Suppose the current equilibrium GDP for a country is $14.5 trillion and potential GDP is $14.3 trillion. Will decreasing government purchases by...

Neither of these fiscal policies will restore the country’s economy to its potential gross domestic product (GDP).  Both of them will close the inflationary gap, but they will both go too far and create a recessionary gap instead of bringing the economy exactly to its potential GDP.  The reason for this is the multiplier effect.

When actual GDP is higher than potential GDP, a country has what is called an inflationary gap.  It is producing more than it can sustainably produce in the long term.  Therefore, it will experience inflation.  In order to do away with this gap, the country should engage in contractionary fiscal policy.  That is, it should decrease spending and/or increase taxes.  In your scenario, the country would take the correct kind of action because it would either reduce spending or increase taxes.

However, when the government changes spending or tax levels, it cannot just do so by the exact amount of the inflationary gap.  This is because of the multiplier.  If the government reduces spending by $200 billion, GDP will actually fall much more than that.  Let us say that the government reduces spending by this much. GDP immediately falls by $200 billion, erasing the inflationary gap.  But then GDP falls further.  When the government paid out that $200 billion, the people who received it then went out and spent most of it.  They bought goods like groceries and services like haircuts.  The people who provided the groceries and haircuts got paid, and GDP increased.  Now, when the government stops spending the $200 billion, the people who used to receive it (and then spend it) will no longer do so.  They will no longer spend this money on groceries and haircuts.  Therefore, the total amount spent on all goods and services will decline much more than $200 billion.

When we look at fiscal policy, we have to understand that there is a multiplier effect.  If the government increases spending, GDP goes up by much more than the amount of the spending increase as people use their new income to buy more goods and services.  Conversely, if the government decreases spending, GDP drops but much more than the amount of the decrease because people cut back on their purchases as consumers.  Therefore, either of these changes will decrease the country’s GDP much more than is needed to close the inflationary gap.