  In this article we consider the Merton problem in a market with a single
risky asset and transaction costs. We give a complete solution of the problem
up to the solution of a free-boundary problem for a first-order differential
equation, and find that the form of the solution (whether the problem is
well-posed, whether the problem is well-posed only for large transaction costs,
whether the no-transaction wedge lies in the first, second or fourth quadrants)
depends only on a quadratic whose co-efficients are functions of the parameters
of the problem, and then only through the value and slope of this quadratic at
zero, one and the turning point.
  We find that for some parameter values and for large transaction costs the
location of the boundary at which sales of the risky asset occur is independent
of the transaction cost on purchases. We give both a mathematical and financial
reason for this phenomena.
