A price ceiling is an upper boundary on the price of a good or service.
Imposing a price ceiling on a product, according to economic theory, results in a shortage of that product as long as the ceiling is below where the equilibrium price would naturally be.
If there is a price ceiling, the price is artificially held down. When this happens, the quantity demanded is greater than the quantity supplied and there is a shortage.
A price ceiling prevents a market from reaching its equilbrium price and quantity. Therefore, it is not efficient.
The question is somewhat confusing. Efficiency in economics generally refers to allocative efficiency refers to use of economic resource that produces the maximum level of satisfaction possible with given technology and inputs. It is not clear what is meant by upper and lower bound of efficiency, or price ceiling being upper or lower.
In a perfectly competitive market the allocative efficiency is achieved automatically, and in such economy there is no need for price ceilings or price floors. Price ceilings refers to an upper limit placed on the price that suppliers are allowed to charge. And floor price that the buyers have to pay for some specific product they buy.
Both floor prices are and price ceilings are used as mechanism to counter the effect of monopolistic practices that tend to reduce the allocative efficiency. But there is a lot of difference between intentions and reality. Exact impact of price ceiling on allocative efficiency will depend on how appropriate these were for the specific situation.
When applied appropriately, price ceilings increase or at least retain the allocative efficiency. Price ceilings are supposed to be applied when the suppliers are able to produce and supply more quantities, but restrict there production below the optimum level to maintain higher prices and profit for themselves at the cost of the consumer. The floor prices are intended to make the suppliers supply either more or at least same quantities but at lower prices and at same or lower cost. This reduces the profit of suppliers but increase or at least maintains the allocative efficiency of the economy.