After recently watching the movie ‘Sweeney Todd‘ one question popped into my mind, is the welfare policy he derives optimal? Below the flap I will discuss his welfare policy – if you haven’t seen the movie or watched the broadway show then read at your own risk. Although I don’t talk about the movie itself, and the welfare policy won’t tell you anything you wouldn’t find by watching the trailer.
Mr Todd starts his model with the conclusion “they all deserve to die”. This is an interesting policy prescription, but one that he wishes to explain to us in more detail.
He states that his model involves two types of agents, those “staying put in their proper place” let us term these nice, and those “with their foot in the other one’s face”, lets term these mean.
Then he moves on to discuss why it is optimal for both groups to be killed, he states:
” Because the lives of the wicked should be made brief
For the rest of us death will be a relief”
So here he is saying the following. State that the benefit for living for the mean agent is a+y(c) where c is their choice of how cruel to be, and y(c) is an increasing function in c, and a is their intrinsic value from living. Assume then that the benefit from living for the nice agent is b+x(C) where b is there intrinsic benefit from life and x(C) is a negative function of the sum of the mean agents choice of c – furthermore x(C) is falling in c (this is required or there would be no reason to kill our mean agents later!).
Using his value judgments (as you almost always have to in order to get a policy statement) Mr Todd states that given the population of both agent types, and given the optimal choice of c, the value of C will be so high that nice agents receive a negative from living. If not living provides zero payoff, then he can kill the nice agents and increase welfare.
Next we have the mean agents, although they receive a positive payoff from living, Mr Todd realises that they cause an externality through their choice of c. In welfare terms they add a+y(c)+x(c) to welfare. Now since x(c) is negative, then it is possible that the overall welfare impact of these agents could be negative. Mr Todd assumes that abs(x(c))>a+y(c), thereby stating that killing a mean agent will increase total welfare.
Although Mr Todd is very confident of his welfare policy, as he states:
“But the work waits!
I’m alive at last!
And I’m full of joy!”
I fear that his value judgments may be a tad inappropriate. Ultimately this is not the sort of policy I would like to see the New Zealand government adopt in order to increase national welfare.