Econ question please help?

Question

Suppose the impact on the interest rate of a $3 increase in government spending can be eliminated by a $1 increase in money supply. If the income multiplier with respect to government spending is 4, the money multiplier is 5 and the income multiplier with respect to money supply is 3, what mix of central bank bond purchases and higher governemtn spending is required to increase income by $6000 without changing the interest rate?

Answer 1

If apples were oranges, ...

It is tenet of mathematical logic that a statement of the form "If False then A" is always true no matter what A is. For example, it is true that "If I'm the greatest that the world has ever seen, then so are you"

The notion that "the impact on the interest rate of a $3 increase in government spending can be eliminated by a $1 increase in money supply" is completely false.

What happens if you increase government spending depends on how you get the money to spend: is the government just printing it? raising taxes? selling bonds to the public?

Your question ignores the big picture to concentrate on the individual formulas - very dangerous. That approach leads to the feeling that you are in control, which is madness.

But as for the answer you want (as opposed to the one you got), just set up the equations and solve:

Let S be the increase in government spending, M the increase in the money supply, B be the amount of central bank bond purchases, and I be the increased income.

So the equations look like:

I = 6000

M = S/3

I = 4S + 3M

etc.

All very simple algebra.