Question

Nepal and Tibet can both produce butter [B] or tea [T].

        If Nepal allocates all resources to butter, it can produce a maximum of 500 units a year. If all its

        resources are allocated to tea, it can produce a maximum of 2500 units.

If Tibet allocates all resources to butter, it can produce a maximum of 1500 units a year. If all its resources are allocated to tea, it can produce a maximum of 3000 units of tea.

[a] Political considerations initially mean that trade is not possible between Nepal and Tibet.

        If Nepal produces 1250 units of tea for itself, how many units of butter does it produce for itself?

               

        If Tibet also produced 1250 units of tea for itself, how many units of butter does it produce for itself?

        What is the combined amount of tea produced by the countries when trade is not possible? The combined amount of butter?

[b] If political considerations change and trade becomes possible, which good will Nepal trade to

        Tibet? Prove your answer.

[c]   If Nepal and Tibet pursue complete specialization in the production of their comparative advantage products when initiating trade, what is the combined amount of tea produced by the countries?

        Under complete specialization in comparative advantage, what is the combined amount of butter?

        Comparing combined production prior to the possibility of trade [see [a]] with combined production available under specialization, what are the potential gains from trade as measured by additional butter and/or tea?  

[d] Assuming complete specialization by both countries, identify a specific trade [i.e. an amount of tea traded for an amount of butter] that will leave both countries better off when compared to their positions in [a].

Answer 1

Considering the functions N and T for Nepal and Tibet respectively, both have domain in [0, 1]

where N(b)=500b+2500(1-b)=2500-2000b and T(b)=1500b+3000(1-b)=3000-1500b

where b represents the fraction of resources, then we have

N(1)=500, the amount of butter produced by Nepal while using full resources for Butter, and zero resources for tea

N(0)=2500, the amount of butter produced by Nepal while using zero resources for Butter, and full resources for tea

T(1)=1500, the amount of butter produced by Tibet while using full resources for Butter, and zero resources for tea

T(0)=3000, the amount of butter produced by Nepal while using zero resources for Butter, and full resources for tea

a) When Nepal producing 1250 unit of tea, we have 2500(1-b)=1250, so the amount of butter produced will be

500b=500(1-(1250/2500))=250 units

and

When Tibet producing 1250 unit of tea, we have 3000(1-b)=1250, so the amount of butter produced will be

1500b=1500(1-(1250/3000))=875 units

The combined amount of tea is 2500 units and the combined amount of butter is 1125 units

b) Nepal Should trade Tea with Tibet, as we have for a particular b, the ratio of the amount of tea and amount of butter produced by Nepal is (2500(1-b))/(500b)=(5(1-b))/b and for Tibet is (3000(1-b))/(1500b)=(2(1-b))/b and (5(1-b))/b>(2(1-b))/b

so Nepal has a better production value for Tea than Tibet.

c) For specialization, The total amount of tea will be 2500, and the total amount of butter will be 1500