You are given the following information about the capital market: Supply Q=10+100r ; Demand Q=15-100r
a) Explain the meaning of the number “10” in the first equation, using an if/then statement.
b) Explain the meaning of the number “100” in the second equation, using an if/then statement.
c) Find the equilibrium levels of the real interest rate, private savings, and the quantity of investment demanded.
d) Draw a simple graph of the capital market and show the equilibrium from part b. Make sure to label all axes and curves.
e) Due to technological innovation, MPK increases at every given interest rate, causing the investment demand curve to shift to the right by the amount of 2 units of financial capital. Show the new equation of the investment demand curve.
a) The first equation in this question is meant to allow us to derive a supply curve for a capital market. It is meant to tell us the quantity of capital supplied at every possible interest rate (the variable r stands for the interest rate as the interest rate is, in essence, the price of capital). What the number 10 in the equation stands for is the amount of capital that would be supplied if the interest rate were zero. Using an if-then statement, we can say “if the interest rate in this capital market were zero, the quantity of capital supplied would be 10 (of whatever units the quantity is being measured in).”
b) The second equation is the equation that allows us to derive a demand curve for this market. It gives us the quantity demanded of capital at every possible interest rate. What the number 100 in the equation stands for is the slope of the demand curve. It tells us how rapidly the quantity demanded changes when the interest rate changes. As an if-then statement: “if the interest rate changes by 1, the quantity demanded changes by 100.”
c) In order to find the equilibrium interest rate and quantity of capital supplied and demanded, we simply need to set the two equations equal to one another and solve for Q (the quantity demanded or supplied).
10 + 100r = 15 – 100r subtract 10 from both sides
100r = 5 – 100r Add 100r to both sides
200r = 5 divide both sides by 200
r = .025 (since this is an interest rate, it is better to think of this as 2.5%)
So, our equilibrium interest rate is 2.5%.
We can now plug that value in for r in either of the two equations to get the equilibrium quantity.
Q = 10 + 100(.025)
Q = 10 + 2.5 = 12.5
So, our equilibrium quantity is 12.5 of whatever unit we are using. That means that 12.5 is the total quantity of investment demanded.
e) If the demand curve shifts to the right, all that changes is the intercept, not the slope. What we have to do is add 2 to the constant in the demand equation. That would give us a new equation of Q = 17 – 100r.