Suppose the government can buy all of the cheese it wants at the world price, then it sells the cheese at a lower domestic price. What happens to total economic surplus?
If the world price is $3, consumers will demand 2 pounds of cheese. Consumer's surplus is equal to the yellow area or $2 (1/2BH). Producer's surplus is zero since the supply is a straight line. Now, if the governement subsidies the consumption of cheese by buying three pounds of cheese from the world and selling the cheese at $2, consumers will want 3 pounds. Consumers surplus is now, $4.5. Since consumer's surplus has increased, this has got to be good for society, right? (Click on image to expand in new window.)
Wrong! The total cost of buying the cheese is $9 but the total benefit is only $4.5 as shown by the addition of the yellow and green areas. So society is worse off by $4.5. The loss is shown by the hazy red triangle. Subsidies reduce benefits to society and waste scarce resources.
A better approach would be to give those who demand cheese and income subsidy in the form of a voucher that can be used in anyway the recipient sees best. In this case, maybe a young mother needs milk more than cheese. She wouldn't buy the cheese just because it was part of a government program, but mild that her child demands.