Suggested answer for Exercise 4

In the sentence Jim took his shoes off we find a phrasal verb take off. The main verb take occupies the V head, assigning a theme thematic role to the DP in its specifier position and it also takes a PP complement, which consists of a mere head. The agent DP occupies the specifier of the vP. The v head is occupied by an abstract light verb, which is a bound morpheme requiring the main verb to adjoin to it. The agent DP has to move to the specifier of the IP in order to receive nominative Case from the finite I head. From the lower vP the verb moves on to the tense vP and I.