How an increase in government spending can affect equilibrium income and interest rate?

Question

(Using IS\LM diagram)

I need a little help with rephrasing my answer as my vocabulary is not so great please help thanks.

My answer is below:

Assume that the economy starts at equilibrium, if the government increases government spending, say purchases more equipment for the military, the manufacturers of military equipment see an unexpected increase in sales, their inventories drop below the desired level and they react by increasing production. This increase in production requires and increase in employment or in hours worked. Thus reducing unemployment and increasing national income. Individuals who make now more money or who now have a job they did not have before, spend part of this income purchasing goods and services -TV sets, cars, furniture,etc.-. Manufacturers of these consumer goods see inventories decrease, and they too increase production and hire more workers or more hours, generating another round of increases in income, consumption and spending.

Answer 1

It's quite simple - if government increases spending (it's part of Y=C+I+G+NX) then IS curve shifts up (right) from IS1 to IS2 leading to higher interest rate from i1 to i2 (thus multiplier is reduced a bit due to crowding-out effect) and higher equilibrium income (GDP) from Y1 to Y2.

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