How might the impact of an increase in government spending on the economy change if the increase in public expenditure is paid for by raising interest rates to encourage people and firms to lend money to the goverment?
In general, this is not a very good idea. These two economic policies will be at cross purposes to one another and may well end up preventing the increased spending from having its desired effect.
The most likely reason to increase government spending is because there is a need for greater economic growth. Government spending stimulates aggregate demand in the short term and thereby increases economic output. The problem is that an increase in interest rates will work in the opposite direction and may well hurt the economy more than the spending increase helps.
If interest rates are raised, people will want to lend more money to the government. However, they will also be less willing to borrow money. This will be true of consumers and it will be true of business. The higher interest rates will make borrowing more expensive and will make it less likely that either of these groups will want to borrow. If consumers and businesses borrow less, aggregate demand will drop. This means that our monetary policy will be contractionary while our fiscal policy is expansionary. The two will cancel each other out. Therefore, this is not a great idea.