Question 1: Assume that China's output (V) is produced using capital (K) and labour (L) with the following production function Y = "? China's rate of population growth() is 0.5%, per year (0.005). The rate of depreciation of capital is 20% per year (020) and assume there is no technical progress a) Prove that the production function displays diminishing returns to capital (10%) b) Prove that the production function displays constant returns to scale (10%) c) Find the capital stock per capita, income per capita, consumption per capita and investment per capita in steady state given that the Chinese savings rate (s) is 50% (0.5) (50%) d) Calculate the Golden Rule" level of capital stock in steady state. Is the Chinese economy dynamically efficient? (30%) Question 1: Assume that China's output (V) is produced using capital (K) and labour (L) with the following production function Y = "? China's rate of population growth() is 0.5%, per year (0.005). The rate of depreciation of capital is 20% per year (020) and assume there is no technical progress a) Prove that the production function displays diminishing returns to capital (10%) b) Prove that the production function displays constant returns to scale (10%) c) Find the capital stock per capita, income per capita, consumption per capita and investment per capita in steady state given that the Chinese savings rate (s) is 50% (0.5) (50%) d) Calculate the Golden Rule" level of capital stock in steady state. Is the Chinese economy dynamically efficient? (30%)