The economy theory developed a model with which we can analyze the solvency situation of a country. It defines the solvency considering the temporal budgetary constraints and the sum of the balance of payments of the public and private sectors.

Initial debt = Actual Value of the Trade balance + Actual Value of the Final Debt

The Actual Value of the final debt should tend to zero to avoid Ponzi scheme’s. Then, the foreign solvency requires that the country generates commercial surplus in the future in order to pay the external and internal debt.

In short, the foreign solvency requires that the country generates commercial surplus big enough to pay the net foreign liabilities.

Therefore:

Initial Debt = ∑_((t=1))^((T-1))▒〖BCt/[(1+i) 〗^t]

Also, i > ∆ Debt > ∆ GDP

Then,

Current Account = CC = Trade Balance (TB) – i x D* = -∆ D*

As D*2 (external debt in the second period) – D*1 (external Debt in the first period) =i x D*1-TB1

We divide by GDP:

d*2 – d*1 = i / [(1 + G) x d*1] – tb1 ; where d is D/GDP and G is (GDP2 – GDP1)/GDP1

d*2 = (1+i)/[(1+G) x d*1–bc1 G= nominal GDP growth

d*2 – d*1 = (1+i-1-G) / (1+G) x d*1 – bc1

d*2 – d*1 = 0 = (i – G) / (1 + G) x d*1 – bc1

If G = g(real G)+p(inflation)

bc = (r-g) x D*1

Then, the formula says that to maintain constant the relation Net Debt / GDP, the TB should increase if the difference between the real interest rate and the potential real GDP growth is rising and also if there is a bigger ratio D*/GDP.

If we apply this theory to USA case:

p = 3% (forecasted average for the next 5 years);

G=5% (forecasted average for the next 5 years) ;

g = 2% real growth (forecasted average for the next 5 years);

D = 11.5trillions (Jun/2009) ; GDP = 14.265 trillions (2008) ;

I = 6% (10 years US treasury bonds rate average forecasted for the next 5 years)

Therefore:

BC =( 3%-2%) x 11.5 trillions

BC = 0.115 trillions or 114.576.404.000 USD (115 billions)

BC 2008= -681 billions

In conclusion, the US should reverse its BC in order to pay it foreign debt by 681 billions + 115 billions, this is786 bllions. The open question is: HOW?