Shredded paper can be used as a mulch. Two concerns you should consider- what kind of paper? And will the paper blow around? Shredded paper under another type of mulch (solid sheets of paper, cardboard, shredded bark, etc) that will not blow away when dry, can reduce the amount of the top layer you would need. Mulch around plants should be 2-4 inches deep. It should not directly touch the stems of the plants. Any mulch helps retain moisture, including paper. I am including an excerpt from Cornell University that discusses paper as mulch:
"Paper and other kinds of organic matter
In various regions of the state and across the country, plant and animal products from lakes, orchards, vineyards and fields are available. Such products as fruit pomace (seeds, pulp, skins), seaweed, brewery waste, buckwheat hulls, mushroom waste, fish industry, zoo, fair and circus waste are only a few kinds of organic matter that may only be available in specific regions.
Several paper products - especially newspaper and cardboard - are useful in the garden and landscape. While it provides no nutrients, paper is organic material, made primarily of wood fibers. It decomposes slowly but provides structure when used in a compost pile.
Shredded newspapers or telephone books are good paper choices for composting or digging into soil directly. They decompose well when mixed with high nitrogen products such as manure. Shredded newspaper may also be used under other mulches in the landscape, where it is broken down by earthworms.
Shredded computer or other office paper and glossy magazine-style paper decomposes slowly and may contain dioxins. There are enough concerns about the dioxin in bleached and glossy paper that it would be wise not to use them in the garden.
Waxed paper almost never breaks down.
There has been concern about using colored paper or ink, which contains heavy metals. Evidence shows such low concentration of heavy metals - if any at all - that colored paper may be used without significant risk. Many inks currently used are soy-based.
Cardboard and newspaper (several sheets thick) are effective mulches around vegetables or flowers, used to block weeds and retain soil moisture. For similar reasons, in landscape plantings, cardboard or paper may be used under other mulches such as wood chips.
This method has several other benefits: the paper products may block the light and prevent weeds longer than less solid mulches, and may decrease the amount of wood chips or other surface mulches needed. In addition, there is the benefit of reusing paper products, which reduces costs and the need for their disposal in overcrowded landfills."
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