we saw previously how the presence of external costs or benefits can create a disconnect between the private and social costs or benefits a positive externality is when there are external benefits enjoyed by Society but not by the people making the production and consumption decisions those result in under production on this graph we see the effects of a negative externality created by producers where the social marginal cost of production is higher than the private marginal cost that defines Supply the result here is over production what can we do about this how can we get a firm to internalize the costs of things like the pollution they create one answer is a tax if there's a Coal Power Plant and every unit of electricity they generate is causing 10 cents worth of damage to People's Health due to the air pollution they create then we can solve this problem by letting a 10 cent tax on every unit of electricity they produce putting a tax on this producer will reduce Supply and if the tax is equivalent to the externality then we will successfully United the private and social marginal costs leading to the most efficient outcome for society taxes create a disincentive which helps correct the problem of overproduction caused by negative externalities If instead we were looking at a positive externality then we would want to incentivize more production which we can do with a subsidy instead of the tax but the logic is just the same you want to unite the private and social costs and benefits this concept was developed by an economist named Arthur C pigalle in the 1920s and now it Bears his name pagovian taxes are taxes designed to correct a negative externality pagovian subsidies are subsidies designed to correct a positive externality let's dig into this with some math let's say that private marginal cost which is Supply is Qs equals 2p minus 50. while social marginal cost which is where we want supplied to be is Qs equals 2p minus 80. if you draw these out on a graph you'll see they look just like our graph on the previous Slide the question is how big of a tax should we put on producers to eliminate that deadweight loss that is how big should the tax be to correct the externality our goal is to find the value for a tax which unites these two lines meaning we're trying to set them equal to each other and when we put a tax on producers it is subtracted from the price they earn so this is where we start I've taken the private marginal cost 2p minus 50 and put a tax on it so that it's now 2 times P minus t minus 50. and I've set that equal to the social marginal cost which is 2p minus 80. now I just need to solve for T the tax I can multiply out 2 times P minus t so that it is 2p minus 2T then I can rearrange the equation to get the tax on one side when I simplify this I get 2T equals 30. since 2p minus 2p is 0 and negative 50 plus 80 is positive 30. the solution is that t equals 15. by putting a fifteen dollar excise tax on producers we've realigned their incentives so that they're now in sync with the social marginal cost we have gotten them to internalize the cost of the externality they're producing this is pretty great and seems like a super easy solution we should apply to all externalities problem solved of course reality is far more complicated than a couple of equations if a firm is polluting a river how do we measure the harm that externality is causing people disagree on what counts as harm and even if we did agree measuring that harm could take decades as we wait and see what the long run effects are pagovian taxes and subsidies seem like a great solution but in reality it's hard to know what the size of the tax or subsidy should be or if it will need to change over time that said if we can measure those things pagovian taxes and subsidies are a great solution externalities are an example of market failure there are instances where the market is not able to reach an efficient equilibrium on its own but unfortunately just like markets the government is not immune from failure to produce the best outcomes human error imperfect information political self-interest limits on administrative capacity and Corruption are all sources of government failure plus the government is sometimes overly influenced by the firms they're meant to regulate or the regulations the government imposes have unforeseen and unintended consequences that are worse than the original problem