Question

An economy is operating with output $400 billion above its natural level, and fiscal policymakers want to close this expansionary gap. The central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. The marginal propensity to consume is 4/5, and the price level is completely fixed in the short run.

Answer 1

Answer:

$\Delta G= 400 billion \frac{1}{5}= 80 billions$

To close the expansionary gap, the government would need to spending by 80 billion

Explanation:

Assuming this question: "To close the expansionary gap, the government would need to spending by ? billion"

Previous concepts

The government expenditure multiplier "denoted by K, the impact of a change in income following a change in government spending".

The marginal propensity to consume denoted by MPC "is a metric that quantifies induced consumption, the concept that the increase in personal consumer spending occurs with an increase in disposable income"

Solution to the problem

Fo this problem we need to find the Government multiplier (K) with the following formula:

$K=\frac{1}{1-MPC}$

Wehre MPC represent the marginal propensity to consume. And if we replace we got this:

$K=\frac{1}{1-\frac{4}{5}}=5$

And now we can find the government decrease with the following formula:

$\Delta G= \Delta Y \frac{1}{K}$

And for this case the output is $\Delta Y = 400 billion$, and we have everything in order to replace:

$\Delta G= 400 billion \frac{1}{5}= 80 billions$

So thn the answer woud be: "To close the expansionary gap, the government would need to spending by 80 billion"