HW4 Q5

Suppose that real GDP is currently 13.1 trillion and full employment real GDP is 14.0 trillion, or a gap of 900 billion. The government purchases multiplier is 5.0, and the tax multiplier is 4.0.

Holding other factors constant, by how much will government purchases need to be increased to bring the economy to equilibrium at potential GDP?

A. 180

B. 225

C. 360

D. 900

Explaination:

Based on the formula of multiplier, we have:

\[\Delta GDP =M_{Gov}\times \Delta Gov\]

where \(M_{Gov}=5\) is government purchase multiplier. \(Gov\) represents government purchase. Thus, to increase GDP by 900 billion, we have:

\[\begin{split} 900&=5\times \Delta Gov \\ \rightarrow \Delta Gov&=900/5=180 \end{split}\]

\(Gov\) need to increase 180 billion.

HW4 Q6

Suppose that real GDP is currently 13.1 trillion and full employment real GDP is 14.0 trillion, or a gap of 900 billion. The government purchases multiplier is 5.0, and the tax multiplier is 4.0.

Holding other factors constant, by how much will taxes need to be decreased to bring the economy to equilibrium at potential GDP?

A. 180

B. 225

C. 360

D. 900

Based on the formula of multiplier, we have:

\[\Delta GDP =-M_{Tax}\times \Delta Tax\]

where \(M_{Tax}=4\) is government purchase multiplier. \(Tax\) represents tax. Thus, to increase GDP by 900 billion, we have:

\[\begin{split} 900&=-4\times \Delta Tax \\ \rightarrow \Delta Tax&=-900/4=-225 \end{split}\]

\(Tax\) need to decrease by 225 billion.

HW4 Q14

You are given the following information about an economy:

2006 2016
National Debt 100000 400000
Nominal GDP 500000 1000000
Price Index 240 250

The debt-to GDP ratio in 2006:

Explaination:

By definition:

\[\mathrm{debt~to~ GDP~ratio=\frac{debt}{nominal~GDP}}=\frac{100000}{500000}=0.2\]

HW4 Q8

Suppose the government increases taxes by 140 billion and the marginal propensity to consume is 0.80. By how will equilibrium GDP change?

A. -700

B. -560

C. 140

D. 700

Explaination:

By definition, tax multiplier is: \(\frac{mpc}{1-mpc}=\frac{0.8}{1-0.8}=4\). Thus, use multiplier formula, we have:

\[\Delta GDP =-M_{Tax}\times \Delta Tax=-4\times 140=-560\]

Equilibrium GDP decreases by 560 billion.