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Let P be the demand price and P' be the supply price.
With Subsidy, the demand price reduces to P = P'-5/3
Qd = 10-2(P'-5/3)
Qs = 3P'-5
At equilibrium, Qd = Qs and solving equations gives P' = 11/3 and Q = 6.
Hence the subsidy reimbursed to the Farmers equals 6*5/3 = 10.
Perhaps this is how it should go.
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