# Consider the following Cobb Douglas production function: Y= K1/4L3/4. The rate of depreciation in the economy is 4% and the marginal propensity to save (mps) is 25%.

Consider the following Cobb Douglas production function: Y= K1/4L3/4. The rate of depreciation in the economy is 4% and the marginal propensity to save (mps) is 25%. Any output that is not saved is consumed and this is a closed economy. Population growth rate is zero.

a. Calculate the steady state capital per worker and output per worker. Show your steps. (2 marks)

b. Continue with the same data with the exception that mps is unknown. Solve for the rate of investment which will ensure golden rule of consumption per capita as covered in posted lectures for Chapter 3.Show all the steps covered in the discussion for the practice problem clearly to avoid grade penalty. (5 marks)

c. Continue with the same data above but introduce the following change. The rate of depreciation changes to 5% for capital per worker greater than or equal to 50. For k<50, the rate of depreciation still continues to be 4%. Use a well labeled graph to show the steady state behaviour in this new scenario. In your answer you must indicate the numerical magnitudes of the associated capital per worker and output worker. Show the steps you have followed to obtain the numerical answers. (2 + 2 marks)

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