# Optimal provision for a Public Good

1. Apr 27, 2013

### JoshMaths

So a homework question so just hints would be appreciated.

we have each persons utility function as Ui = AaiBi

Solve for optimum level of the public good, both goods cost £1/unit

Ok do you use Lagrangian?
Do you need to express it in the set function way as in ui[Aa1+Aa2,(yi - Aai)/p]

or do you already have the expression you need?

Thanks,

Josh

2. May 6, 2013

### JoshMaths

Wow, viewed nearly 500 times and no answers or help?

Maybe this is why we need an Economics forum...

3. May 6, 2013

### D H

Staff Emeritus
A good number of those views were by web crawlers.

You didn't receive help because there's not much to go on. You didn't describe your terms. What does that subscript i on the left hand side represent? How about on the right? Do those subscripts represent the same thing? What are A and B? Why the superscript on A? What motivated your attempt at a solution?

We can't read your mind. You did not give us a well worded problem with which we we can offer help you with.

4. May 6, 2013

### JoshMaths

Hi D H thanks for the reply, i am sure you have helped me in the past, i remember the name.

I assumed that since it was in the Economics section people would be familiar with utility functions and the like, same way when you see an integral or power series you know it without someone having to go through it.

A = A public good B = a private good the 'i's are for each persons differing utility functions, normally constrained at two people so U1 and U2 and all remaining subscripts following that pattern.

A has a superscript same way anything does, because U is a function and A and B are variables.

It was a homework attempt so that is my motivation.