Question 11.8.2: The demand D1 for potatoes in the USA, for the period 1927 t......
The demand D_{1} for potatoes in the USA, for the period 1927 to 1941, was estimated to be D_{1} = Ap^{−0.28}m^{0.34}, where p is the price of potatoes and m is mean income.
The demand for apples was estimated to be D_{2} = Bq^{−1.27}m^{1.32}, where q is the price of apples.
Find the price elasticities of demand, El_{p} D_{1} and El_{q} D_{2}, as well as the income elasticities of demand El_{m} D_{1} and El_{m} D_{2}, and comment on their signs.
According to part (a) of Example 11.8.1, El_{p} D_{1} = −0.28. If the price of potatoes increases by 1%, demand decreases by approximately 0.28%. Furthermore, El_{q} D_{2} = −1.27, El_{m} D_{1} = 0.34, and El_{m} D_{2} = 1.32.
Both price elasticities El_{p} D_{1} and El_{q} D_{2} are negative, so demand decreases when the price increases in both cases, as seems reasonable. Both income elasticities El_{m} D_{1} and El_{m} D_{2} are positive, so demand increases when mean income increases—as seems reasonable.
Note that the demand for apples is more sensitive to both price and income increases than is the demand for potatoes. This also seems reasonable, since at that time potatoes were a more essential commodity than apples for most consumers.