Suppose the own price elasticity of demand for 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 good X will change if:The price of good X decreases by 5%The price of good Y increases by 8%Advertising decreases by 4%Income increases by 4%

Question
Asked Oct 1, 2019

Suppose the own price elasticity of demand for 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 good X will change if:

  1. The price of good X decreases by 5%
  2. The price of good Y increases by 8%
  3. Advertising decreases by 4%
  4. Income increases by 4%
check_circleExpert Solution
Step 1

Part 1) When price of good X decreases by 5% , consumption of good X will increase by 15%

Price elasticity of Demand of Y Percent change in consumption (quantity demanded) of X
Percent change in price of X
AQx
Qx
P
Therefore, Percent change in consumption of X
Price elasticity of Demand of X x Percent change in price of X
AQx
-3 x-5%
Qx
15%
Note: (-5% used in calculations as price decreases)
help_outline

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Price elasticity of Demand of Y Percent change in consumption (quantity demanded) of X Percent change in price of X AQx Qx P Therefore, Percent change in consumption of X Price elasticity of Demand of X x Percent change in price of X AQx -3 x-5% Qx 15% Note: (-5% used in calculations as price decreases)

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Step 2

Part 2)

When price of Y increases by 8%,  consumption for X decreases by 32% as indicated by minus sign.

When price of Y increases by 8%, consumption of y decreases anyway but consumption of X also decreases as per our calculations. This suggests that X and Y are complement goods as their prices move together.

Change in consumption of X = -32%

Percent change in consumption (quantity demanded) of X
Cross Price elasticity of Demand of X =
Percent change in price of Y
AQx
Qx
AP
у
P
Therefore, Percent change in consumption of X= Cross Price elasticity of Demand of X x Percent change in price of Y
=-4 x8%
-32%
Note: (+8% used in calculations as price of y increases)
help_outline

Image Transcriptionclose

Percent change in consumption (quantity demanded) of X Cross Price elasticity of Demand of X = Percent change in price of Y AQx Qx AP у P Therefore, Percent change in consumption of X= Cross Price elasticity of Demand of X x Percent change in price of Y =-4 x8% -32% Note: (+8% used in calculations as price of y increases)

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Step 3

Part 3)

Let Ax represent the units of advertising expenses. 

Consumption of X decreases  by 8% when ad...

Advertising elasticity of Demand of X = rercent change in consumption (quantity demanded) of x
Percent change in advertising expenditure of X
дох,
ДАх,
Ax
Advertising elasticity of Demand of X x Percent change in advertising expenditure of X
Therefore, Percent change in consumption of X
AQx
2 x-4%
Qx
=-8%
Note:(-4% used in calculations as advertising expenditure decreases)
help_outline

Image Transcriptionclose

Advertising elasticity of Demand of X = rercent change in consumption (quantity demanded) of x Percent change in advertising expenditure of X дох, ДАх, Ax Advertising elasticity of Demand of X x Percent change in advertising expenditure of X Therefore, Percent change in consumption of X AQx 2 x-4% Qx =-8% Note:(-4% used in calculations as advertising expenditure decreases)

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