Thanks for adding the note on the tax difference! That doesn't address my point though.

If the salary difference of $33k is the difference between gross salary, that $33k is going to be taxed at the marginal tax rate. My guess at a marginal tax rate would be ~40%. Accordingly, that $33k becomes closer to $20k after tax.

Edit: to clarify, consider a Seattle salary of $100k and a Bay Area salary of $133k. The take-home salary for each location would be:

  Seattle : $100k*(1-0.4) = $60k 
  Bay Area: $130k*(1-0.4) = $78k

Leaving $19.8k in additional income to cover the median rent increase of $18k annually.