Why do export based economies prefer a relatively depriciated currency( example Japan)?

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Why do export based economies prefer a relatively depriciated currency( example Japan)?

In: Economics
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It makes your goods relatively cheap to companies looking to import.

Lets say that you and I make widgets, and they cost us the same to produce – 10 units of currency. So, each widget would cost 10 AnsuzBucks and 10 Wqxecadollars.

If the exchange rate between our two currencies is 1 to 1, then there is no advantage to buying from either you or me. However, if I’m able to depreciate my currency, so the exchange rate becomes 1 AnsuzBuck to 0.9 Wqxecadollars, someone in Wqxecaland can buy a widget from you for 10 or from me for 9 after they exchange currencies. This benefits me, as my goods are now _relatively_ cheaper, even though they have not changed price in my home currency.