 I will now get started because this took up some time so I'll get started by discussing why we want to look at taxis when we discuss poverty minimization and inequality. So the starting point is high inequality in developing countries and I guess that for the audience of this conference I don't have to justify that any further. So this is an observation that we have and regardless of what is the underlying cause of inequality in the developing country there are few things that the country at the government can do to actually influence that and typically the only really direct way that you can immediately impact on inequality and poverty. The income distribution is to use redistributive taxis and transfers as well as public good provision. In developing countries these are of course already quite widely used but in low-income countries they are still innovating their baby years that they are getting started and being developed but they still often consist of perhaps isolated individual programs that need to be operated towards a more holistic comprehensive systems of taxes and benefits that address these issues. So and this is then what we want to do we want to characterize what would a tax and transfer system for a developing country look like. So we consider redistribution therefore we have a labour income tax, commodity taxis in the revenue side and we use them to finance cash transfers and public provision of different kinds of goods. We do this by using the optimal tax theory framework initiated by Merleysen which is basically the core of the public finance literature. It has been used widely but mainly for the developed country context and what we want to do is to depart from some of the assumptions in there or the starting points to make it more applicable for a developing country context. The first thing is that usually this literature considers nonlinear taxis meaning that income tax is progressive, it's different size of tax for different incomes. These might be difficult to implement in a poor developing country that doesn't have that high administrative capacity and tax collection systems are not developed yet. So we think that in this case it makes sense to restrict yourself to a linear income tax. So a flat rate tax that applies the same to everyone and also the benefits are universal and in this we follow the literature, the few literature that there is a linear taxis. However, as a whole this optimal tax framework on nonlinear and linear taxis, they consider as the objective function, the maximization of social welfare and this is another point where we want to wish to depart. The reason is that we want to consider different types of objectives that are perhaps more suitable for a developing country but also more reflect the policy discussion that there is and I think that the opening keynote by Minister Marcelo Neri was an excellent example of this that he said that in Brazil there is an explicit objective to cut down poverty. So we want to take this into the model and see how it impacts on the tax characterizations. There is also a more general non-welfare literature meaning that you depart from the welfare maximization literature and we take this poverty minimization is a kind of a special case, a more detailed case of being non-welfare and we follow the literature on that and you can see that my co-authors have already been active in this field. But this would be the first time that we consider a linear income tax with this poverty minimization objective and also we want to have this more comprehensive tax system approach. And a quick preview of the results where we are heading with this is that we compare the tax results between welfare maximization and poverty minimization and we find that some of the results actually do change so that it matters what the objective is. One thing is that the tax rules become more sensitive to labor supply impacts and another thing is that we find that with commodity taxes we actually wish to, we prefer differentiated commodity taxes so different size of taxes to different commodities. But first I'll have to show you a bit of something about the model to introduce these results a bit better. So I proceed in parts that first we have the simplest case with just the income tax and the benefit and then we add public provision and then commodity taxes. In the end if I have time I will quickly describe what kind of applications we might consider for this model in the future but I will now focus on the results and given the time I of course have to be quite superficial and I try to convey the intuition behind the results. First though the structure of the model so the government has different instruments the linear income tax tau and then the benefit fee so both the tax is the tax per cent so it's the same share of income for each individual a flat rate tax and the benefit is universal so it's for everybody and it's love sum that everybody gets it in the same size as well and then we add public provision G and commodity taxes T in later parts of the model. We have a discrete model with n individuals who are denoted with the superscript I and then their labor income is denoted with Z and consumption is equal to disposable income so this is the after tax income of their labor income and then plus the benefit fee. Individuals of course maximize their utility and behave accordingly but then we consider different objectives for the government. The first is the benchmark case the standard social welfare maximization where we maximize some kind of sum of these individual utilities in direct utility functions V with some transformation function W and of course we always have the government's budget as the constraint. Then the most general non-welfare is objective function would look something like this. We have any kind of function denoted by F here that is the social evaluation function so depending on what is the goal of the government you have a function that evaluates that and in this example we have consumption and labor income in it so we might have some ideas about we want to have reasonable consumption levels for individuals but also some ideas that everybody should work some amount of time so we may have this may include these kind of paternalistic objectives but then what we consider in this paper and this presentation especially is this more detailed type of non-welfare is in the poverty minimization case so we define this evaluation function F to be a function what we call a deprivation function denoted by D so this compares the individual I's consumption level CI to some minimum level that is a subjective assessment what is the minimum level but the C bar reflects that so we measure how far below is an individual's consumption of this minimum level C bar and we sum them overall individuals but we give zero weight to people who are above the threshold level who are considered known for and as an example we could use the poster Priathorbeke index described here but in this presentation it will just be a bit more general and use the index D here and its derivatives just without specifying what the derivatives look like so with this setup we can move on to the model first with the linear income tax and and the benefit so just to get started the benchmark case is that when we maximize social welfare and find the optimal tax rate the rule looks like this that here in the front we have 1 over e is the aggregate labor supply elasticity and this works this gives us the efficiency effect that if people are more sensitive to taxes so that they change their labor supply in response we want to have lower taxes to reduce the amount of distortions and the second part in the brackets we have this omega term and this term takes into account equality considerations such that the more there is inequality the lower omega is and because there's a minus sign this force to increase tax rates so when there's more inequality we'll collect taxes to finance these benefits for redistribution so without going into more detail just to show you that when we change the objective function to be minimization of poverty the rule looks similar it has a similar structure we have the efficiency effect of the labor supply elasticity here but then in the brackets we have a different term and this detail days now quite different from the omega term on the previous slide well it looks like this but we don't have to go into detail but it depends on these derivatives of the of the deprivation index and there is a direct effect over here and an indirect effect so that is the labor supply and we have its derivative with respect to the net of tax rate so depending on how much people react to how much people change their labor supply behavior even these taxes that that also impacts on on their poverty so this detail that measures the relative efficiency of taxes in deprivation reduction and actually if we rewrite it in the other way we can see that because of this labor supply effect we actually have an individual elasticity term here so here in the front we have the same aggregate elasticity effect as in the welfare is the case but this detail that itself includes this individual elasticity term as well and this works so that it means that we want to induce the poorest also to work more because we they are the ones whose whose consumption needs to be increased the most and whose the deprivation index the most sensitive to them so we want to reduce tax rates in order to induce the poor to work more and even though we have a linear tax we still want to do this that when we because even though with the linear tax we have to reduce the tax on everybody because we can't differentiate taxis on individuals and an earlier paper found a similar effect with nonlinear taxis but now we find that with a linear income tax we still have the same impact okay so this is what what I meant with the big result that we find that the result taxis are more sensitive to labor supply impacts and we actually find something similar in that case when we add public provision into the picture so first again the benchmark case for a pure public good the provision rule looks like this just quickly that on the equate the welfare weighted some of marginal rates of substitution to the modified marginal rate of transformation so kind of a modified Sami Olson rule on the right-hand side the P is the price of the good so the direct marginal rate of transformation and then we have these effects multiplied by how the tax rate so we have again tax revenue implications so these affect how costly it is for the government to provide this good if providing the good G increases labor earnings on the average then you have more tax revenue and it's less costly than to provide relatively less costly to provide the good and when we change the objective to be deprivation minimization the right-hand side says the same but on the left hand side we again have something different and here now this D star measures the relative efficiency of the public good in reducing deprivation so we have the direct impact the derivative of the index with respect to the root G but again we have an additional indirect impact so we again have this labor supply derivative with respect to the group so depending on how people react change their labor supply their earnings in response this this food will also impact on other good other consumption and therefore we have this derivative of index in here as well so in this case we are more more sensitive to these labor supply impacts because they affect people's disposable income and that has an impact on poverty measurement and I won't have time for this but just to mention quickly that we can use this model to analyze different types of goods as well so this was for a pure public good we can have was I private goods such as education or goods that don't directly impact on deprivation but that that can affect people's productivity so they may for example impact on wages but I will go through them in this presentation then the final case is with commodity taxes and in here actually because the rules get a bit more versatile I have to be perhaps even more superficial on them so just show you quickly what they what they look like to give you an idea that's on the in the poverty minimizing tax what's important here is that we find that they again they of course depend on the derivative of the deprivation index so that means that we're interested in how much do consumption sorry how much do we impact on the deprivation measure when we change the prices of the goods so when we change the commodity tax we change the prices sorry the prices here you should have mentioned that so we have a direct impact depending on the level of the good and level of the consumption of the good and an indirect impact depending on the on the change of demand of that good but there are other types of interactions here that I won't won't have time to to go through so just quickly the intuition is that with this both the welfare risk and poverty minimizing rule we the interpretation is quite similar and they basically tell us that we want to encourage the consumption of goods that poor people consume relatively more compared to to less poor people and conversely discourage consumption of goods that are consumed by richer people and this is because we have a higher highest weight in the welfare is it case we have high welfare weight on the poor people and in the poverty minimization case then the impact on the deprivation index is highest for the poorest people and in this framework we have this this result that I referred to that earlier research has found to the state and 79 paper found that with when you have a linear income tax uniform commodity taxes so having the same tax rate on all goods is optimal only under some very strict assumptions regarding the preference structure and when we do the same same analysis we find that even under these same assumptions uniform taxes are not optimal so contrary we want to have differentiated commodity taxes so rather different tj's for each good j then that's it for just the same team for each and this this will then we can use to benefit the poor and obviously then we can have also negative taxes so subsidies on some goods so this is an interesting result that our our model is us and then quickly to to summarize what we actually did here in case you got lost in the in the equations so when we use this optimal tax framework we can characterize what kind of taxes and transfer systems that all the countries that want to minimize poverty can shoot in the implement so we restrict ourselves to use the linear income tax and and this universal benefit but then we see what kind of characteristics these instruments have and when we illustrate the key results we find that it actually does matter that we have color diminution as the objective rather than the standard social welfare maximization we find that there is at least additional indirect impacts on the tax rates via the labor supply reactions and we also find that we want to use differentiated commodity taxes combined with this linear income tax and just a quick preview that you can also use this model for other types of applications rather than this optimal tax framework one one example is in the morning so the informal sector is obviously quite well known that is quite widespread in in the poorest countries so this means that not everybody for example registered to pay taxes or they might their their labor income might be informal that is not the employers don't report this anywhere so obviously if you collect less taxes because not everybody is in the formal sector you will you can have a lower benefit size because of that because tax revenue is lower and this of course impacts on poverty reduction and however we think that there are probably some some more versatile effects so if for example the poorest people are more often in the informal sector then they are benefited by the fact that they don't pay the taxes so their disposable income is higher so that is one thing that you could consider here and another thing is for example low administrative capacity so if you have lower tax collection capacity or administrative capacity in the country some of the tax revenue might disappear in the process so even though you collect tax revenue not all of that is available to to use for the benefit for example if administration is really effective or there is corruption that somebody steals the money then this of course would have an impact on poverty reduction but this would be my presentation so I thank you for your attention and we'll be asking answering your questions later thank you