1. Suppose a household has log period utility and only cares about consumption, and discounts the future with a discount factor, B = .9. Firms have Cobb-Douglas produc- tion functions, with an elasticity of output with respect to capital a = .3. Suppose the capital stock fully depreciates each period, i.e. 8 = 1. Suppose there is no growth, and let A= 1. a. What is the Golden Rule capital stock, kGR? b. What is the steady state capital stock, kss that is a solution to the Social Planner's Problem? c. Explain why they differ. d. Suppose an economy maintains the golden rule level of capital stock. Given kGR, what is the consumption, CGR? What is the lifetime utility of the household that consumes this level of consumption every period? (Recall, 2039 = 1 1. Suppose a household has log period utility and only cares about consumption, and discounts the future with a discount factor, B = .9. Firms have Cobb-Douglas produc- tion functions, with an elasticity of output with respect to capital a = .3. Suppose the capital stock fully depreciates each period, i.e. 8 = 1. Suppose there is no growth, and let A= 1. a. What is the Golden Rule capital stock, kGR? b. What is the steady state capital stock, kss that is a solution to the Social Planner's Problem? c. Explain why they differ. d. Suppose an economy maintains the golden rule level of capital stock. Given kGR, what is the consumption, CGR? What is the lifetime utility of the household that consumes this level of consumption every period? (Recall, 2039 = 1