$6.($a$)$ Autoland wants to set up an automobile industry.

The free trade price of an automobile is $$8000$ and the imports of auto$-$components which go into the making of an automobile are priced at $$4000.$ Answer the following questions:

$($i$)$ If the government imposes an ad valorem tariff of $20$ percent on automobile imports, what is the effective rate of protection $($ERP$)$ offered to the industry?

$($ii$)$ Suppose Autoland wants to set up its own auto$-$components industry and hence the government imposes an ad valorem tariff of $10$ percent on imports of auto$-$ components, with no tariffs on automobiles. What would be the new ERP offered to the automobile industry?

$($iii$)$ In continuation to Part $($i$),$ now suppose, the government of Autoland imposes an ad valorem tariff of $10$ percent on imports of auto$-$components along with the existing tariff on automobiles. What would be the new ERP offered to the automobile industry?

$($iv$)$ Critically analyze which of the three policies used by the government of Autoland to develop its own automobile industry, protects the domestic automobile producers the most.