Consider a world with two good

Consider a world with two goods, corn and electronics, and two identical countries, Home and Foreign.
There is only one factor of production, labor, and there are 1,500 workers in each country, each of whom takes all prices as given. Corn is produced with constant returns to scale, and in both countries, one unit of labor is required to produce one unit of corn. However, electronics are produced with increasing returns to scale that are national and external. Thus, the productivity of any one electronics worker depends on how many other workers in the same country are producing electronics. Specifically, if LE is the number of workers producing electronics in a given country, then the productivity of any one electronics worker in that country is equal to LE/300.
(a) Suppose that under autarky 40% of each country’s labor force is devoted to electronics.
What must be the autarchy relative price of electronics?
(b) From this, deduce the budget line of a typical worker in autarchy.
(c) Now, suppose that the two economies are opened up to trade. Suppose that in the free-trade equilibrium we still have the same total number of workers producing electronics worldwide, but that they are all located in Foreign. Compare the equilibrium worldwide quantity of electronics and corn produced under autarchy and free trade. Which outcome is more efficient?
(d) Under the assumption in (c), is the equilibrium relative price of electronics higher or lower under free trade than it is under autarky?
(e) Have Home workers suffered as a result of losing their electronics industry? Explain using the budget set of a typical Home worker.
(f) Has the percentage change in real income been higher in Foreign than in Home? Put differently, did Foreign disproportionately gain from trade, in virtue of having captured the high-tech sector?

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