Question

In the Ricardian model, the labour input requirements per unit of output for the two goods, X and Y, are: ax 16 and a, = 2 in the home country,

A; and they are: bx = 3 and by =3 in the foreign country, B. The home country has 32 units of labour, L, = 32 and the foreign country has 18 units of labour, L, =18. Preferences in the home country can be represented by the Cobb-Douglas utility function: Ua = XaYa,.Therefore, the demand functions for the two goods in the home country are:Xa= Ma/2px and Ya = Ma/2py,, where M, is the income of consumers in the home country. Preferences in the foreign country can be represented by the CES utility function: Un (xa+Ya. Therefore, the demand functions for the two goods in the foreign country are: Xa = Ma„Py/(Px (Px + P; )) and Ya = Mx,Px/(Px, (Px (px+px P:)),where Ma is the income of consumers in the foreign country. What is the autarky relative price in the home country? How much of each good is produced and consumed in the home country under autarky? What is the utility of the home country under autarky?[15 marks] What is the autarky relative price in the foreign country? How much of each good is produced and consumed in the foreign country under autarky? What is the utility of the foreign country under autarky? [15 marks] Derive the equilibrium price under free trade. How much of each good does each country produce and consume under free trade? Describe the pattern of trade. What is the utility of each country under free trade and do both countries gain from trade?[50 marks] Comment on your results about the gains from trade.

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