Suppose the government wants to increase farmers’ incomes.  Why do price supports or acreage limitation programs cost society more than simply giving farmers money?

Price acreage and supports limitations cost society more than the dollar cost of these programs as the higher price that results in either case will decrease quantity demanded and hence consumer surplus, leading to a deadweight loss since the farmer is not able to capture the lost surplus.  Giving the farmers money does not result in any type of deadweight loss, but is merely a redistribution of surplus from one group to another.