Questions about welfare and government

Dear all, after a lot of effort I was able to work a multi-sector model. Now I am trying to include a government sector where government levy taxes on external borrowing. I have two questions:

  1. is there a difference between government makes government spending or transfer payments with the revenues it obtains by collecting taxes?

  2. I want to calculate the optimal tax on external borrowing. Welfare maximizing tax level. From Prof. Pfeifer’s GitHub page I found an m file named return_Welfare. I modified my mod file and worked this m file to find an optimal tax rate. However, when I read the forum I am confused. There is a debate about conditional vs unconditional welfare and consumption equivalent welfare gains. I am new to welfare analysis so can anyone recommend me some resources I can use as a beginner? Is the welfare mentioned in the above-mentioned code conditional or unconditional welfare?

  1. Yes, because there is a difference between the private use of resources after a tax rebate and the public use of resources in the form of government spending.
  2. The thing about “consumption equivalent welfare gains” is about how to express the welfare gains/losses in terms of units, but is not immediately relevant for optimization.
  3. Whether you want to consider conditional or unconditional welfare mostly depends on whether you want to consider transition behavior from one regimes to another. If yes, you need to consider conditional welfare.

Prof. Pfeifer thank you for your response. Could you please elaborate what is transition from one regime to another? from no tax to low tax or high tax rate ?

I guess in my case unconditional welfare will suffice since I am only interested in welfare maximizing tax rate.

Unconditional welfare considers where the dynamic system will be in the long-run. Say you want to know whether the introduction of a tax is beneficial. When you compare unconditional welfare, you are asking what welfare in the new regime will be once it has settled to its new long-run equilibrium. That may be very misleading if there is a long transition period.

Conditional welfare in contrast considers welfare when starting at a particular point in the state space. So you can consider what happens if you introduce a tax, but you are still at the state values of the old regime.