Question

a country has a full - employment gdp ($q^f$) of $1,000 billion and net foreign wealth ($nfw$) of $200 billion, with a world interest rate ($r^*$) of 2%. what is the country’s national income ($y^f$)? if $nfw$ decreases to -$100 billion in the next period, what will be the new level of $y^f$?
initial: $1,004 billion; new: $998 billion
initial: $1,005 billion; new: $998 billion
initial: $1,004 billion; new: $997 billion
initial: $1,005 billion; new: $997 billion

Explanation:

Step1: Recall the formula for national income

The formula for national income \( Y^f \) is \( Y^f = Q^f + R^* \times NFW \), where \( Q^f \) is full - employment GDP, \( R^* \) is the world interest rate, and \( NFW \) is net foreign wealth.

Step2: Calculate the initial national income

Given \( Q^f=\$1000 \) billion, \( NFW = \$200 \) billion, and \( R^*=2\% = 0.02 \).
Substitute into the formula: \( Y^f=1000+0.02\times200 \)
First, calculate \( 0.02\times200 = 4 \)
Then, \( Y^f=1000 + 4=\$1004 \) billion.

Step3: Calculate the new national income when \( NFW=- \$100 \) billion

Substitute \( Q^f = 1000 \), \( R^*=0.02 \), and \( NFW=- 100 \) into the formula \( Y^f=Q^f+R^*\times NFW \)
\( Y^f=1000+0.02\times(- 100) \)
First, calculate \( 0.02\times(-100)=- 2 \)
Then, \( Y^f=1000-2=\$998 \) billion.

Answer:

Initial: $1,004 billion; New: $998 billion