Sure! It is allowed for lay people, as long as they observe [the five precepts][1] and [virtue (sila)][2], which includes [Right Livelihood (samma ajivo)][3]. Please also see [this answer][4].

The [Vanijja Sutta][5] states:

> "Monks, a lay follower should not engage in five types of business.
> Which five? Business in weapons, business in human beings, business in
> meat, business in intoxicants, and business in poison.
> 
> "These are the five types of business that a lay follower should not
> engage in."

The [Sigalovada Sutta][6] states:

> The wise endowed with virtue    
> Shine forth like a burning fire,    
> **Gathering wealth as bees do honey    
> And heaping it up like an ant hill.    
> Once wealth is accumulated,    
> Family and household life may follow.**
> 
> By dividing wealth into four parts,    
> True friendships are bound;    
> One part should be enjoyed;    
> **Two parts invested in business;**    
> And the fourth set aside    
> Against future misfortunes."

The [Dighajanu Sutta][7] states:

> "And what does it mean to maintain one's livelihood in tune? There is
> the case where a lay person, knowing the income and outflow of his
> wealth, maintains a livelihood in tune, neither a spendthrift nor a
> penny-pincher, [thinking], 'Thus will my income exceed my outflow, and
> my outflow will not exceed my income.'

The [Adiya Sutta][8] talks about the five types of benefits that can be obtained from wealth, which are summarized below:

> 'My wealth has been enjoyed,     
> my dependents supported,     
>     protected from calamities by me.     
> I have given supreme offerings    
>     & performed the five oblations.     
> I have provided for the virtuous,    
>     the restrained,    
>     followers of the holy life.    
>
> **For whatever aim a wise householder    
>     would desire wealth,    
>         that aim I have attained.**    
> I have done what will not lead to future distress.'    
> When this is recollected by a mortal,    
> a person established in the Dhamma of the Noble Ones,    
> he is praised in this life    
>     and, after death, rejoices in heaven.

Also from the [Anana Sutta][9] which talks about "the four kinds of bliss that can be attained in the proper season, on the proper occasions, by a householder partaking of sensuality", summarizes it as follows:

> Knowing the bliss of debtlessness,    
> & recollecting the bliss of having,    
> enjoying the bliss of wealth,    
> the mortal then sees clearly with discernment.    
> Seeing clearly — the wise one —     
> he knows both sides:    
> that these are not worth one sixteenth-sixteenth    
> of the bliss of blamelessness.

Billionaire businessmen can support society by creating jobs, fulfilling the needs and wants of the people through supply for demand, and be philanthropists (similar to Bill Gates and Warren Buffett) who donate to charitable causes and also to Buddhism.

  [1]: http://www.accesstoinsight.org/ptf/dhamma/sila/pancasila.html
  [2]: http://www.accesstoinsight.org/ptf/dhamma/sila/index.html
  [3]: http://www.accesstoinsight.org/ptf/dhamma/sacca/sacca4/samma-ajivo/index.html
  [4]: https://buddhism.stackexchange.com/a/8518/471
  [5]: http://www.accesstoinsight.org/tipitaka/an/an05/an05.177.than.html
  [6]: http://www.accesstoinsight.org/tipitaka/dn/dn.31.0.ksw0.html
  [7]: http://www.accesstoinsight.org/tipitaka/an/an08/an08.054.than.html
  [8]: http://www.accesstoinsight.org/tipitaka/an/an05/an05.041.than.html
  [9]: http://www.accesstoinsight.org/tipitaka/an/an04/an04.062.than.html