Describe what happens when there is a shortage?

By free market I am assuming that it means the government has no role in controlling the markets. If in such a market there occurs a shortage it will simply drive the prices high up by the demand and supply rule thus constricting the output only to those who outbid the other. The solution generally is a government control on this for example LPG in India is highly subsidised to make it affordable, but the solution is definitely not robust because the people with the ability to buy from the private market end up consuming subsidised products meant for the poorer sections.