please show all work this is my second time posting this que

please show all work, this is my second time posting this question, please do not answer it if you are not going to show the work (that isn\'t helpful).

GIVEN:

please show all work, this is my second time posting this question, please do not answer it if you are not going to show the work (that isn\'t helpful).

Assume the following for the long run:    

1. For every 1% increase (decrease) in interest rate, planned investment decreases (increases) by $5 billion.

2. For every $10 billion increase (decrease) in government spending, interest rate increases (decreases) by 1%.

3. The MPC = 0.8

QUESTION (show all steps): Taking the crowding-out effect into consideration, if government spending increases by $30 billion, equilibrium output increases by ___ billion.

please show all work, this is my second time posting this question, please do not answer it if you are not going to show the work (that isn\'t helpful).

Solution

MPC = 0.8

Spending multiplier = 1 / (1 - MPC) = 1 / (1 - 0.8) = 1 / 0.2 = 5

This means, as government spending rises by $1, output increases by $5.

As spending rises by $30 billion, output rises by $30 billion x 5 = $150 billion.

Also,

As government spending rises by $10 billion, interest rate rises by 1%.

As government spending rises by $30 billion, interest rate rises by [($30 billion / $10 billion) x 1%] = 3%.

Given, as interest rate rises by 1%, investment falls by $5 billion.

As interest rate rises by 3%, investment falls by $5 billion x 3 = $15 billion.

Therefore,

Net increase in output = Increase due to government spending - Decrease in investment

= $(150 billion - 15 billion)

= $135 billion