Question 1 Consider the following economy. The production function is FULL} = K~\"(AL)"'5. The saving rate and the depreciation rate are respectively: 5 = 0.20 and 45 = 0-05. There is no population growth. The growth rate of technological progress is 2%, i.e. g = 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: 3 = 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)