Policy to maintain cleanliness In countries where littering is a problem and the regulations and rules alone cannot give the desired effect due to vary high population,large surface area,etc.. ,will it be effective if the government starts buying garbage on a price per kg basis?
(This money spent can be compensated by reducing the number of sanitary workers and other departments if this method proves effective)
How effective it will be in the end depends on how the policy is shaped and enforced exactly.

Buying garbage is in fact the same as subsidizing people to pick-up the garbage. In theory, by setting the subsidy at the appropriate level (where the marginal damage of an additional kg of litter on the street equals the marginal cost of picking up that garbarge and handing it in) one would achieve the "optimal amount of litering".

I do see a problem though,especially for the longer term. If people get paid for handing in their garbage, there are no incentives to reduce the overall amount of garbage, in fact people might be tempted to buy products that come with extra packaging so they can cash in on the garbage. 

I think a better solution in the long term would be a tax on material that is likely to end-up on the streets.