Prof. Evsey. D. Domer states that the burden of the debt or the average tax rate covering the interest charges, equals, roughly speaking, the ratio of the interest charges to income; or the ratio of the debt to income multiplied by the interest rate paid on bonds.
It will be assumed that this interest rate is a given constant. Domer further says that in-order to find out the effects of deficit financing on the tax rate, we will have to examine its effects on the magnitude of the debt and of the national income.
E.D. Domer, in his article “the burden of the debt and the national income”, published in the “American Economic Review”, December, 1944, defined the burden of public debt as the ratio of total debt to total national income.
According to him, if the national income remains constant, but the volume of public debt increases, the burden will rise. On the other hand, if national income and public debt of the country increases simultaneously, the burden will increase or decrease, depending on the ratio in which public debt and national income increases.
If public debt increases more rapidly than national income, the debt burden will increase. When national income increases, the tax paying capacity of the country increases. Coupled with this, suppose the public debt also increases but lesser than the increase in national income, then the burden will decline even with increasing volume of public debt.
Prof. Domer through the following mathematical expression lays down the conditions under which the burden would increase or decrease overtime:
Let ‘D’ stands for the amount of debt outstanding at the beginning of a year, ‘i’ stands for rate of interest paid on debt, ‘T’ stands for amount of tax necessary for covering the interest charge on debt
Then T = Di
Let ‘t’ stands for the fraction of income (Y) mobilized through tax to pay interest,
Then t = T/Y = Di/Y = i x D/Y
From the above equation, it follows that the tax rate necessary to pay interest on debt depends on the ratio of the size of the debt multiplied by the rate of interest to income.
This tax rate may be related to growth of income and the budget deficit.
This can be expressed in the following equation form:
T = l/ (l/i) x (G/b) = i x b/G
Where ‘G’ stands for rate of growth of income and ‘b’ for ratio of deficit to income. This equation shows the situation when the burden of debt would increase or decrease.
Domer argues that, theoretically there is the possibility for an infinite number of patterns which the national income may be assumed to follow.
However, he considers only three possibilities, of national income, debt growth rates:
The first is the case when national income remains constant. The government keeps borrowing as a definite fraction of national income. Then the debt will increase at a constant absolute rate.
Then “ratio of the debt to national income will grow without limit and the tax rate will approach asymptotically 100 percent. The net income after taxes of non-bond holders will approach zero. The picture is rather dismal”.
Second is the case when national income increases at a constant absolute rate. Here also the fraction of income borrowed is assumed to be constant. “When income grows at a constant absolute rate, the annual deficit becomes larger and larger, so that the debt itself grows at an accelerated absolute rate. Therefore the ratio of the debt to national income will rise.
The third case arises when national income increases at a constant relative rate. Domer states that case 3rd is the most important model and he places his entire analysis upon the 3rd case.
Let ‘x’ be the fraction of national income borrowed; T interest rate paid on bonds and ‘r’ relative annual rate of growth of income. To analyses the relationship between the debt and the income in this case, Domer make use of the following two propositions, on which the whole analysis rests.
1. If a variable ‘Q’ is the sum of q1, q2, q3, q4, … and so on, each of which is larger than the preceding one by ‘r’, then the addition of more and more q’s makes ‘Q’ itself increase at a rate approaching ‘r’
2. If any two variables increase at the same relative rate, the ratio between them remain constant
Now according to the assumption national income grows at a constant relative rate ‘r’. Since, every year a constant (x) fraction of that income is being borrowed, it is clear that the deficits also grow at the rate of ‘r’ per year.
The total debt is simply the sum of all deficits. Therefore according to the first proposition the ratio between the debt and the national income will approach a constant. This conclusion of Domer presents a striking contrast with the results obtained in case I and case II, where the ratio of the debt to income increased without limit.
By inserting numerical values, the above expression can be stated as follows. The equation for calculating taxes necessary for debt servicing (t) is
T = i x b/G.
In the light of this we can examine the following cases:
T = 3%; ‘G’ = 3% and ‘b’ = 3%.
Then taxes necessary for debt servicing (t) will be 3%.
T = 3%; ‘G’ = 6%; ‘b’ = 3%,
That is when T and ‘b’ remains constant, a doubling of the rate of growth of income (6%) means halving the tax rate. That is ‘t’ = 1.5%. This also means that debt burden is also reduced to half.
Case – III:
T = 3%; ‘G’ = 3%; ‘b’ = 1.5%, Then ‘t’ = 6%. That is a fall in the rate of growth of income increases the debt burden.
T = 3%; ‘G’ = 4%; ‘b’ = 4%,
Then ‘t’ remains at 3% as in case I, This means that an increase in deficit (rise in public debt) followed by and equal rate of increase in income leaves the debt burden unaltered.
Domer states that greater is the rate of growth of income, the lower will be the tax rate, even though a more rapidly rising income results in a larger absolute magnitude of the debt.
Hence, Domer concludes that “problem of the debt burden is a problem of an expanding national income”.
He further states that “if all the people and organization who worry and spend sleepless nights – all because of the fear of debt – could forget about it for a while and spend even half their efforts trying to find ways of achieving a growing national income, their contribution to the benefit and welfare of humanity and to the solution of debt problem would have been great”.
So the appropriate method to reduce debt burden is to increase national income.