Question 1 [12 marks] Two countries, Alpha and Beta, have the same Cobb-Douglas production function: Y = KOALO'. Suppose the Solow growth model describes both economies. The parameters of the two economies are as follows. -- Depreciation rate (6) -10% -10% ' 0 0 Population growth rate (n) Based on the above information, answer the following questions. (a) Derive the per-worker production function: y = f (k). (2 marks) (b) Solve for the following steady-state levels for Alpha. Show all workings. Round your answers to two decimal places. i. Capital per worker (k*) (2 marks) ii. Output per worker (y*) (1 mark) iii. Marginal product of capital (MPK) (2 marks) (c) Draw a well-labelled graph that illustrates the steady states of the Solow model for both ph_a and %. Comment on the differences in the steady-state levels of capital per worker and output per worker of Alpha and Beta. Briefly discuss the reasons for the difference. Note: No calculations are required