Supermarkets should only use biodegradable plastic bags!

Its known fact that plastic is dramatically harming our environment, all around the world. There are many places in the Pacific Ocean with more plastic than plankton.
A small but very powerful step to rectify this or at least slow down the destruction of the environment would be if supermarkets around the world simply only offered biodegradable plastic bags to customers.

Millions of plastic bags are used every day all around the world (normally only once). The impacts of this on a global level are catastrophic.

Implementing this may be at a slightly greater cost to normal plastic bags - which would not be a problem if governments assisted these chains with subsidising the cost.
Alternatively, supermarket chains could charge the minimal difference to the customers depending on bags used (would be a matter of a few cents).

This movement would also encourage more people to carry reusable bags when shopping.

Populations around the world would see & recognise this movement, would no doubt value the companies & governments implementing much more (good for business image/government popularity), and greater awareness to environmental matters would result.