Consider the following economy. The production function is (, ) = ^0.4()^0.6. The saving rate and the depreciation rate are respectively: = 0.20 and = 0.05. There is no population growth. The growth rate of technological progress is 2%, i.e. = 0.02. (i) Derive the capital accumulation equation for this economy. (30 marks) (ii) Find the steady state value of the capital stock per effective worker. (20 marks) (iii) Assume that the economy is at the steady state. Now suppose that the saving rate increases to: = 0.30. Calculate the effect on the steady state of the economy and discuss the process of convergence to the new steady state using a diagram. (20 marks) (iv) Discuss the following statement: 'An increase in the saving rate induces an increase in the rate of economic growth in the long- run only if the production function is linear in the accumulating factor (i.e. capital).' (30 marks)