I have an assignment question regarding the impact of reducing the government's budget deficit by reducing government purchases.

I have to develop a S/D graph with curves to illustrate this impact.

I know that when the government makes purchases and runs a deficit, supply of investments and savings (loanable funds) shifts left.

When the government reduces purchases, does the demand curve shift left or does the supply curve shift back to the right?

Also what is the shifting for an income tax increase to lower the budget deficit?

Government purchases are a component of aggregate demand. Reducing government purchases means reducing aggregate demand; the demand curve shift inward. GDP falls, Prices decline.

I would not necessarily shift the supply of loanable funds curve when governments run a deficit. Rather, a deficit leads to an increase in demand for loanable funds. With movement along the supply curve, interest rates rise (and as a result, private investment falls) This is the so-called crowding out effect.

Income taxes reduce disposable income which in turn reduces consumption, a component of aggregate demand.