Asset Prices and the Interest Rate

 


A consul is a bond that pays a fixed rate of interest based on the sale price forever. For example, a $1000 consul with a 5% interest rate would pay the owner $50 each year forever.

Market rate of interest for consuls depends on the supply and demand for consuls. The contract interest rate for a consul does not adjust. What adjusts is the price of the consul so that the effective interest rate: roughly payment/price equals the market rate of interest.

Suppose the government sells a large number of consuls at 5% interest. The next year the demand for consuls drops and the government has to raise the interest rate to 10% to attract buyers. What happens to the price of the consuls issued at 5% interest. To see what happens suppose a buyer of a 5% consul tried to sell his consul in a market where buyers could buy 10% consuls. If a buyer bought a 10% $1000 consul he would receive $100 a year. The price of the 5% $1000 consul would have to fall to $500 in order for the buyer to obtain 10% interest. The buyer would be indifferent between purchasing two of the old 5% $1000 consuls at $500 each or one of the new 10% $1000 consuls. In either case he would receive $100 a year for his $1000 investment. The price of consuls adjusts such the interest payment equals the market rate of interest.

Buy $2000 consul at 10% interest, market interest drops to 5%. Sell at ______
Buy $2000 consul at 4% interest, market interest rises to 16%. Sell at ________
Buy $2000 consul at 12% interest, market interest drops to 9%. Sell at ______
Buy $2000 consul at 3% interest, market interest rises to 4%. Sell at ________


The purpose in introducing consuls was to eliminate the problem with the time horizon of current bills, notes and bonds. Currently at the end of the stated time horizon, for example a 30 year bond, the government pays back the principal in full. What this means the longer the time horizon before repayment of principal the more the bond acts like a consul. For short term debt the price changes only slightly with varying interest rates. The longer the time horizon the greater the change. For example, if you buy a 30 year bond at 9% and the next year interest rates fall to 8% your bond increases in price by about 15% so that the effective interest rate is 8%.


Summary of Fed Actions


 





UP??? means if expand too much, inflation will definitely occur.
Down?? means if contract too much, it will cause a recession and inflation will abate.






Bank expansion problem: Note: The theory of bank expansion and contraction is adequately covered in the text. The following problem is an exam type problem:

1. Given a very large number of standard banks whose initial position is:


where R is reserves, GS is government securities, L are loans, D is demand deposits and the required reserve ratio is 20%. (Do not expect 20% on quiz)

1. To expand the money supply should the FED buy or sell securities?
2. What will happen to interest rates?
3. Assuming the FED's transaction to expand the money supply is $10M and to maximize profits the banks keep reserves down to the legal minimum explain numerically what happens if the FED transaction is with a bank. Consider a plausible course of action at the first two banks. (The first two terms of the geometric series.)
4. Explain in words the mechanism which causes the expansion.
5. Briefly discuss a contraction.
6. What is the money multiplier resulting from part 3. What is
DM? (Change in the money supply)
7. Why is this multiplier larger than the empirical monetary expansion multiplier? Discuss with words or symbols.

On quiz, discussion questions will be multiple choice.