  We consider an optimization problem in a given region $Q$ where an agent has
to decide the price $p(x)$ of a product for every $x\in Q$. The customers know
the pricing pattern $p$ and may shop at any place $y$, paying the cost $p(y)$
and additionally a transportation cost $c(x,y)$ for a given transportation cost
function $c$. We will study two models: the first one where the agent operates
everywhere on $Q$ and a second one where the agent operates only in a
subregion. For both models we discuss the mathematical framework and we obtain
an existence result for a pricing strategy which maximizes the total profit of
the agent. We also present some particular cases where more detailed
computations can be made, as the case of concave costs, the case of quadratic
cost, and the onedimensional case. Finally we discuss possible extensions and
developments, as for instance the case of Nash equilibria when more agents
operate on the same market.
