Suppose an Economy Uses Only Two Inputs in Production: Capital

Essay

Suppose an economy uses only two inputs in production: capital and labour. The following table describes a production function, where y stands for output per worker and k is capital per worker.
a) Draw approximately this production function with y on the vertical axis.
b) Show that this production function exhibits diminishing returns to scale.
c) 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-labour 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.