From the end of 2005 to the end of 2006,the United States ran a deficit of about $309 billion.The debt at the start of this period was about $4,592 billion.Which of the following combinations of inflation and real GDP growth would have allowed the government to run this deficit while keeping the ratio of real GDP to the debt about the same?
A)about 3% inflation and about 2.2% real GDP growth
B)about 3% inflation and about 3.2% real GDP growth
C)about 3.4% inflation and about 3.3% real GDP growth
D)about 3.4% inflation and about 4% real GDP growth

Question

Quizplus · Accepted Answer

To keep the ratio of real GDP to debt about the same, we need the nominal GDP to increase by the same percentage as the increase in debt. 
The increase in debt over this period is approximately: 
$4,592 billion - $309 billion = $4,283 billion

We need nominal GDP to increase by a similar amount, say $4,200 billion, to maintain the ratio.

Let P be the rate of inflation and Y be the real GDP growth rate. Then:

Nominal GDP in 2005 = (1 + P) x (1 + Y) x Real GDP in 2005

Nominal GDP in 2006 = (1 + P) x (1 + Y) x Nominal GDP in 2005

If we assume that Real GDP in 2005 is approximately the same as Real GDP in 2006 (which is reasonable for a one-year period), then we have:

(1 + P) x (1 + Y) x Real GDP in 2005 = (1 + P) x (1 + Y) x Nominal GDP in 2005

(1 + P) x (1 + Y) = (4,200 / Real GDP in 2005)

We know that the inflation rate is between 3% and 3.4%, so we can try different values of real GDP growth to see which one satisfies the equation.

For option A:

(1 + 0.03) x (1 + 0.022) ≈ 1.052

(4,200 / 4,592) ≈ 0.914

(1 + P) x (1 + Y) ≈ 1.052 / 0.914 ≈ 1.151

This combination of inflation and real GDP growth would result in a nominal GDP increase of approximately:

(1 + P) x (1 + Y) x Real GDP in 2005 ≈ 1.151 x Real GDP in 2005

This is an increase of approximately 15%, or $687 billion, which is not enough to keep up with the increase in debt.

For option B:

(1 + 0.03) x (1 + 0.032) ≈ 1.066

(4,200 / 4,592) ≈ 0.914

(1 + P) x (1 + Y) ≈ 1.066 / 0.914 ≈ 1.166

This combination of inflation and real GDP growth would result in a nominal GDP increase of approximately:

(1 + P) x (1 + Y) x Real GDP in 2005 ≈ 1.166 x Real GDP in 2005

This is an increase of approximately 17%, or $780 billion, which is closer to the required increase in nominal GDP.

For option C:

(1 + 0.034) x (1 + 0.033) ≈ 1.069

(4,200 / 4,592) ≈ 0.914

(1 + P) x (1 + Y) ≈ 1.069 / 0.914 ≈ 1.169

This combination of inflation and real GDP growth would result in a nominal GDP increase of approximately:

(1 + P) x (1 + Y) x Real GDP in 2005 ≈ 1.169 x Real GDP in 2005

This is an increase of approximately 17.5%, or $805 billion, which is even closer to the required increase in nominal GDP.

For option D:

(1 + 0.034) x (1 + 0.04) ≈ 1.08

(4,200 / 4,592) ≈ 0.914

(1 + P) x (1 + Y) ≈ 1.08 / 0.914 ≈ 1.181

This combination of inflation and real GDP growth would result in a nominal GDP increase of approximately:

(1 + P) x (1 + Y) x Real GDP in 2005 ≈ 1.181 x Real GDP in 2005

This is an increase of approximately 18.1%, or $833 billion, which is more than the required increase in nominal GDP.

Therefore, option C is the best choice as it comes closest to the required nominal GDP increase while keeping inflation at a reasonable level.

From the End of 2005 to the End of 2006,the