Suppose the own price elasticity of demand for good X is -4, its income elastici

Question

Suppose the own price elasticity of demand for good X is -4, its income elasticity is -2, its advertising elasticity is 3, and the cross-price elasticity of demand between it and good Y is 2. Determine how much the consumption of this good will change if:

Instructions: Enter your answers as percentages. Include a minus (-) sign for all negative answers.

a. The price of good X decreases by 4 percent.

percent

b. The price of good Y increases by 9 percent.

percent

c. Advertising decreases by 3 percent.

percent

d. Income increases by 2 percent.
percent

Explanation / Answer

consumption of this good will change in each of the scenarios as below

a. The price of good X decreases by 4 percent.

Given that, own price elasticity of demand for good X is -4

We know Price Elasticity of Demand = % Change in Quantity Demanded / % Change in Price

i.e. -4 = % Change in Quantity Demanded / -4%

or % Change in Quantity Demanded = -4 * -4% = 16%

Thus, when the price of the good X decreases by 4%, the demand for it increases by 16%

b. The price of good Y increases by 9 percent.

Given, cross-price elasticity of demand between it and good Y is 2.

We know cross-price elasticity of demand for X = % Change in Quantity Demanded of X / % Change in Price of Y

i.e. % Change in Quantity Demanded of X = % Change in Price of Y * cross-price elasticity of demand for X
= 9% * 2
                   = 18%

Thus, when the price of good Y increases by 9%, demand for Good X increases by 18%

c. Advertising decreases by 3 percent.

Given, advertising elasticity is 3

and advertising elasticity = % Change in Quantity Demanded / % Change in advertising expenditure

i.e. % Change in Quantity Demanded of X = % Change in advertising expenditure * advertising elasticity
= -3% * 3
                   = -9%

When the advertising expenditure reduces by 3%, consumption of good X would reduce by 9%

d. Income increases by 2 percent.

Given, income elasticity is -2

and income elasticity of demand = % change in quantity demanded / % change in income

or % change in quantity demanded = income elasticity of demand * % change in income
               = -2 * 2%
               = -4%

So, when income increases by 2%, demand for good X reduces by 4%

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