Unfortunately I don't know enough about Vijayanagara's economic history, but you might be interested in the work of Nalini Rao who has written quite a bit on the topic. E.g. in the essay "Multi-Zonal Integration and Network Relations at Vijayanagara" in: Nationalism and Imperialism in South and Southeast Asia, where she discusses the centrality of the markets (nagaram) and merchant guilds to the state's economy. The markets' connection to temples (another big economic factor due to royal patronage) and to royal power are also discussed.
Apart from the internal structures, it's also important to keep in mind the role of international trade for Vijayanagara, cf. Carla Sinopolo, From the Lion Throne:
The coastal seaport city-states of south India, such as Calicut and Basrur, were vibrant cosmopolitan centers inhabited by South Asian, Middle Eastern, and East Asian merchants. South Indian merchants, artisans, and agriculturalists were involved in economic relations that linked Vijayanagara with areas far outside its political sway, including northern regions of South Asia, Central Asia, the Middle East, East Africa, and East Asia. By the early 16th century, Europe also had a direct presence on the western coast of India. Following the Portuguese capture of Goa in 1511, Vijayanagara's rulers were drawn into complex diplomatic and economic relations with the Portuguese Estada da India.
I've written earlier about religion and art in Vijayanagara, in case you're interested. Hope this helps.
Follow up question how do you even say Vijayanagara? I heard some Englishmen say it vagina-gara. How do you pronounce it properly?
Follow up questions: Was the bureaucracy of the directly ruled territories same as the vassals (chiefs of Tulu Nadu, Ummattur, Reddis) and autonomous kingdoms like Calicut and Tamil regions? Did the far flung territories like Jaffna, Calicut and Southern Tamil Nadu actually pay yearly tribute or was it just an acknowledgement of suzerainty? I am interested in knowing about pre Nayaka era, around 15th century.