The cheapest car in the world is the Tata Nano. The car was initially launched with a price tag of Rs. 1 lac (around $1600).
It is a cute little model that is suited for four people: a driver and 3 passengers. This car is manufactured in India, though it was later rolled out across the world. India is no stranger to making cheap cars. In fact, many of the cheapest cars in the world are made in India.
Other very cheap cars manufactured in India are the Maruti Alto which is a 5 door hatchback and another model from Tata: the Tata Indica. It is worth noting that the price of the materials that are needed to make a car has risen over the past few years. Thus, the Tata Nano now costs more than it originally did as it costs more to make.
Wikipedia link: https://en.wikipedia.org/wiki/Tata_Nano