Tax system is progressive or regressive Let´s discuss a little!

When the direct effect of a tax or transfer policy (compared to what would happen in the absence of the policy) is a reduction in inequality, it is called progressive policy. If a policy’s direct effect is a rise in inequality it is called regressive. Policies that are neither progressive nor regressive are called distributionally neutral.

In the book on the website https://core-econ.org/the-economy/book/text/19.html#1910-redistribution-taxes-and-transfers there is an exercise 19.10.

There are question such as 

1) Suppose you learn that the richest 10% of people pay 30% of income tax. Does it mean that the tax system is progressive?
2) Some governments of developing countries give scholarships for some of their best students to go to graduate school abroad. If there are no eligibility restrictions, is this policy likely to be progressive or regressive? What might justify this policy?

My answers 
1) From the information given we can not say whether tax system is regressive or progressive. First of all we do not know what percentage do the lower-income earners get. Secondly, if poorer people are paying less percentage we could say that the tax system is progressive. If lower-income earners pay the less or equal percentage as the richest 10% of the society then we could say that the tax is regressive.

2) I do not understand exactly the question even though i translated it to my mother language. I do not understang preciecly this part ¨ If there are no eligibility restrictions, is this policy likely to be progressive or regressive? What might justify this policy?¨. However answering this questiong i would like to say that if students who got scholarship get a good education abroad and then return bqck with good knowledge and will transfer this knowledge to other citizens (for example being teacher or professor researchers) or even politicians or economists then in a long-run situation in a country could prosper. 

My question 
What is your opinion? Do you agree with my opinion? Or you maybe can say something in contrary?
Suppose you learn that the richest 10% of people pay 30% of income
  tax. Does it mean that the tax system is progressive?


You are right. It cannot be determined without knowing the income tax of lower-income earners.


  If there are no eligibility restrictions, is this policy likely to be
  progressive or regressive? What might justify this policy?


That is even more uncertain than the previous question because it requires assumptions that are not inherent to --or implied by-- the policy. In fact, giving scholarships to some of the best students contradicts that there are no eligibility restrictions, but that is irrelevant.

First, not all degrees (whether earned at home or abroad) lead to a profitable career. For instance, graduates in graphical design usually earn significantly less than physicians.

Second, the effect of scholarships also depends on whether those students become high-income earners and decide sever ties with their home country. This could lead to a "progressive" scenario of lower inequality notwithstanding that the population that remains in the home country is the poorer sector.

It is just impossible to conjecture about the effects of the policy based on the information given.