The demand for rice in Japan for a particular year was estimated by the general function q = f (p) =Ap^(-0.13), where p represents the price of a unit of rice, A represents a constant that can be calculated uniquely for a particular year, and q represents the annual per capita rice demand. Calculate and interpret the elasticity of demand.

To calculate the elasticity of demand for rice in Japan, we need to find the formula for the elasticity (E) using the given function:

E = (dq/dp) * (p/q)

Let's calculate each component step by step:

1. Find the derivative of the demand function with respect to price (dq/dp):
To find dq/dp, we differentiate the given function with respect to p:

dq/dp = d(Ap^(-0.13))/dp
= A * (-0.13) * p^(-0.13 - 1)
= -0.13Ap^(-1.13)

2. Substitute the derivative (dq/dp) and the demand function (q = Ap^(-0.13)) into the formula for elasticity:
E = (-0.13Ap^(-1.13)) * (p / (Ap^(-0.13)))
= -0.13Ap^(-1.13) * (p / Ap^(-0.13))
= -0.13 * (p / p^(-0.13))
= -0.13 * (p^(1 + 0.13) / p)
= -0.13 * (p^1.13 / p)
= -0.13 * p^(1.13 - 1)
= -0.13 * p^(0.13)

So, the elasticity of demand for rice in Japan is given by E = -0.13 * p^(0.13).

Interpreting the elasticity of demand:
The magnitude of the elasticity value, regardless of its positive or negative sign, indicates the responsiveness of demand to a change in price. In this case, the magnitude of the elasticity is always positive (due to the exponent value being positive).

Since the elasticity value is less than 1 (absolute value |E| < 1), it suggests that rice demand in Japan is inelastic. This means that a change in the price of rice will result in a proportionally smaller change in the quantity demanded. In other words, the demand for rice is relatively insensitive to changes in price.