Consider two countries, Egypt $($E$)$ and Turkey $($T$),$ that use the same technology for the production of two goods: chili peppers $($G$)$ and oregano $($O$).$ The production of one ton of chili peppers requires $5$ units of labour and $4$ units of capital. The production of one ton of oregano requires $5$ units of labour and $6$ units of capital. Egypt has $6,000$ units of labour and $3,000$ units of capital. Turkey has an endowment of $12,000$ units of labour and $40,000$ units of capital.

a$)$ Define and determine the relative intensity of the goods and the relative abundance of the countries. Determine the comparative advantage of each country and explain what the trade pattern would be if both countries decided to trade.

b$)$ Using graphical analysis and the functions of relative supply and demand, represent and indicate the relative price of chili peppers$/$oregano in autarky for each country, and where the relative price of chili peppers$/$oregano would be with trade. Indicate the trade pattern between the two countries on the graph. Relate this result to the comparative advantage of each country.

c$)$ If in Turkey the autarky price of one ton of chili peppers is $3,000$ monetary units $($m$.$u$.),$ and the price of one ton of oregano is $3,200$ m$.$u$.,$ graphically represent and calculate the prices of the factors of production in autarky equilibrium.

d$)$ When Turkey trades with Egypt, the price of one ton of oregano changes to $3,900$ m$.$u$.$ Using the graph from the previous part, represent this change and calculate the new prices of the factors of production in equilibrium with trade in Turkey. Explain in detail the change produced in the factor prices using the corresponding theorem$/$effect$.$