Trade liberalization and the fragmentation of production processes have promoted greater international exchange of inputs. There is a growing consensus about its benefits 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 jump may take place at the initial or at the terminal time only when the Hamiltonian is strictly concave and price variable paths are continuously differentiable too. However, even if the Hamiltonian is linear as in our setting, it can be shown that a capital acquisition is optimal at the beginning of the time span. Parameter sensitivity analysis shows how optimal capital inflow negatively depends on depreciation and interest rates and positively on the time horizon and capital productivity.
