Falcao arrived at Old Trafford on a lucrative one-year loan deal from Ligue 1 giants Monaco on transfer deadline day to bolster an impressive array of attacking options which already boasts club captain Wayne Rooney, Van Persie and Juan Mata.
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"I am happy with the arrival of Falcao," the Dutchman told Fox Sports.
"He makes us a better team. You always have to aim for the best at a big club. That's my philosophy as well. Falcao has to fight for his place, just like me. The two of us and Wayne Rooney and James Wilson will have to fight it out."
In addition to Falcao, United recruited Ander Herrera, Luke Shaw, Daley Blind, Marcos Rojo and Angel Di Maria for a combined outlay of around £150 million this summer.