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 = $\frac{\frac{dQ}{Q} }{\frac{dP}{P} }$ .

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 = $\frac{\frac{dQ}{Q} }{-5}$ , 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 = $\frac{\frac{dQ}{Q} }{8}$ , 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 = $\frac{\frac{dQ}{Q} }{-4}$ , 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 = $\frac{\frac{dQ}{Q} }{4}$ , therefore percentage increase in quantity of goods demanded is (1 x 4) = 4 percent

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3 years ago