Answer:
COMPLETE QUESTION:
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 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 5 percent.
b. The price of good Y increases by 8 percent.
c. Advertising decreases by 4 percent.
d. Income increases by 4 percent.
ANSWER
a) The quantity demanded of good X will change by 15 percent
b) The demand for X will change by -32 percent.
c) The demand for good X will change by -8 percent
d) The demand of good X will change by 4 percent
Step-by-step explanation:
Price elasticity of demand measures how responsive quantity demanded is to a change in the price of a commodity.
price elasticity = [tex]\frac{\frac{dQ}{Q} }{\frac{dP}{P} }[/tex] .
Note: Same applies to income,advertising and cross-price elasticity.
where, P is the price of the demanded good and Q is the quantity of the demanded good and dQ and dP are the changes in quantities of demanded goods and prices respectively.
a) Quantity demanded on goods X due to decrease by 5 percent in price is ;
-3 = [tex]\frac{\frac{dQ}{Q} }{-5}[/tex] , therefore percentage increase in quantity of goods demanded is (-3 x -5) = 15 percent
b) Cross- Price Elasticity; Quantity demanded on goods X due to increase by 8 percent in price in goods Y is;
-4 = [tex]\frac{\frac{dQ}{Q} }{8}[/tex] , therefore percentage decrease in quantity of goods demanded is (-4 x 8) = -32 percent
c) Advertising Elasticity ; Quantity demanded on goods X due to decrease by 4 percent in advertising is;
2 = [tex]\frac{\frac{dQ}{Q} }{-4}[/tex] , therefore percentage decrease in quantity of goods demanded is (2 x -4) = -8 percent
d) Income Elasticity ; Quantity demanded on goods X due to increase by 4 percent in income is;
1 = [tex]\frac{\frac{dQ}{Q} }{4}[/tex] , therefore percentage increase in quantity of goods demanded is (1 x 4) = 4 percent
