Consider an imaginary country named Solowakia. Solowakia has no technological progress and no population growth and its production function is given by Y = K(1*')N"' where Y is output, K is capital, and N is the number of workers. Assume that oz is 2/3. (a) Mathematically show whether the function satises (i) contant returns to scale and (ii) diminishing returns to capital. (b) Rewrite the production function in \"per worker\" basis and denote it as f (k) where k = K N (c) What is the steady state level of capital per worker (k*) and state level of output per worker (y*) ? (Show in terms of the saving rate 3, and the depreciation rate 5) (d) What is the golden rule level of capital? (Emplain in words the meaning of the concept) Suppose that the depreciation rate is 5%. Find a saving rate SGOLD for which the golden rule level of capital is satised