In: Economics
A federal government budget deficit means that the federal government is spending more in government expenses that it earns in taxes. So to spend more than it earns, the federal government must borrow and this leads them to budget deficit (G>T).
Now recall that National Savings = Public savings+Private savings.
Public savings = T-G<0.
Private saving is unchanged as there is no mentioned change of Y,T or C.
So national savings fall due to fall in public savings.
Now let's consider the options -
Savings function will shift inwards is correct. A decrease in national saving will cause the savings curve to shift inwards (or leftwards) which will raise interest rates.
Investment function to shift inwards is incorrect. Investment is a function of interest rate and Y. Here Y is unchanged while interest rate rises due to fall in savings which causes quantity of Investment to decrease. The function itself is not affected.
Savings function to shift outwards is incorrect. A outward shift of savings curve means an increase in savings of the nation and not a decrease (which is the case here).
Investment function to shift outwards is incorrect. As explained under the second option a budget deficit does not affect investment function. It only impacts the quantity of investments by affecting the interest rate.