Question

Suppose that a person’s wealth is $50,000 and that her yearly income is $60,000. Also, suppose that her money demand function is given by: Md = $Y(0.35 − i). (a) Derive the demand for bonds.

a) What is the effect of an increase in the interest rate of 10% (from, say, 2% to 12%) on the demand for bonds?

(b) What are the effects of an increase in wealth on money demand and on bond demand? Explain in words.

c) What are the effects of an increase in income on money and on bond demand? Explain in words.

(d) "When people earn more money, they obviously want to hold more bonds." What is wrong with this statement?

Answer 1

Low Interest Rates and Bonds

When interest rates are low, bond prices are high. Because low-interest rates cause higher bond prices and result in a lower return on investment, the demand for bonds is lower. However, the supply of bonds increases as bond prices increase and interest rates decrease.
When bond prices rise, yields fall, and vice versa. Hence, when fear rises and money flows into bonds, it pushes prices higher and yields lower. Therefore, when interest rates rise, bond prices fall, and bond investors, especially those who remain in bond funds, will feel some degree of pain
As if rising interest rates weren’t bad enough for bonds, if you are a shareholder in a bond fund during a period such as this, your pain will likely be greater than an investor invested in an individual bond. For example, a given bond fund will hold hundreds, perhaps several thousand individual bonds. When interest rates rise, to avoid further losses, shareholders in a bond fund will liquidate their shares. When this occurs, the fund manager may be forced to sell bonds prematurely in order to raise enough cash to meet its redemption requests. This can have a destructive effect on the average price of a bond fund, called its net asset value (NAV). Hence, bond funds have an additional risk during periods of rising interest rates, referred to as redemption risk. Redemption risk exaggerates the pain for those who remain in the fund. However, if you own an individual bond, as long as you hold it until maturity, none of this price fluctuation means very much because when your bond matures, you will receive its par value or 100% of its original value.
we have to remember that money is a stock not a flow, and that income and wealth are not money. Demand for money is a question of how much of your wealth you wish to hold in the form of money at any point in time. (Supply of money is also a stock concept.)
Your demand for money is how much of your wealth you wish to hold as money at any moment in time. It is thus a stock demand. Your wealth is a stock, and you must decide how to allocate that stock of wealth between different kinds of assets -- for example a house, income-earning securities, a checking account, and cash.
Why would you hold any of your wealth as money -- as cash or checking deposits? Those assets earn little or no interest. Wouldn't it be more sensible to hold all your wealth in the form of assets that yield income? Note that:
1. There is a cost associated with holding money balances (you give up interest payments),
2. There is no intrinsic value in the money balances you hold except in their use as a medium of exchange. Generally, you acquire money in order to get rid of it -- to buy things. While you hold it, money does not keep you warm, entertain you, or provide any other benefit.
Economists identify two reasons why people will demand money balances, or desire to hold a certain stock of money even if there is no intrinsic value for the money balances they hold.
It is costly, in terms of time and resources, to keep moving in and out of bonds or other assets and money. Since this is the case, I will desire to hold a certain level of money balances on average, to meet my needs to pay for transactions. This is called the transactions demand for money.
If the interest payments I receive on bonds and other assets is high, then it is worth my while to move in and out of stocks and bonds and money, so that I can earn this interest payment instead of holding money balances. If the interest rate is not that high, then it is not worth it to move in and out of money and bonds in order to receive this interest payment.
Another way to look at it is that the interest rate describes the cost of holding money balances. This is because the interest rate tells you the amount of interest income you have to forego by holding money balances instead of lending out that money and holding an asset like a bond.
This is enough to generate a curve which plots the demand for money -- the amount you wish to hold as opposed to holding wealth as bonds -- as a function of r. This curve will slope downward.