Suppose an economy uses only two inputs in production: capital and labor. The following table describes a production function, where y stands for output per worker and k is capital per worker.

Suppose there are two countries, A and B. The economies of the two countries can be described by this production function. If Country A has initially a capital-labor ratio k = 0.167 and Country B has k = 0.412, show that an equal increase in capital produces more extra output in country A than in Country B.

Explain with words (computations) + graph

y	k
0.000	0.000
0.173	0.030
0.302	0.091
0.408	0.167
0.480	0.231
0.535	0.286
0.577	0.333
0.612	0.375
0.642	0.412
0.667	0.444
0.688	0.474
0.707	0.500
0.724	0.524
0.739	0.545