Effect of a subsidy on a monopoly I'm trying to understand how a subsidy on a monopoly would affect the deadweight loss. I know a subsidy shifts the marginal cost curve downwards, creating a new equilibrium price (price decreases) and quantity (quantity increases), but my question is if the deadweight loss is going to be bigger than before the subsidy?
The deadweight loss from the monopoly decreases. This is because the deadweight loss comes from the price being too high (higher than the marginal cost), which leads to not enough goods being consumed in equilibrium. Since the subsidy redices the price, the deadweight loss decreases. The subsidy itself does not increase the deadweight loss, because the only thing it does is reduce the price and there are no other effects. One issue may be that additional deadweight loss is caused by the taxes required to finance the subsidy. If these are lump-sum taxes then they do not affect the deadweight loss as they are non-distortionary and do not affect prices.

In fact it is possible to completely remove the deadweight loss with a subsidy. This requires lump sum taxes to be an available tax instrument, so that raising the money for the subsidy doesn't cause deadweight loss itself. This is an old result that goes back to Robinson (1934). However, although she first noticed the result, she did not advocate that this would be a good policy, unless the subsidy was financed by taxing the monopolist's rents. This is because of concerns such a policy would have on income distribution.