Suppose that the production function for output in an economy is given by Y_t= Kt^0.75N^0.25The number of workers, N, is constant. The saving rate is ,s, and the depreciation rate of physical capital is delta.

a) Write down the equation showing the evolution of the physical capital stock over time. Explain in words. (2 marks)

b) Derive the steady-state levels of capital per worker and output per worker in terms of the saving rate and the depreciation rate. (2 marks)

c) Show these steady-state values in a well-labeled diagram of the Solow-Swan growth model. (2 marks)

d) Suppose that depreciation = 10% Calculate/derive the steady-state level of consumption per worker (C/N) as a function of the saving rate. Show this relationship between C/N and savings in a diagram (2 marks)

e)At what value of savings would C/N be maximised? (1 mark)

f) If s = 0.4, compute the steady state level of Y/N, K/N and C/N (3 points)