage change in price of good Y).
Substituting values given in the question:
6 = (percentage change in the quantity demanded of good X)/7%
percentage change in the quantity demanded of good X = (6)(7%) = 42%.
So, the goods are substitutes and the quantity demanded of good X increases by 42%.
(c.) The advertising elasticity of demand for a commodity (Ead) is as follows:
Ead = (percentage change in the quantity demanded of the good)/(percentage change in advertising expenditures).
Substituting values:
3 = (percentage change in the quantity demanded of the good)/-3%
percentage change in the quantity demanded of the good = (3)(-3%) = -9%.
So, with the reduction in advertising, quantity demanded declines by 9%.
(d.) The income elasticity of demand for a commodity (Einc) is as follows:
Einc = (percentage change in the quantity demanded of the good)/(percentage change in incomes).
Substituting values:
2 = (percentage change in the quantity demanded of the good)/2%
percentage change in the quantity demanded of the good = (2)(2%) = 4%.
So, with the increase in incomes, quantity demanded increases by 4%.
