In order to conjecture the circumstances in these two countries under free trade, consider the following hypothetical scenario based on Ricardian model. Assume throughout that those two countries (Armenia and Costa Rica) are the only two countries in the world, at least for purposes of trade. There are two goods: computers and headphones. Consumers in both countries always spend half of their income on computers and half of their income on headphones. The only factor of production is labour. Each Armenian worker can produce 2 computers or 3 headphones per unit of time. Each Costa Rican worker can produce 1 computer or 4 headphones per unit of time. There are 50 workers in Armenia and 50 workers in Costa Rica.

1. a)Derive the relative demand curve relating the relative demand for headphones to the relative price of headphones. Do algebraically, and then show what the curve looks like in a diagram (put the relative price of headphones on the vertical axis and the relative quantity of headphones demanded on the horizontal axis).
2. b)Derive the world relative supply curve of headphones (put the relative price of headphones on the vertical axis and the relative quantity of headphones supplied on the horizontal axis).
3. c)Put in the same figure the relative demand curve for headphones that you found in part (a) and the world relative supply curve of headphones that you found in part (b). Determine the equilibrium relative price of headphones and the equilibrium relative quantity of headphones under free trade.