Answer:
Step-by-step explanation:
To derive a linear equation for the demand for bonds using prices instead of interest rates, we need to convert the interest rates into prices. We can do this by using the loanable funds framework, which states that the interest rate is determined by the intersection of the supply and demand curves for loanable funds. In this case, the loanable funds are bonds.
Let's start by converting the interest rates into prices. The price of a bond is simply the present value of the future cash flows it generates, discounted at the market interest rate. Therefore, we can calculate the price of a bond using the following formula:
Price = Coupon Payment / (1 + Market Interest Rate)^n + Coupon Payment / (1 + Market Interest Rate)^(n-1) + ... + Coupon Payment + Face Value / (1 + Market Interest Rate)^n
where Coupon Payment is the annual coupon payment, n is the number of years until maturity, and Face Value is the face value of the bond.
Using the given data, we can calculate the prices of the bonds last month and this month as follows:
Last month:
Price = 250 / (1 + 0.118)^1 + 250 / (1 + 0.118)^2 + ... + 250 / (1 + 0.118)^n + 1000 / (1 + 0.118)^n
Price = 2144.37
This month:
Price = 25 / (1 + 0.122)^1 + 25 / (1 + 0.122)^2 + ... + 25 / (1 + 0.122)^n + 1000 / (1 + 0.122)^n
Price = 2136.87
Now that we have the prices of the bonds, we can use them to derive a linear equation for the demand for bonds. We know that the demand curve for bonds is downward sloping, meaning that as the price of bonds increases, the quantity demanded decreases. We can express this relationship using a linear equation of the form:
Qd = a - bP
where Qd is the quantity demanded, P is the price of bonds, a is the intercept, and b is the slope.
Using the values from the previous calculation, we have:
b = (Q1 - Q2) / (P2 - P1)
b = (1250 - 250) / (2136.87 - 2144.37)
b = -100
Substituting the value of b into one of the demand equations, we can solve for the intercept, a. Let's use the first equation:
Q1 = a - bP1
250 = a + 100(2144.37)
a = -212,887.5
Therefore, the correct linear equation for the demand for bonds using prices instead of interest rates is:
Qd = -212,887.5 - 100P
This equation shows that the quantity demanded of bonds decreases as the price of bonds increases.