Questions: Consider an economy with the money demand function is [ (m/p)^d=1/2 times y/i ]

To analyze the given money demand function, we need to understand the components and their economic implications. The function is:

\[ \left(\frac{\mathrm{m}}{\mathrm{p}}\right)^{\mathrm{d}}=\frac{1}{2} \times \frac{\mathrm{y}}{\mathrm{i}} \]

Where:

• \(\left(\frac{\mathrm{m}}{\mathrm{p}}\right)^{\mathrm{d}}\) is the real money demand.
• \(m\) is the nominal money supply.
• \(p\) is the price level.
• \(y\) is the real income or output.
• \(i\) is the nominal interest rate.

1. Real Money Demand: The left side of the equation, \(\left(\frac{\mathrm{m}}{\mathrm{p}}\right)^{\mathrm{d}}\), represents the demand for real balances. This is the amount of money people want to hold, adjusted for the price level.

2. Income and Interest Rate Relationship:

   • The right side of the equation, \(\frac{1}{2} \times \frac{\mathrm{y}}{\mathrm{i}}\), shows that real money demand is directly proportional to real income (\(y\)) and inversely proportional to the nominal interest rate (\(i\)).
   • Income Effect: As real income (\(y\)) increases, people demand more real balances because they have more transactions to conduct.
   • Interest Rate Effect: As the nominal interest rate (\(i\)) increases, the opportunity cost of holding money increases (since money held as cash does not earn interest), leading to a decrease in the demand for real balances.

3. Coefficient: The coefficient \(\frac{1}{2}\) indicates the sensitivity of real money demand to changes in income and interest rates. It suggests that for a given level of income and interest rate, the real money demand is half of the ratio \(\frac{\mathrm{y}}{\mathrm{i}}\).

The money demand function \(\left(\frac{\mathrm{m}}{\mathrm{p}}\right)^{\mathrm{d}}=\frac{1}{2} \times \frac{\mathrm{y}}{\mathrm{i}}\) implies that real money demand is positively related to real income and negatively related to the nominal interest rate. The coefficient \(\frac{1}{2}\) moderates the impact of these variables on real money demand. This function reflects typical economic behavior where higher income increases money demand for transactions, while higher interest rates reduce it due to the higher opportunity cost of holding money.