1. Suppose a household has log period utility and only cares about consumption, and discounts the future with a discount factor, if} = .9. Firms have lCobb-Douglas produc- tion functions. with an elasticity of output with respect to capital or = 3. Suppose the capital stock fully depreciates each period, i.e. c5 = 1. Suppose there is no growth, and Let .4: Z 1. h. d. h. . 'What is the lGolden Rule capital stock, kGR? \"That is the steady state capital stock, at\" that is a solution to the Social Planner 's Problem? . Explain why they differ. 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, Zut = .) . Suppose the Social Planner has an initial capital stock of k 2 staff. Given what we know about the utility function and parameter values, compute the capital stock for as many periods as needed to converge to the steady state level of capital. i.e.._ solve for Fri, kg, k3, until the capital stock converges. I would like to see this calculation to 4 digits. lGiven what you computed in part e, what are the corresponding levels of con- sumption? i,e, compute c", cl, ca, (:3, c4, until consumption converges to its steady state level. . lCompare the consumption path in part f._ to that in the economy that maintains the golden rule capital stock. How many periods does the former have higher consumption than the latter? lCompute the lifetime utility for the household under the Social Planner that starts with Fr\". 2 AIGR. . 'Which parts of this exercise depend on the assumption of log utility