Consider a world with two countries (US and China) and two products (Computer and iPhone). In the US it takes 1 worker to make one computer or 1 worker to make one iPhone. In China, it takes 2 workers to make one computer or 2 workers to make one iPhone. Let the utility of the representative agent in each country be:

U = (C)^1/3 (I)^2/3 where C is the consumption of computers, I is the consumption of iPhones.

Will the two countries trade with each other? Why or why not?

Suppose now China receives a techonolgical upgrading in its iPhone sector and only takes 1 worker to produce 1 iPhone (this condition preserves for the rest of the questions). Will the two countries trade now? Which country has a comparative advantage in computers? Predict the trade patterns between the two economies (who exports what? who imports what?)

Suppose the US has 9 workers (L US = 9), solve for and state the autarky national equilibrium for the US. Show all your steps! (your final answer should have the national consumption and production on computers and iPhones, and a relative price p US computer p US iPhone )