The Age Pension is assessed under national rules, so living in Melbourne does not create a separate pension rate or eligibility test. Services Australia generally considers your age, Australian residence history, income and assets, with your principal home usually treated differently from other assets. The amount you may receive, including any Pension Supplement or Rent Assistance, depends on your circumstances and is determined by Services Australia. You can check eligibility and claim through myGov linked to Centrelink, or visit servicesaustralia.gov.au for current rules and payment rates.