The economics of Mrs Lovett
Posted February 27, 2008on:
Most economic research is a process of adding to ideas that have already been thought of. In Mrs Lovett’s case her grand plan involves adding concepts to Sweeney Todd’s welfare policy.
Now if you haven’t seen the movie yet, this might be a bit more of a spoiler than the previous post. As a result, think carefully before you click below the flap.
If I remember correctly, Sweeney Todd decided that it would be socially optimal for everyone to die. However, while forming this welfare policy he had a problem brewing – there was a dead ‘Italian’ barber in his room. Following the derivation of this welfare policy he moved his thoughts towards this problem.
His initial suggestion was to just go somewhere and bury the body. This would be a low cost solution and would remove the problem. Furthermore, as Mr Todd held the value judgment that what happens to a body once the person is dead does not matter (as the body’s value to the person living in it is zero), it does not matter where they dump him. However, Mrs Lovett had other ideas.
Seems a downright shame…
Seems an awful waste…
Such a nice, plump frame
Wot’s ‘is name has…
Mrs Lovett decides to think outside the square in order to come up with a welfare maximising use for the dead barber – mince his body up and put it in pies. As both Mrs Lovett and Mr Todd assume that what happens to his body does not change the value he receives from being dead (which is zero), we simply have to think how this action will impact on general welfare.
Mrs Lovett and Mr Todd know it would be to their benefit, because when they sell these pies they receive money which exceeds the cost to them of making the pies. Furthermore, as people are willing to pay a positive price for the pies, they must receive some value from consuming the pie – which is good for them. As a result, this action appears to be pareto superior to Mr Todd’s plan, and so as a result they decide to do it.
Combining the values judgments of Sweeney Todd’s welfare policy and Mrs Lovetts own partial equilibrium model gives us the new Lovett-Todd welfare policy. How does this work, well first lets hear what the authors have to say:
Think about it!
Lots of other gentlemen’ll
Soon be comin’ for a shave,
The solution to the Lovett-Todd welfare policy is that it is optimal for them to kill people and put them in pies. This may seem weird at first, but if we take as given the fact that Mr Todd proved the social optimality of killing people, and then we take as given that the socially optimal way to dispose of the body is to put it in pies and get people to eat it, then this policy solution follows naturally.
Assume that we have a representative agent that gains negative utility A from living. Now assume that there is a population of these agents, and that one is killed – social welfare will invariably increase (Todd-principle).
Next, assume that the same agent receives b(p) utility when they consume pies (the number of which is denoted by p), and b(p) is positive. Furthermore, the first derivative of b(p) is positive, but the second is negative. Individual utility takes the form u=A+b(p), and there must be some price that gives us an optimal value for the number of pies to consume. If we allow the market to set the price, we will tend towards the socially efficient allocation of pies and social welfare will be higher than it was earlier (Lovett-principle).
Now we can combine the two, by killing people to put in the pies we are taking two policies that improve social welfare and putting them together. If we have X agents, we go from having social welfare of A*X to A*(X-k)+b(p(k)), where k is the number of people killed. The price for pies may have to be controlled by a central authority in this case, to make sure it covers it impact on both parts of the welfare equation (as demand does not account for the welfare improvement from the people dieing). A*X<A*(X-k)+b(p(k)) as A*X<A(X-k) (given k is non-negative) and b(p(k))>0 (read less than etc as less than or equal to) – which implies that the new policy is socially optimal.
As I mentioned in the Sweeney Todd post, I am not sure that I subscribe to the same set of value judgments as Mr Todd, as a result I do not personally believe that this is a policy that should be instituted in New Zealand. However, Mrs Lovett’s policy does raise some interesting questions – which may be covered at another time.