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 (245.46 KiB) Viewed 21 times

6. Consider an economy where aggregate output Y is produced using capital K and labour L according to the production function Y = F(K, L). The produc- tion function F(K, L) has constant returns to scale and positive but diminishing marginal products of capital and labour individually. The change in the capital stock over time is AK = I and & is the constant rate at which capital depreciates. Investment I is equal to SK, 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 = f(k) and use a diagram to show that there is a steady state for capital per worker k* and 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 k and output per worker y immediately afterwards? What about income per person ỹ? (c) [4 marks] Explain why the economy will experience growth in income per person ÿ 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. Now suppose the economy experiences permanently faster growth of its popu- lation (higher n) with the same labour-market participation rate p. (e) [3 marks] Use the diagram from part (a) to find the long run effects on the levels of y and ỹ. (f) [3 marks] Suppose owners of capital receive an income equal to the marginal product of capital minus the depreciation rate per unit of capital. Explain whether they gain or lose in the long run from the increase in population growth analysed in part (e).