If the income elasticity of demand is 3/4 and the interest elasticity of demand is -1/4, by what percent does money demand rise if income rises 10% and the nominal interest rises from 4% to 5%.
Thanks!
To find the percent change in money demand, we need to consider both the income elasticity of demand and the interest elasticity of demand. Let's break it down step by step:
Step 1: Calculate the percent change in income.
The income elasticity of demand is given as 3/4, which means that for a 1% increase in income, money demand increases by 3/4 percent. In this case, income is rising by 10%, so the percent change in income is:
Percent Change in Income = (Increase in Income / Initial Income) * 100%
= (10% / 100%) * 100%
= 10%
Step 2: Calculate the percent change in nominal interest rate.
The interest elasticity of demand is given as -1/4, which means that for a 1% increase in the interest rate, money demand decreases by 1/4 percent. In this case, the interest rate is increasing from 4% to 5%, so the percent change in the nominal interest rate is:
Percent Change in Interest Rate = (Increase in Interest Rate / Initial Interest Rate) * 100%
= ((5% - 4%) / 4%) * 100%
= (1% / 4%) * 100%
= 25%
Step 3: Calculate the combined effect on money demand.
Since the income elasticity and interest elasticity have opposite signs (positive for income elasticity and negative for interest elasticity), they will have a compensating effect on money demand.
Percent Change in Money Demand = (Income Elasticity * Percent Change in Income) + (Interest Elasticity * Percent Change in Interest Rate)
= (3/4 * 10%) + (-1/4 * 25%)
= 7.5% - 6.25%
= 1.25%
Therefore, the money demand rises by 1.25% when income rises by 10% and the nominal interest rate increases from 4% to 5%.