We consider a pure exchange asset model with a finite number of agents and a finite number of states of nature where short sells are allowed. We present the definition of weak no-arbitrage price, a weaker notion of noarbitrage price than the one of Werner, and prove that if the utility functions satisfy the maximal and closed gradients conditions we propose in this paper, then there exists an equivalence between existence of a general equilibrium and existence of a price which is weak no-arbitrage price for all the agents.