Learn Swedish: Du har arbetat hårt och förtjänar att unna dig en lång semester. - You have worked hard and deserve to treat yourself to a long vacation.

In this sentence, dig acts as the indirect object, showing who benefits from the action. The verb unna (to treat, to grant, or to allow) takes two objects: the person receiving the treat (dig) and the treat itself (en lång semester). Since the person receiving it is the same as the subject (du), we use the reflexive pronoun.

Could I just say förtjänar att unna en lång semester and leave out dig?

No, that would sound incomplete. The verb unna almost always requires you to specify who is being granted or treated to the thing. If you leave out the indirect object dig, a Swedish speaker will be left wondering who is getting the vacation.

Why is the word for "hard" written as hårt here instead of hård?

Here, "hard" is describing how you worked, which makes it an adverb modifying the verb har arbetat. In Swedish, you form an adverb from an adjective by adding a -t to the end (matching the neuter form), which is why hård becomes hårt.

Is it grammatically correct to leave out the subject before förtjänar?