There are two “countries,” an OECD country such as the U.S. that is large enough to be treated as a large open economy, and the Rest of the World (ROW). There are two productive sectors in the OECD country, X (the tradable goods sector) and Y (the non- tradable goods sector). The ROW has one consolidated sector Z, and no assumption is made about it except that the good is tradable.
Capital is perfectly mobile all over the world. Following Harberger (1962) we assume that the net rate of return to capital is always equal around the world. Since we assume ( as in Harberger 1962) that the pure, risk-free rate of return to capital can be isolated in the large OECD country while the rest of the world pays a risk premium for capital, the OECD country cannot tax the premium at all with its differential existing tax, only the pure rate of return is taxed.
If we were to include a risk premium for any sectors or the ROW or OECD country, it would have been added to the pure rate of return, and it need not be constant. We could have a risk premium/premia that is/are increasing in the proportion of capital stock attracted by a particular country or sector(s) as implied in Gravelle and Smetters (2006). To the extent that such risk premia are paid in some sector of the OECD country, they are taxed by the (differential) tax on capital, when they apply to the ROW
exclusively; they are not taxed. This need not be taken literally to mean that the ROW never taxes its capital. We have discussed in earlier sections how the tax on capital in
OECD may be viewed as an excess or differential tax, over and above the worldwide rate.
The tax rate on capital in OECD is Tko initially, and is assumed to be a known
parameter, as is the proposed rate change dTko. The gross rate of return to capital in the
OECD country is defined as Pk*(1+Tko), and is the same in both OECD sectors, X and Y.
The rate of return to capital in the ROW is simply Pk. The total amount of capital is fixed
worldwide and the model is static; there is no saving, capital accumulation or growth in productive resources. = Kx + Ky + Kz is fixed. While dKx ≠ 0, dKy ≠ 0 and dKz ≠ 0 in
general, we get the relationship dKx + dKy + dKz =0 for the world as a whole. Since Tko ≠
0 and dTko ≠ 0 and (Tko + dTko) ≠ 0 in general, we always have a positive tax on capital.
Labor is constant and confined within each country. Since the ROW is treated as one country and one sector (Z), the total labor available to sector Z is equal to the total ROW labor and is fixed at which is equal to Lrow. The total labor available to the
OECD country is Loecd and this is also fixed as the sum of the labor employed in sectors
X and Y.
There is one consumer in each country. The consolidated demand function refers to the OECD single consumer and the ROW single consumer. The country superscript is interchangeable with the consumer subscript. The issues of factor ownership and income calculation have been discussed in chapter one and are not repeated here.
We also assume that the government good G is an input into production in the OECD sectors X and Y, it is a non-rival and non-excludable public good and its quantity is dependent solely upon available tax revenues in the current period. We can assume
therefore that it is government current services and not investment that is being provided with the tax revenue. Alternative construction is possible as in McLure (1969). This would involve G being produced using K and L, and would have a price that would be a weighted average of the prices of K and L. The total amount of G produced, weighted by the price of G or PG would be equal to tax revenues. The demand for G would not be
derived demand since producers don‟t pay directly for G.
However, implications of the simpler model would also exist in a more
complicated one as well, there would of course be further elements added to the analysis by fully defining production of G. In the interests of simplicity and transparency, and keeping in mind that we can gain the essentials without repeating McLure‟s (1969) more developed analysis of G where G was a final consumption good and not an input, we have chosen not to model production of G fully and left this for future models.
The differential tax on capital in the OECD is collected like an excise tax on capital employed by the X and Y sectors only. The ROW sector has no tax on its capital and no government input in its production function. The government good G, once provided, can be used by both X and Y in the same quantity, and no separate payment is made for its use, other than the tax on capital employed by X and Y.
The production functions in each sector X, Y and Z are homogenous of degree one (HOD 1) in capital and labor. When the Government input G is added in the OECD sectors, the production functions behave like they are homogeneous of degree greater than one (increasing returns to scale) in all three inputs. This can be modeled as a case where the government input is both labor and capital augmenting, or where the addition
of G acts a shift factor to the supply curve which is drawn for capital and labor. If we define the production functions as Cobb-Douglas, the G would enter as a scale or shift factor, in a manner similar to technology or human capital in growth models. This point is illustrated more fully below.
Perfect competition is assumed and taxes are the only distortion. Changes are instantaneous, the model is an exercise in comparative statics, and there is no time dimension or dynamic factors such as savings, accumulation and growth. Following Harberger (1962), we concentrate only on first difference terms based on small changes. To illustrate, this means that for a pair of variables P*X that can both change, the total change is calculated thus: d(P*X) = (P+ dP)*(X+dX) – P*X = dP*X + dX*P + dX*dP. However, if both dP and dX are small, their product dX*dP is even smaller and is ignored.
Following Harberger (1962), we employ the convenient formulation that all prices (output and input) are set to unity to begin with and are allowed to change with respect to the numeraire (Pz), and that all quantity units are defined accordingly to make their prices
equal to one. We can do this since we use quantities only as ratios in our equations, and so their units do not matter. This allows us to measure quantities as dollar amounts in the initial state. Accordingly, Pk, Plo and Plr (factor prices) and Px, Py and Pz (output prices)
are all equal to 1 and to each other to begin with and are allowed to change with respect to the numeraire. There is no price for G, so we are in effect formulating G as invariant to inflation. Since our existing tax is ≠ 0, this implies that Pk*(1+Tko) ≠ 1.
The total amount of the public good provided, G is simply equal to the tax
revenue or government expenditure. It is assumed that every dollar of expenditure on the government good leads to one unit of increase in the level of G (and the reverse is also true). There is no price for the government good since it is not a produced input.
Lastly, we take the price of the ROW tradable good Pz as the numeraire good, so
dPz = 0. We have effectively imposed the condition that imports equal exports while
formulating the demand equations and choosing elasticities in chapter five. We could have instead had trade imbalance with BOP balance. To do this, we could have borrowed an idea from open economy macroeconomics where the capital account balances the trade account. The capital account in this model could have been represented by net capital inflows or outflows that balance the trade deficit or surplus. BOP balance conditions have been imposed in some of the other models cited but has not been
attempted here, and the simpler formulation of trade balance has been used instead. This allows us to retain the real model with no currency considerations, and the use of the single foreign good Pz as the numeraire allows us to treat other goods prices Px and Py as
some measure of terms of trade between OECD and ROW.