Consider the following linear demand curve.Q(p, m, pr) = ap + bm + cpr where m i

Question

Consider the following linear demand curve.Q(p, m, pr) = ap + bm + cpr where m is income, pr is the price of a related good, and a,b, and c are real numbers. Also, note that for a linear function, such as f(x, y) = a + bx + cy, | = b. a. The income elasticity of demand is defined as the percentage change in quantity given a one percent change in income. Mathematically it is expressed as em = ' q- 111 terms of the variables, what is the income elasticity of demand? Given that m and Q are positive, what do you expect the sign of em to be if the good is a normal good? An inferior good? b. The cross price elasticity of demand is defined as ePr = Jj In terms of the variables, what is the cross-price elasticity of demand? Given that pr and Q are positive, what do you expect the sign of epr to be if the related good is a complement? A substitute?

Explanation / Answer

A) Income Elasticity of Demand = % change in quantity demanded / % change in income

NORMAL GOODS are the goods whose consumption increases with increase in income. Example clothes. Normal goods have a positive income elasticity of demand i.e E>0.

INFERIOR GOODS are the goods whose consumption decreases with an increase in income. Typically inferior goods exist where superior goods are available i.e consumer has higher income to be able to buy superior goods. Example low-priced own label foods in supermarkets. Inferior goods have a negative income elasticity of demand (E<0).

B) The cross-price elasticity of demand measures the change in demand for one good in response to a change in price of another good.

Complementary goods have a negative cross-price elasticity: as the price of one good increases, the demand for the second good decreases.

Substitute goods have a positive cross-price elasticity: as the price of one good increases, the demand for the other good increases.

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