Jesus instructed his disciples go about and cure the sick without cost, because, "Without cost you have received; without cost you are to give." St. Benedict made this hospitality to travelers a hallmark of his monasteries as a sign of the coming Kingdom of God, and we are also called to carry on this tradition today.
Based on Matthew 10:7-15:
Jesus said to his Apostles, 'As you go, proclaim the good news, “The kingdom of heaven has come near.” Cure the sick, raise the dead, cleanse the lepers, cast out demons. You received without payment; give without payment. Take no gold, or silver, or copper in your belts, no bag for your journey, or two tunics, or sandals, or a staff; for labourers deserve their food. Whatever town or village you enter, find out who in it is worthy, and stay there until you leave. As you enter the house, greet it. If the house is worthy, let your peace come upon it; but if it is not worthy, let your peace return to you. If anyone will not welcome you or listen to your words, shake off the dust from your feet as you leave that house or town. Truly I tell you, it will be more tolerable for the land of Sodom and Gomorrah on the day of judgement than for that town.
(New Revised Standard Version Bible: Anglicized Edition, copyright © 1989, 1995 National Council of the Churches of Christ in the United States of America. Used by permission. All rights reserved worldwide. http://nrsvbibles.org)