Question

The price elasticity for rice is estimated to be -0.4 and the income elasticity is 0.8. At a price of $0.40 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 luxury? Explain

b. If per capita income increases to $20,500, what will be the quantity demanded of rice?

c. If the price of ruce increases to $0.41 per pound and income per capita remains at $20,000, what will be the quantity demanded?

Answer 1

ANSWER

a) The income elasticity is 0.8. This value is less than 1 and greater than 0. Hence, it is necessity good. The share of this good in the total expenditures decreases if the total income will be increased.

b) Let's write a formula for the income elasticity:

$IE=\frac{PC(Qd)}{PC(Income)}$ ,

where PC(x) can be calculated as follows:

$PC(x)= \frac{x(i)-x(i-1)}{x(i-1)}$

Let's calculate the $PC(Income)$ :

$PC(Income)= \frac{20,500-20,000}{20,000}=0.025$

based on above the $PC(Qd)$ can be calculated

$0.8=\frac{PC(Qd)}{0.025}$ , hence

$PC(Qd)=0.8\times0.025=0.02$

Using a formula for PC(x) we can calculate new demand (denoted by Qd):

$0.02= \frac{Qd(new)-50}{50}$

Hence,

Qd(new)=51 million tons per year.

c)

The price elasticity of demand measures the responsiveness of the quantity demanded for a good to a change in the price of this good.

Hence, the formula for the price elasticity can be written as follows:

$E(Qd)=\frac{PC(Qd)}{PC(P)}$ ,

where PC(x) can be calculated as follows:

$PC(x)= \frac{x(i)-x(i-1)}{x(i-1)}$

Let's calculate the PC(P):

$PC(P)= \frac{0.41-0.40}{0.40}=0.025$

based on above the $PC(Qd)$ can be calculated

$-0.4=\frac{PC(Qd)}{0.025}$ , hence

$PC(Qd)=-0.4\times0.025=-0.02$

Using a formula for PC(x) we can calculate new demand (denoted by Qd):

$-0.02= \frac{Qd(new)-50}{50}$

Hence, Qd(new) is equal to 49 million tons per year.