Suppose the own price elasticity of demand for good X is -5, its income elasticity is 2, its advertising elasticity is 3, and the cross-price elasticity of demand between it and good Y is 6

(a.) The price elasticity of demand for a commodity (E) is given by the following formula:

Ep = (percentage change in the quantity demanded of the good)/(percentage change in price).

If the price of the commodity decreases by 4 percent and E=-5, then from the formula:

-5 = (percentage change in the quantity demanded of the good)/-4%

percentage change in the quantity demanded of the good = (-5)(-4%) = 20%.

So, quantity demanded of the good increases by 20%.

(b.) The cross-price elasticity of demand between a good X and good Y (Exy) is given by the following formula:

Exy = (percentage change in the quantity demanded of good X)/(percentage change in price of good Y).

Substituting values given in the question:

6 = (percentage change in the quantity demanded of good X)/7%

percentage change in the quantity demanded of good X = (6)(7%) = 42%.

So, the goods are substitutes and the quantity demanded of good X increases by 42%.

(c.) The advertising elasticity of demand for a commodity (Ead) is as follows:

Ead = (percentage change in the quantity demanded of the good)/(percentage change in advertising expenditures).

Substituting values:

3 = (percentage change in the quantity demanded of the good)/-3%

percentage change in the quantity demanded of the good = (3)(-3%) = -9%.

So, with the reduction in advertising, quantity demanded declines by 9%.

(d.) The income elasticity of demand for a commodity (Einc) is as follows:

Einc = (percentage change in the quantity demanded of the good)/(percentage change in incomes).

Substituting values:

2 = (percentage change in the quantity demanded of the good)/2%

percentage change in the quantity demanded of the good = (2)(2%) = 4%.

So, with the increase in incomes, quantity demanded increases by 4%.