The demand for good X is given by the following equation: Q x = 10 P x -2.4 P y

Question

The demand for good X is given by the following equation:
               Qx = 10 Px-2.4 Py I1.2 Ax0.001 Ay-0.003
where Px and Py are the prices of X and Y, I is per capita income, Ax is advertising on good X, and Ay is advertising on good Y.
(a) Should the price of X be increased or decreased if the firm is interested in maximizing revenue?
(b) Are goods X and Y gross substitutes or complements?
(c) By how much must the price of X change if per capita income decreases by 4% and the goal is to keep QX constant?
(d) Calculate the elasticity of demand for good X with respect to advertising on good X. Interpret your answer. Can you tell whether the firm is spending too much or too little on advertising?
(e) If the manufacturer of good Y stops advertising completely, what would be the impact on demand for good X according to this demand equation?

Explanation / Answer

(a) Price of X should be increased if the firm is interested in maximizing revenue because increase in the price of good X increases its quantity demanded. So, when quantity demanded rises with the rise in the price of commodity then, total revenue of firm will definitely increases.

(b) Good X and Y are complements because if Py decreases then quantity demanded of good X increases and vice-versa. Complementary goods are those goods which jointly satisfy a particular want of consumer. Increase or decrease in the price of one good decreases or increases the demand of other good.

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