Answer to Question #162905 in Microeconomics for Lutuf Ali

Question

The price elasticity for rice is estimated to be -0.4 and the income elasticity is 0.8. At a price of S0.40 per pound and a per capita income of $20.000, the demand for rice is 50 million tons per year,

a. Is rice an inferior good, a necessity. or a luxury? Explain.

b. If per capita income increases to $20.500, what will be the quantity demanded of rice?

c. If the price of rice increases to $0.41 per pound and income per capita remains at $20.000, what will be the quantity demanded

Answer 1

(a) Rice is a necessity good (because the necessities have an income elasticity of demand between 0 and +1).

(b) By the definition of the income elasticity of demand, we have:

$$E_y=\dfrac{\%\Delta Q}{\%\Delta Y}=\dfrac{\%\Delta Q}{\dfrac{Y_2-Y_1}{Y_1}},$$ $$\%\Delta Q=E_y\dfrac{Y_2-Y_1}{Y_1},$$ $$\%\Delta Q=0.8\cdot\dfrac{\$20500-\$20000}{\$20000}=0.02\times100\%=2\%.$$

So, the quantity demanded increases by 2%:

$Q=50000000\cdot0.02=1000000$ tons. Therefore,  the quantity demanded of rice will be 50 million tons + 1 million tons=51 million tons.

(c) By the definition of the price elasticity of demand, we get:

$$E_d=\dfrac{\%\Delta Q}{\%\Delta P}=\dfrac{\%\Delta Q}{\dfrac{P_2-P_1}{P_1}},$$ $$\%\Delta Q=E_y\dfrac{P_2-P_1}{P_1},$$ $$\%\Delta Q=-0.4\cdot\dfrac{\$0.41-\$0.40}{\$0.40}=-0.01\times100\%=-1\%.$$

So, the quantity demanded decreases by 1%:

$Q=50000000\cdot0.01=500000$ tons. Therefore,  the quantity demanded of rice will be 50 million tons - 0.5 million tons=49.5 million tons.