A price ceiling imposed by the government will always (according to economists) result in a shortage of the good or service whose price is being capped.
The reason for this is that the price will be capped (presumably) at a level below the market equilibrium. At this price point, the quantity demanded will be greater than the quantity supplied. This will result in a shortage.
Perhaps the classic example of this (used in many textbooks) is the case of rent control. When rents are capped, landlords tend to get out of the rental business even as more tenants wish to rent at the capped prices. This leads to a shortage of apartments.
Please follow the link for an excellent discussion of this complete with an interactive graph.
A price ceiling is an upper limit to the price that can be charged by producers to the buyers for a product sold. Price ceilings are usually implemented by governments on items that are considered a necessity and the government’s policy is to try to make them accessible to all. For example the government could say that pharmaceutical companies cannot charge more than $1 for a dose of a medicine for fever.
The price ceiling makes it affordable for the consumers to buy products. But, producers are now forced to manufacture at a cost below the ceiling price to make a profit. Those who are able to, can make a small profit. The others have to quit the business as they make a loss. Due to the reduced profits from selling the product, there are no new producers and a majority of the older ones stop production completely or reduce the amount produced.
The price ceiling ultimately leads to a shortage of the product in the market.