Answer:
A perfectly competitive market is always economically efficient due to the fact that each business sells at the lowest point of Average total cost ATC thereby achieving Productive efficiency and allocative efficiency when the price is equal to the marginal cost in a perfectly competitive market. A fish market may be an example of something similar to this (though true "full competition" doesn't really exist.) At the fist market, lots of vendors come together to try to sell the same wares, and lots of buyers seek to purchase them with a clear knowledge of what they are purchasing. There's nothing to deter someone from selling in or leaving the market entirely.
However in monopoly, suppose the local electricity supplier in the neighborhood is a monopoly, it is a monopoly since there is only one such service provider on the market and there are major obstacles to business access, i.e. other service providers can not so easily enter the market.
In terms of efficiency, a company is not effective in the monopoly market as it still operates with excess capacity and maximizes the profit generated at the point where the MR and the MC are equivalent.