Abstract
1. The regional development policy by means of subsidizing the location of particular industry at particular area is a popular political device not only for the local governments but also for the central government. The direct effect of this policy is to restore the profitability for the industry at a particular location which was non-existent before the policy.
Following the analysis by G. H. Borts, the situation can be formulated with the productivity function f(k) of the industry which is derived from its linear homogeneous production function X=F(K, L) where X, K and L are the amounts of output, capital and labor respectively, i.e. A ‘profitable’ set of prices is one which satisfies the following relation for some capital-labor ratio k0:
where P0 and PK the prices of output and capital, w is the wage rate, and r is the rate of interest. If the actual price, say P1, at the particular location where some amount of idle labor force is available is lower than P0, a private firm cannot operate there without subsidy.
2. Net social benefit gained by the employment of a unit of idle labor force is:
and its maximum value will be attained at k=k* for which
This equation implies that neither the price subsidy nor the interest subsidy is ‘optimal’ therefore the wage subsidy, say y, which makes
is recommended.
However, the ‘optimality’ of k* does not assure a positive net benefit, and if the latter is negative, then of course none of the subsidizing policies is desirable. This problem and the comparison of alternative subsidizing policies are diagrammatically demonstrated.
3. The ‘strong’ criteria for the efficiency evaluation should take the opportunity cost of the subsidy itself into account. Let the rates of subsidy for price, wage and interest be x, y and z respectively, then we should have the system of:
and the rate of return for this mixed-subsidy-policy will be
The normal equation of deduces the optimality of k* again. Of course the maximum θ may not be greater than the discount rate for the public policy general in which case none of the subsidizing policies is (strongly) efficient.
