Question

: Money and Inflation (20 Marks) Suppose that the moncy demand function Mᵈ is given by: Mᵈ = PY⁰.²⁵

where P stands for the price level and Y for output.
(a) What is the income elasticity of money demand (ηY)?

Answer 1

The income elasticity of money demand (ηY) measures the responsiveness of the demand for money to changes in income. It can be calculated using the percentage change in money demand divided by the percentage change in income.

Step-by-step explanation:

The income elasticity of money demand (ηY) measures the responsiveness of the demand for money to changes in income. It is calculated as the percentage change in money demand divided by the percentage change in income.

To calculate the income elasticity of money demand, we can assume that the price level (P) remains constant. Therefore, the change in money demand is solely due to changes in income (Y). Using the given money demand function Mᵈ = PY⁰.²⁵, we can differentiate it with respect to income to find the income elasticity of money demand:

ηY = dMᵈ / Mᵈ * dY / Y

Using the power rule of differentiation, we find:

ηY = 0.025 * (PY⁰.²⁵) / (PY⁰.²⁵) * dY / Y

Simplifying, we get:

ηY = 0.025 * dY / Y

So, the income elasticity of money demand (ηY) is equal to 0.025 times the percentage change in income (dY / Y).