We consider a discrete time market with several assets such each of them has bid and ask prices. Given utility from terminal wealth functional we consider the price (called shadow price) such that the value function is the same as in the case of transaction costs (with bid and ask prices). The construction is based on a direct backward programming approach contrary to the works of W. Schachermayer and his group of collaborators (they use dual aproach). The result is a joint paper with T. Rogala completes other joint papers. The novelty is in the fact that we have several assets, general strictly concave utility function and general discrete time prices, and the only assumption is a nondegeneracy of conditional laws.