algebraic formula

S

squid

Registered Senior Member
help:

Mr. Midas has a wealth of $100,000 that he invests entirely in money ( a checking account) and government bonds. Mr. Midas intructs his broker to invest $ 50,000 in bonds, plus $5,000 more in bonds for every percentage point that the interest rate on bonds exceeds the interest rate on his checking account.

a) Write an algebraic formula that gives Mr. Midas's demand for money as a fraction of bond and checking account interest rates.

b) Wite an algebraic formula hat gives Mr. Midas's demand for bonds. What is the sum of his demand for money and his demand for bonds?

c) Suppose that all holders of wealth in the economy are identical to Mr. Midas. Fixed asset supplies per person are $80,000 of bonds and $20,000 of checking acounts. Checking accounts pay no interest. What is the interest rate on bonds in asset market equilibrium?


thanks!
 
Financial mathematics is not my cup of tea. I doubt it is for many other people here on the physics and maths forum, either.
 
As far as I can see part a & b make no sense as written. However, I will try to answer the question anyway. Assume:

C = amt in chequing account $
B = amt in bonds $
b = rate of bonds %
c = rate of chequing acct %

a. C = 50000 - 5000*int(b-c)
I would say that a good measure of demand for money would C/100000(total wealth) ie at the same rate of interest the demand for money in your chequing account is 0.50.

This is not what the question asks for it asks for some kind of ratio of the two interest rates. However, the ratio of a 2% bond rate to a 1% chequing is the same as a 20%bond to a 10% chequing account, but this cannot represent the demand for money given what the problem says above.

b.B =50000 + 5000*int(b-c). Demand for bonds could equal B/100000(total wealth), by this scenario the sun of the demand for money and the demand for bonds is 1.0

c. is relatively straight forward.

Given B=80000 and c=0

then 80000=50000 - 5000*int(b-0)

which reduces to 6=int(b)

int a reduces to a number to the closest integer below it (ie int(6.9999)=6

Thus b is somewhere between 6% and 6.99999(repeating)%.

Cheers,

BTW, I don't blame you for finding this question confusing.
 
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