Q$\mathrm{.}1.($a$)$ Yellow land and Indigoland are two countries producing only two commodities, X and Y$,$ using only labour $($L$)$ as the factor of production. Labour endowments in the two countries are $2400$ and $800$ respectively. The unit labour requirements of X and Y at Yellowland are $3$ and $2$ respectively. The unit labour requirements of X and Y in Indigoland are $5$ and I respectively. The tastes and preferences are assumed to be same in both the countries, and is given by: U$($X$,$ Y$)=$ sqrt$($XY$).$ Discuss the pattern of specialization when trade is opened up between them. Explain with the help of a diagram.

$10$

$($b$)$ Does the Gravity model of trade have the potential to explain why some countries may not trade with each other? Illustrate with the help of an example.

$3\mathrm{.}75$

$($c$)$ If the nominal rate of protection of good X is x$\%,$ can the effective rate of protection be negative. Explain with a simple algebra. $($Assume that for the production of one unit of X at world price of $$100,$ one unit of Y at world price of $$50$ is required$)$

$5$

$($HO$)$ Model where two