6. Consider an economy where aggregate output Y is produced using capital K and labour L according to the production fun

[answerhappygod]

6 Consider An Economy Where Aggregate Output Y Is Produced Using Capital K And Labour L According To The Production Fun 1 (76.61 KiB) Viewed 18 times

6. Consider an economy where aggregate output Y is produced using capital K and labour L according to the production function Y = tion function F(K, L) has constant returns to scale and positive but diminishing F(K,L). The produc- marginal products of capital and labour individually. The change in the capital stock over time is AK and & is the constant rate at which capital depreciates. Investment I is equal to I-6K, where I is investment saving, which is a constant fractions of income Y. The increase over time in the number of workers L is AL=nL, where n is the population growth rate. Output per worker and capital per worker are denoted by y=Y/L and k == = K/L. (a) [4 marks] Derive the per-worker production function y = diagram to show that there is a steady state for capital per worker & and f(k) and use a output per worker y* (such a steady state must feature AK/K = AL/L). Explain intuitively why there is no long-run growth in GDP per worker, al- though total GDP is still growing. The population of the economy is N, not all of whom are workers L. The labour- market participation rate p is p=L/N. Income per person is ÿ= Y/N. Starting from the steady state found in part (a), suppose there is a large one-off increase in labour-market participation p. (b) [3 marks] What happens to capital per worker & and output per worker y immediately afterwards? What about income per person ÿ? (c) [4 marks] Explain why the economy will experience growth in income per person in the years after the increase in labour-market participation. Will this growth continue in the long run? (d) [3 marks] What are the long-run effects of higher labour-market participa- tion on the levels of k, y, and y? Justify your answers.