Here is a diagram of a subsidy.
The area of deadweight loss is the cost to society created by market inefficiency. This is because total surplus with a subsidy is under that of when it is in a free market.
The size of the subsidy is the difference between P1 and P2. The cost of the subsidy is whole shaded area. You work it out by finding new equilibrium point taking it across, then taking it up to original supply curve then taking it across
Subsidies are usually seen as government intervention when there is an under consumption of a merit good. Therefore a way of solving an externality. I will go into detail on another post.
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