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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?

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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.

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The deadweight loss of a monopoly is depends on the game changing competition demands, not the monopoly itself.

The essence of the monopoly is always about its rent seeking nature to maximise it profit than investment on cost.

Without a carrot and stick model, subsidy always increase deadweight loss:

  1. Subsidies used for dumping to further corner the market
  2. Cause monopoly to reject innovation to reduce production cost, since there is no incentive to do it

(update)

It is impossible to find example of institutional subsidies on monopoly subsidies that increase supply WITHOUT policy intervention.
The argument of subsidies increase supplies is mostly bias argument. In fact, subsidies just increase the demands, make the good/services looks cheaper, which in fact has nothing to do with product efficiency.

e.g. Many countries subsidies on utilities does not make production of electricity, water and gas more efficient.

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  • $\begingroup$ The deadweight loss (DWL) OP refers to is most certainly a variant of thr harberger triangle/area which has nothing to do with innovation or any dynamic implications (such as further cornering the market). If we look at a monopoly in equilibrium there is no further cornering the market through the subsidy,as the market is already cornered. The subsidy, even if preventing further entry will increase market supply thereby reducing the DWL. A monopolist in equilibrium already has no incentive to innovate and innovation is irrelevant to standard DWL considerations. $\endgroup$ – BB King May 24 '17 at 18:49
  • $\begingroup$ @BBKing : Seriously, are you real ? Can you prove any real world example of monopoly subsidies that lead to "increase supply" when there is NO POLICY enforcement involved? $\endgroup$ – mootmoot May 26 '17 at 7:35
  • $\begingroup$ That's what the theory predicts and it makes sense. If the monopolist gets paid more per unit then it will be profitable for him to produce more. Many papers use this, for example Judd (2002) etc. I don't know of amy real world examples however as I don't know any monopolists that are subsidized. Also just because the dead weight loss is reduced (which it unambiguously is through a subsidy), which was OP's question, doesn't mean it's a good policy idea, because there could be other problems such as innovation. That was not OPs question though. $\endgroup$ – BB King May 26 '17 at 10:16

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