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We investigate the classical optimal investment problem of the Merton model in a discrete time with market friction due to loss of wealth in trading. We consider the case of a finite number of investors, with the friction for each investor represented by a convex penalty function. This model cover the transaction costs and liquidity models studied previously in the literature. We suppose that each investor maximizes their utility function over all controls that keep the value of the portfolio after liquidation non-negative. In the main results of this paper, we prove the existence of an optimal strategy of investment by using a new approach based on the formulation of an equivalent general equilibrium economy model via constructing a truncated economy, and the optimal strategy is obtained using a classical argument of limits. [ABSTRACT FROM AUTHOR]