There is a growing consensus about the benefits of input trade liberalization in terms of variety gains and capital accumulation. We tackle the latter wondering if there is any reason to delay input trade liberalization. In this paper we focus on production over a finite time horizon where capital can be domestically accumulated or bought in international market with free trade. Capital is then used to produce a commodity that is sold at a fixed price even abroad. Labour, that cannot move freely, is allocated in both production technologies over time. Within this setting Arrow and Kurz conjectured that if the Hamiltonian is strictly concave in the state variables than a capital purchase can never be optimal except possibly at the initial time point. Léonard and Van Long state an optimal inward jump may take place at the initial time only when the Hamiltonian is strictly concave and price variable paths are continuously differentiable too. In this paper it’s shown that such a theorem is false. Moreover we provide a counterexample where the adjont variable (capital shadow price) is continuous but not continuously differentiable and it s actual price can increase over time too. Hence if capital purchase price is not too large an interior jump can suddenly shift optimal control
from capital accumulation to commodity production alone.
