The change in capital stocks overtime is [change in K = I - depreciation(K)], where I = investment. Investment I equal t

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The change in capital stocks overtime is [change in K = I - depreciation(K)], where I = investment. Investment I equal to saving, which is a constant fraction of income Y. the increasw over time in the number of workers L is [change in L = nL, where n is the population growth rate.
Output per workee and capital per woeker are denoted by y = Y/L and k = K/L.
a) Derive the per-worker production function y = f(k) and use a diagram to show that there is a steady state for capital per workee k* and output per worker y* (steady state must feature [change in K/K = change in L/L]. Explain why no long run growth in GDP per worker, although GDP is growing.
The population of the economy is N, not all of are workers L. the labour market partipation rate p is p = L/N. income per worker is ÿ = Y/N. Starting from steady state in (a), suppose there is a large one time increase in labour market participation p.
b) what happens to capital per worker k, income per worker ÿ and output per worker immediately afterwards?
c) explain why the economy will experience growth in income per person ÿ in the years after the increase in labour market participation and will it carry on into the long run?
d) What are the effects of higher labor market participation on k, y and ÿ in the long run? Justify your answer