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, we need to use the formula:

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

where E is the elasticity of demand, dq/dp represents the derivative of q with respect to p, p represents the price, and q represents the quantity demanded.

In this case, q = Ap^(-0.13). To find the derivative of q with respect to p, we can use the power rule:

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

Simplifying the equation:

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

Now, we can substitute this derivative back into the elasticity of demand formula:

E = (-0.13A * p^(-1.13)) * p / (Ap^(-0.13))

Simplifying further:

E = -0.13 * p^(-1.13) * p / p^(-0.13)

E = -0.13 * p^(-2.26) / p^(-0.13)

E = -0.13 * p^(-2.26 + 0.13)

E = -0.13 * p^(-2.13)

Now, interpreting the elasticity of demand:
- If E < -1, the demand is elastic, meaning a 1% increase in price will result in a more than 1% decrease in quantity demanded.
- If E > -1, the demand is inelastic, meaning a 1% increase in price will result in a less than 1% decrease in quantity demanded.
- If E = -1, the demand is unitary elastic, meaning a 1% increase in price will result in a 1% decrease in quantity demanded.

In this case, we have:
E = -0.13 * p^(-2.13)

Since we don't have a particular price value, we cannot determine whether the demand is elastic, inelastic, or unitary elastic without further information.

elasticity e = df/f ÷ dp/p = df/dp * p/f

df/dp = A(-0.13)p^(-1.13)

so, e = -0.13Ap^(-1.13) * p/A p^(-0.13)
= -0.13/p^0.26

so, we have negative elasticity, meaning that demand will go down if price goes up.

It also shows that for larger prices, the elasticity changes, becoming less significant.