Suppose that the government allocates $1 billion for new roads. It also raises taxes by $1 billion to keep the deficit from growing. The absolute value of the government purchase multiplier is 10 and that of the tax multiplier is 9. What is the effect on equilibrium GDP?

GDP does not change.

GDP increases by $10 billion.

GDP increases by $900,000.

GDP increases by $1 billion.

Answer:

Change in government expenditure = $1 billion, change in tax revenue = $1 billion, so change in budget deficit = change in tax revenue - Change in government expenditure = 0

Change in equilibrium GDP = government purchase multiplier*change in government purchase + tax multiplier*change in tax revenue

Note that we are given the multipliers in absolute terms, also we know that govt purchase multiplier is positive, thus = +10, while tax multiplier is negative, thus = -9 (refer Q3), so accordingly,

Change in equilibrium GDP = government purchase multiplier*change in government purchase + tax multiplier*change in tax revenue

Change in equilibrium GDP = 10*$1 billion +(-9)*$1billion

Change in equilibrium GDP = $10 billions - $9 billions

Change in equilibrium GDP = $1 billion (with positive sign, so increase in GDP of $1 billion)

Correct option is D.