Before revision:  Assuming market makers have exponential preferences, we show for general utility functions that a large investor's optimal investment problem with price impactcan be re-expressed as a constrained optimization problem in fictitious market without price impact. While typically the (random) constraint set is  neither closed nor convex , in several important cases of interest, the constraint is non-binding.
After revision:  Assuming market makers have exponential preferences, we establish two effects due to price impact: constrained trading, and non-linear hedging costs. To the former, wealth processes in the impact model are identified with those in a model without impact, but with constrained trading, where the (random) constraint set is neither closed nor convex , in several important cases of interest, the constraint is non-binding.