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Suppose that the economy is in recession with a recessionary gap of $1 trillion. The MPC is 0.9 and the tax rate on income is 30%. Answer the...

In this scenario, we are faced with a $1 trillion recessionary gap.  That means that the economy is producing $1 trillion less than it could be.  In order to eradicate this gap, the government needs to spend more money (according to Keynesian economics).  But how much more does the government need to spend?  To find this out, we need to find the value of the multiplier because every dollar that the government spends will be multiplied by this figure.


The simple equation for the multiplier is 1/1- MPC.  In this scenario, you have told us that the MPC (marginal propensity to consume) is .9.  This means that every time someone in this economy gets another dollar, they will spend $.90 of it and only save $.10.  If we plug this value into the equation, we get 1/1-.9 = 1/.1 = 10.  This means that our multiplier is 10.  Every dollar the government spends will cause a $10 increase in GDP. 


Because the AS curve is completely flat, the increase in GDP is all real.  That is, none of it is diluted by inflation as it would be if the AS curve had a positive slope.  Therefore, we have an easy calculation.  We simply have to divide $1 trillion (the size of the gap we need to fill) by 10 (the value of the multiplier).  When we do this, we find that the answer is $100 billion.  This means that the government will have to increase spending by $100 billion.  So, the answer is that the change in G (government purchases) needs to be $100 billion.

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