For cheaper alternatives to cheddar and Parmesan cheese in the gratin recipe, you can try:

- Cheddar: Monterey Jack, Colby, or a mild gouda. These have a milder flavor than cheddar but will still provide gooeyness.
- Parmesan: A mixture of Pecorino Romano and ricotta salata, or just ricotta salata. These have a saltier, tangy flavor like parmesan but are less expensive.

You can also leave out the Parmesan altogether and just use the other cheese. The Parmesan provides a flavor boost but is not essential to the recipe.
The end result may be slightly different in flavor but it will still be tasty and the substitutions will allow you to make the recipe more budget-friendly. Let me know if you have any other questions!
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