Question

(4) A researcher estimated a demand function for commodity "A" using weekly data collected over a 30-month period. The estimated model is presented below. Od 200 - 2Pa 4.51 + 3.0 Py. where Pa Price of commodity "A" 1 = Consumer incomes Py Price of commodity Y (a)On aggregate, does the behavior of the consumers of this product follow the LAW OF DEMAND? Explain. (b) is commodity "A" a normal or an inferior good? How did you know? (c) Comment on the relationship between commodity "A" and commodity (d) For Pa 10, 100, Py8, find the price, income and cross price elasticities of demand for this! product and interpret the results.

Answer 1

a) The quantity of commodity A and the price of commodity A, Pa are inversely related. This implies that commodity A follows the law of demand where price rise results in a fall in quantity demanded and vice versa

b) Income coefficient which is used in the calculation of income elasticity, is positive. This ensures that the income effect is positive and so when income increases, quantity demanded rises. Hence commodity A is a normal good

c)the price coefficient of commodity Y is positive (+3). this indicates that the cross price elasticity between the two commodities is positive and hence commodity Y and commodity A are substitutes.

d) Own price elasticity = -2 x 10 / (200 - 2*10 + 4.5*100 + 3*8) = -0.0306. This value is less than 1 in absolute terms so demand is price inelastic

Cross price elasticity = 3 x 8 / (200 - 2*10 + 4.5*100 + 3*8) = 0.0367. This value is positive so the two commodities are substitutes

Income elasticity = 4.5 x 100 / (200 - 2*10 + 4.5*100 + 3*8) = 0.6881. This value is positive which implies commodity A is a normal good.