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Homework answers / question archive / Suppose the own price elasticity of demand for a good X is -3, its income elasticity is 1, its advertising elasticity is 2, and the cross-price elasticity of demand between it and good Y is -4
Suppose the own price elasticity of demand for a good X is -3, its income elasticity is 1, its advertising elasticity is 2, and the cross-price elasticity of demand between it and good Y is -4. Determine how much the consumption of this good will change (in percent) if
a. The price of good X decreases by 5 percent.
b. The price of good Y increases by 10 percent.
c. Advertising decreases by 3 percent.
d. Income increases by 4 percent.
a. The price of good X decreases by 5 percent.
Price elasticity of demand (PED) = percentage change in quantity / percentage change in price
But PED = -3
percentage change in price = -5%
hence
-3 = %change in quantity / -5%
%change in quantity = -3 * -5% = 15%
If price decreases by 5%, Consumption of good X will increase by 15%.
b. The price of good Y increases by 10 percent.
Cross Price Elasticity of Demand (XED) = %Change in Quantity Demanded of Good x / %Change in Price of Good Y
But XED = -4
%Change in Price of Good Y = 10%
Hence,
-4 = %Change in Quantity Demanded of Good x / 10%
%Change in Quantity Demanded of Good X = -4 * 10% = -40%
Good X and good Y are complements because XED is negative. Hence, if the price of good Y increases by 10%, consumption of good X reduces by 40%.
c. Advertising decreases by 3 percent.
Advertising elasticity of demand (AED) = the percentage change in the quantity demanded / the percentage change in advertising expenditures
But
AED = 2
the percentage change in advertising expenditures = - 3%
2 = the percentage change in advertising expenditures / -3%
the percentage change in advertising expenditures = 2 * -3% = -6%
when advertising expenditure reduces by 3%, the consumption of good X decreases by 6%.
d. Income increases by 4 percent.
Income elasticity of demand (YED) = %change in demand / %change in income
But
YED = 1
%change in income = 4%
1 = %change in demand / 4%
%change in demand = 1 * 4% = 4%
If income increases by 4%, the consumption of good X increases by 4%.