Suppose an Economy Uses Only Two Inputs in Production: Capital

question 189

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.
$$\begin{array} { l l } y & \mathbf { x } \\0.000 & 0.000 \\0.173 & 0.030 \\0.302 & 0.091 \\0.408 & 0.167 \\00.480 & 0.231 \\0.535 & 0.286 \\0.577 & 0.333 \\0.612 & 0.375 \\0.642 & 0.412 \\0.667 & 0.444 \\0.688 & 0.474 \\0.707 & 0.500 \\0.724 & 0.524 \\0.739 & 0.545\end{array}$$

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