Suppose the production function in per capita terms is f(k) = Ak. The model parameters are:...

 

 

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Suppose the production function in per capita terms is f(k) = Akº. The model parameters are: 0 = (Capital share of income) A = 2 (Level of technology) n = 0.15 (Population growth rate) 60.25 (Depreciation rate) s = 0.3 (Savings rate) (a) Solve for the steady state level of: i. Capital per capita (k*) ii. Income per capita (y*) iii. Savings/Investment per capita iv. Consumption per capita Show all workings. No additional explanations required. (1.5 marks) (1.5 marks) (1.5 marks) (1.5 marks) (b) Draw an appropriate diagram to illustrate your answer from part (a). Be sure to draw and label the production curve, savings curve, required investment curve, and steady state level of output and capital per capita. No explanation required. (4 marks) (c) Given the production function, the marginal product of capital is f(k) k MPK(k)= = 0: Solve for the Golden Rule steady state level of: i. Capital per capita (k) ii. Output per capita (y) Show all workings. No additional explanation required. (2 marks) (2 marks) (d) Consider your answers for parts (a) and (c). State whether the government should increase or decrease the savings rate from s = 0.3 in order to reach the Golden Rule steady state. Briefly explain your answer in one or two sentences. (2 marks) (e) Disregard your answers for parts (a) to (d). Suppose increasing affluence decreases the rate of population growth. State the impact of increasing affluence on steady state levels of capital per capita and output per capita. (2 marks) Suppose the production function in per capita terms is f(k) = Akº. The model parameters are: 0 = (Capital share of income) A = 2 (Level of technology) n = 0.15 (Population growth rate) 60.25 (Depreciation rate) s = 0.3 (Savings rate) (a) Solve for the steady state level of: i. Capital per capita (k*) ii. Income per capita (y*) iii. Savings/Investment per capita iv. Consumption per capita Show all workings. No additional explanations required. (1.5 marks) (1.5 marks) (1.5 marks) (1.5 marks) (b) Draw an appropriate diagram to illustrate your answer from part (a). Be sure to draw and label the production curve, savings curve, required investment curve, and steady state level of output and capital per capita. No explanation required. (4 marks) (c) Given the production function, the marginal product of capital is f(k) k MPK(k)= = 0: Solve for the Golden Rule steady state level of: i. Capital per capita (k) ii. Output per capita (y) Show all workings. No additional explanation required. (2 marks) (2 marks) (d) Consider your answers for parts (a) and (c). State whether the government should increase or decrease the savings rate from s = 0.3 in order to reach the Golden Rule steady state. Briefly explain your answer in one or two sentences. (2 marks) (e) Disregard your answers for parts (a) to (d). Suppose increasing affluence decreases the rate of population growth. State the impact of increasing affluence on steady state levels of capital per capita and output per capita. (2 marks)

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a To solve for the steady state levels of capital per capita and income per capita we can use the fo... View the full answer