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I was wondering if there is still welfare loss for example there is a positive externality in production of a good and the government decides to subsidise the good?

I think it does still have welfare loss, because the subsidy has to be payed for but I am not sure.

Is it because the government taxes things that have negative externalities and then uses this money to subsidise things that have positive externalities that in the end there is no welfare loss?

Thank you for your help in advance.

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Yes. While producer and consumer surplus rise, the total cost to government exceeded the increase, leaving deadweight loss.

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Actually, I worked it out, there is DWL when it is not subsidised. When the government subsidises the production with a unit subsidy valued at the external effect. Then there will be DWL gain and loss at the same time, thus leaving us at a socially optimal point.

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