Question

12. Suppose that money demand is given by Md= SY (.25 - i) where SY is $100. Also, suppose that the supply of money is $20.

1. What is this person's demand for money when the interest rate is 5%? 10%?
2. Explain how the interest rate affects money demand.
3. Suppose that the interest rate is 10%. In percentage terms, what happens to this person's demand for money if her income is reduced by 50%?
4. What is the equilibrium interest rate?
5. if the Federal Reserve Bank wants to increase i by 10 percentage points (g., from 2% to 12%), at what level should it set the supply of money?

Answer 1

Md = Y x (0.25 - i)

(a)

(i) i = 5% = 0.05

Md = 100 x (0.25 - 0.05) = 100 x 0.2 = 20

(ii) i = 10% = 0.1

Md = 100 x (0.25 - 0.1) = 100 x 0.15 = 15

(b)

When interest rate increases (decreases), money demand decreases (increases), so interest rate and demand for money are inversely related.

(c)

New Y = 100 x 50% = 50

When i = 10% = 0.1,

New Md = 50 x (0.25 - 0.1) = 50 x 0.15 = 7.5

Change in Money demand = (7.5/15) - 1 = 0.5 - 1 = - 0.5 = - 50% (decrease)

(d)

In equilibrium, Md = Ms

100 x (0.25 - i) = 20

0.25 - i = 0.2

i = 0.05 = 5%

(e)

Since Md = Ms,

Y x (0.25 - i) = Ms

% change in Y + 0 - % Change in i = % Change in Ms

Assuming Y is unchanged, % change in Y = 0

0 + 0 - % change in i = % change in Ms

- 10% = % change in Ms

So, Ms should be decreased by 10%, and

New Ms = 20 x 90% = 18