2. Assume the following: i. The public holds no currency. ii. The ratio of reser

Question

2. Assume the following: i. The public holds no currency. ii. The ratio of reserves to deposits is 0.1. iii. The demand for money is given by Md=$Y(.8-4i) Initially, the monetary base is $100 billion, and nominal income is $5 trillion.
a. What is the demand for central bank money? b. Find the equilibrium interest rate by setting the demand for central bank money equal to the supply of central bank money. c. What is the overall supply of money? Is it equal to the overall demand for money at the interest rate you found in part (b)? d. What is the impact on the interest rate if central bank money is increased to $300 billion? e. If the overall money supply increases to $3,000 billion, what will be the impact on i? [Hint: Use what you learned in part (c) 2. Assume the following: i. The public holds no currency. ii. The ratio of reserves to deposits is 0.1. iii. The demand for money is given by Md=$Y(.8-4i) Initially, the monetary base is $100 billion, and nominal income is $5 trillion.
a. What is the demand for central bank money? b. Find the equilibrium interest rate by setting the demand for central bank money equal to the supply of central bank money. c. What is the overall supply of money? Is it equal to the overall demand for money at the interest rate you found in part (b)? d. What is the impact on the interest rate if central bank money is increased to $300 billion? e. If the overall money supply increases to $3,000 billion, what will be the impact on i? [Hint: Use what you learned in part (c) 2. Assume the following: i. The public holds no currency. ii. The ratio of reserves to deposits is 0.1. iii. The demand for money is given by Md=$Y(.8-4i) Initially, the monetary base is $100 billion, and nominal income is $5 trillion.
a. What is the demand for central bank money? b. Find the equilibrium interest rate by setting the demand for central bank money equal to the supply of central bank money. c. What is the overall supply of money? Is it equal to the overall demand for money at the interest rate you found in part (b)? d. What is the impact on the interest rate if central bank money is increased to $300 billion? e. If the overall money supply increases to $3,000 billion, what will be the impact on i? [Hint: Use what you learned in part (c)

Explanation / Answer

= ratio of deposit to reserves

c = 0, public holds no currency

(a) Hd = [c + (1-c)] $Y (0.8 – 4i) = 0.1 $Y (0.8 – 4i) = 0.1 Md

(b) 0.1*(5000)*(0.8 – 4i) = 100

500*(0.8 – 4i) = 100

400 - 2000i =100

300 / 2000 = i

=0.15

or 15%

solving for i yields i = 0.15 = 15%

(c) Ms = (1/0.1) 100 = 100; Md = 5000 [0.8 – 4(0.15)] = 1000

(d)  300 = 0.1 (5000) (0.8 – 4i);

300 = 500*(0.8 – 4i)

400 - 2000i = 300

2000i = 100

i = 100/2000

solving for i yields i = 0.05 = 5%

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