Chapter 7, Problem 3NP

a)

To determine

To write: The algebric form of demand for money as a function of bond and checking account interest rates.

Answer to Problem 3NP

The equation for Person M’s money demand is $\boxed{M^d=\$50000-\$500000(i-i^m)}$ .

Explanation of Solution

Given information:

Value of bonds = $50000

2^nd bond = $5000

Net wealth = Total wealth − Amount invested.

For second bond, interest rate is more compared to checking account.

So to complete the formula, subtract $50000 and the formula $\$5000(i-i^m)100$ from $100000 . This is done because $50000 is invested and $5000 is value of bond which gives interest .

So, Demand for money is,

  $M^d=\$100000-\$50000-\$5000(i-i^m).100$

  $M^d=\$50000-\$500000(i-i^m)$

Value of bond = $5000

Interest rate on bond = i

Interest rate on checking account = i^m

In percentage form, value of bond is written as $\$5000(i-i^m)$

Hence the equation for Person M’s money demand is $M^d=\$50000-\$500000(i-i^m)$ .

Economics Concept Introduction

Introduction:

Equilibrium in asset market occurs when demand of money is equal to supply of money.

b)

To determine

To write: The algebric formula of demand for bonds.

Answer to Problem 3NP

Algebric formula of demand for bonds is $B^d=\$50000+\$500000(i-i^m)$

Explanation of Solution

Person M’s demand for bonds is simply the sum of the amount of his money that is wanted for investment in bonds, $\$50000$ and $\$500000(i-i^m)$ .So the formula for demand for bonds is:

  $\boxed{B^d=\$50000+\$500000(i-i^m)}$

To fund the sum of demand for money and demand for bonds, add the formulas of the demand for money from part a, $M^d=\$50000-\$500000(i-i^m)$ and the demand for bonds, $B^d=\$50000+\$500000(i-i^m)$ .

  $M^d+B^d=\$50000-\$500000(i-i^m)+\$50000+\$500000(i-i^m)$

  $=\$50000+\$50000$

  $=\$100000$

So the sum of Person M’s demand for money and bonds is $\boxed{\$100000}$ , the amount of wealth.

Economics Concept Introduction

Introduction:

Equilibrium in asset market occurs when demand of money is equal to supply of money.

c)

To determine

To find: The interest rate on bonds in asset market equilibrium

Answer to Problem 3NP

The i8nterest rate on bonds in asset market equilibrium is 6%.

Explanation of Solution

In order to find the interest rate on bonds in asset market equilibrium, either set money supply, $20000, equal to money demand from part a. or set bond supply, $80000, equal to bond demand from part b., set $i^m=0$ and solve for i.

  $M^d=M^s$

  $50000-500000(i-i^m)=20000$

  $50000-500000(i-0)=20000$

  $50000-500000i=20000$

  $-500000i=-30000$

Continue by dividing through by -500000

  $\frac{-500000i}{-500000}=\frac{-30000}{-500000}$

  $i=0.6$

So, the interest rate on bonds in asset market equilibrium is $i=0.6=6\%$ .

Economics Concept Introduction

Introduction:

Equilibrium in asset market occurs when demand of money is equal to supply of money.