(30 marks) Consider the following two period model with a representative household with the following preferences over consumption today and tomorrow: u(c, c') = ln(c) + ,61n(c') Suppose the representative household has an endowment of 37 > 0 in the current period, (9 but y' = f (k) where M Pk = i = 22W. The household has an Option to either invest in capital today k: or save for the future buying bonds B that pay a real rate of return of 1 + T. To make life easier, assume that the capital has a 100% depreciation rate (there's no ability to salvage left over k). (a) (10 marks) Suppose the household is indifferent between investing in capital and buying bonds (in other words, both give the same rate of return which is why you are given the M Pk). What level of capital is would the household select (note: It will be a function of exogenous variables: r and 2)? How does an increase in technology 2 change this level of capital Is? How does an increase in the real interest rate 1" change this level of capital k