Question

Question 22 to 25: Consider a money market model with the following setup. The central bank money supply is H, where H = $Y. For each dollar the households want to hold c dollars as cash and 1–c dollars as checkable deposits. The reservation ratio is 10%. The nominal GDP is equal to real money supply. The money demand function is written as Md = $Y / (0.2 + i) where $Y is the nominal GDP and i is the interest rate. Answer the following questions by analyzing the money market model.

10. (3pt) What is the currency demand by the households. Please write it as an expression of the interest rate, i.

11. (3pt) What is the reserve demand by the commercial banks. Please write it as an expression of the interest rate, i.

12. (3pt) Recall: central money demand = currency demand by the households + reserve demand by the commercial banks. Use this central money market equilibrium condition to compute the equilibrium interest rate.

13. (3pt) How does the equilibrium interest rate change if people hold less cash, i.e. c decreases.

Answer 1

a) For each dollar, the households want to hold c dollars as cash and 1-c dollars as deposista.

For each dollar, the currency demand for households is c

For Y dollars, the currency demand for the households will be $Yc

b) The reserve demand, is the minimum amount of currency that the commercial banks should hold as reserves. The reserve ratio of the bank is 10%. This means that, the banks must hold 10% of their available cash, which comes from the deposits, as reserve.

The deposits of the bank for each dollar of currency is 1-c

The deposits of bank for Y dollar of currency is Y(1-c)

The commercial banks ust old 10% of this deposits available to them as reserves.

Thus, the reserve demand for the banks becomes,

10%*[Y(1-c)]

= Y(1-c)/10

c) We know that, central money demand= Currency demand by households + reserve demand by banks.

The money demand function is given as:

Md = Y / (0.2 + i)

So, Y / (0.2 + i)= Yc +Y(1-c)/10

From this equation, we get,

This is the equilibrium value of i.

d) From the obtained equilibrum value of i, it is visible that c is inversely proportional to interest rate.

So, if c decreases, i would increase.