(¹) This is not a new definition of public goods, but one which is natural if we assume that pure public goods are not financed by benefit taxes, an assumption which I make throughout this paper.

(²) I return to this question in Section III.

(³) Mundell, R.A., A Theory of Optimum Currency Areas, in American Economic Review, sept. 1961 Google Scholar.

(⁴) To put it differently, equalizing the production of mousetraps between two regions can usually be achieved at a lower real cost in terms of resources than equalizing the production of steel. This conclusion is easily established by writing the standard measure of welfare cost in terms of the proportion of the expenditures on a given component to all expenditures.

(⁵) Referees commenting on an earlier draft of this paper have pointed out that in practice the various bases of definition of regional balance would be highly correlated with one another and that consequently I was making much ado about nothing. It is important that confusion be prevented on this point. A statistical correlation, if it is shown to exist, among the various bases of definition is a mechanical phenomenon without economic, but especially without any policy, meaning except the negative meaning that would attach to it if policies were designed on the assumption that it reflected a true economic phenomenon. Indeed, the social costs of achieving regional balance will be different if one pursues one goal instead of another, even if they are correlated; and, secondly, the policy instruments used will also be different. Statistical correlation of definitional bases can be dispensed with completely.

(⁶) I am in fact assuming two scales of measurement on the abscissa and on the ordinate: one for real output value and the other for the share of industrial output in total output.

(⁷) It is not OB which describes the demand for regional balance, but its slope, or to put it differently, the angle θ. The factors influencing the demand for regional balance must therefore be seen as influencing θ. If the list or vector of factors affecting the demand for regional balance is represented by X, the demand function could be written as θ = F(X).

(⁸) The feasibility of such a policy is discussed in Section IV below.

(⁹) On “second-best” transformation functions, see Bhagwati, J. and Ramaswamy, V. K. Domestic Distorsions, Tariffs and the Theory of Optimum Subsidy, in Journal of Political Economy, febr., 1963 CrossRefGoogle Scholar, and Johnson, H. G., Factor Market Distortions and the Shape of the Transformation Curve, in Econometrica, July, 1966 Google Scholar.

(¹⁰) v ₂ needs not always be to the left of v ₁; the exact location of both points depends on the shape and position of the second-best transformation curve and on the characteristics of the indifference map. See Fishlow, A. and David, P., Optimal Resource Allocation in an Imperfect Setting, in Journal of Political Economy, December, 1961 CrossRefGoogle Scholar.

(¹¹) Proof of these assertions can be found in any standard treatment of these issues. For example, Hoteixing, H., The General Welfare in Relation to Problems of Taxation and of Railway and Utility Rates, in A.E.A., Readings in the Economics of Taxation, Irwin, 1959 Google Scholar; Harberger, A. C., Taxation, Resource Allocation and Welfare in NBER, The Role of Direct and Indirect Taxes in the Federal Revenue System, Princeton, 1964 Google Scholar.

(¹²) Samuelson, P. A., The Pure Theory of Public Expenditure, Review of Economics and Statistics, Nov., 1954 Google Scholar; see also Musgrave, R. A., The Theory of Public Finance, New York, 1959, pp. 6-15, 61-89 Google Scholar.

(¹³) Breton, A., Discriminatory Government Policies in Federal Countries, Montreal, Canadian Trade Committee, 1967 Google Scholar, Ch. VI.

(¹⁴) This argument would have to be modified if monopolies and other distorting factors could be removed, thus leading to an over-all increase in total output.

(¹⁵) See Rahman, M. A., Regional Allocation of Investment, Quarterly Journal of Economics, February, 1963 Google Scholar; also Dorfman, R., Regional Allocation of Investment: Comment, Quarterly Journal of Economics, February, 1963 Google Scholar.

(¹⁶) I am still neglecting the case where the policies used to satisfy the demand for regional balance are so inefficient that the level of income is less after than before the subsidy.

(¹⁷) This is true since the central government, like the government of any other juris-diction, must seek re-election.

(¹⁸) The argument that federal structures are institutionally better equipped than unitary structures to achieve regional balance is, of course, a ceteris paribus argument, that is, one which assumes that in other respects the two structures are equivalent. If the citizens of a unitary system have a strong preference for regional balance and those of a federation do not, it is clear that a federal structure by itself will not “generate” more regional balance.

(¹⁹) Breton, op. cit.

(²⁰) This term is general and covers all junior governments whether they be called states, republics, local authorities, cantons, provinces, etc.

(²¹) Rahman, M. A., Regional Allocation of Investment, Quarterly Journal of Economics, February, 1963 Google Scholar; Dorfman, R., Regional Allocation of Investment, Quarterly Journal of Economics, February, 1963 Google Scholar; Boudeville, J. R., Problems of Regional Economic Planning, Edinburgh University Press, 1966 Google Scholar; Reiner, T. A., Sub-national and National Planning-Decision Criteria, Regional Science Association, Papers and Proceedings, 1966 Google Scholar; Vietorisz, T., Locational Choices in Planning in NBER, National Economic Planning, Columbia University Press, 1967 Google Scholar; Mera, K., Tradeoff between Aggregate Efficiency and Interregional Equity: A Static Analysis, Quarterly Journal of Economics, November, 1967 Google Scholar.

(²²) In reading much of the planning literature on “regional balance,” I gain the distinct impression that it is conceived for a context of national planning where the “national” refers to a non-trading entity. It is as if one were preoccupied with regional balance to correct the allocation of resources generated by tariffs. For example, T. Vietorisz, op. cit., mentions that the case for balanced regional growth rests on the possibility of larger markets for many lines of production! That seems to assume that markets are nothing but national markets—and if not, that production has some intrinsic virtues of its own—and strikes me as a way of wasting resources to by-pass the effects of tariffs.

(²³) A. Breton, op. cit.

(²⁴) I neglect the case where P is so small relative to W that any action taken in P practically leaves Win the status quo ante; in that case Wwill presumably not retaliate, and P can pursue the policies it wishes.

(²⁵) These two regions can be considered as of equal size for the purpose of this illustration.

(²⁶) The USSR has presumably not been “democratic” enough to make inferences about the extent to which the policy yielded satisfaction to the “electorate”; as a consequence it is really not possible to say that the sacrifice of real output was the price paid for a higher non-monetary income. It may well have been the price paid to change the interregional (i.e., domestic) distribution of monetary and non-monetary income.

(²⁷) This should not, however, hide the fact that the income-maximizing basis of definition may not be real output, but some narrow partial basis.

(²⁸) Breton, A., Discriminatory Government Policies in Federal Countries, Montreal, The Canadian Trade Committee, 1967 Google Scholar.

(²⁹) I again assume a two-region world, with one poor region (P) and another wealthier one (W).

(³⁰) If the “transportation agency” is assumed to balance its budget, it would have to tax the “exports” of the W region.