Question

To produce output, a firm in the United States uses a series of inputs indexed by x, where x ranges from 0 to 1. These labels describe the "sophistication of an input, such that x=0 is the "least sophisticated" input, x=0.5 is the input of median sophistication, and x = 1 is the most sophisticated" input. To produce one unit of output, the US firm requires one unit of each input. There are two countries that can supply inputs, the US and China. One hour of US labor can produce one unit of each input. That is, American labor productivity in input x is Ax.US = 1 for every x. One hour of Chinese labor can produce 1 - x units of input x. That is, Chinese labor productivity in input x is Ax.China = 1 -x. The Chinese wage is $1 per hour. Inputs are supplied competitively. The US firm incurs no trade costs when purchasing inputs from US suppliers. a) Consider two inputs, x=0.35 and x = 0.65. In terms of these two goods, does the United States have comparative advantage in neither, x=0.35, x = 0.65, or both?

Answer 1

a) x=0.35 US can produce 1 unit of x each hour

For China it can produce 1-0.35=0.65 units per hour hence US has comparative advantage for production of x= 0.35

For x=0.65 US can produce 1 unit each hour

China can produce 1-0.65 =0.35 unit each hour hence US has comparative advantage in producing both x=0.35 and x=0.65