SA 3 - First Half Review This question combines some of the concepts from the first half of class. . There is one firm, which produces each period using the technology Y = VKN. . The initial capital stock is K = 25. . There is a population of 100 people, no population change, and each person inelasticity supplies 1 unit of labor. This means that aggregate labor supply is 100 units. . This is a closed economy, so there are no imports or exports. . There is full depreciation, meaning that o = 1. . This takes place in a model with infinite time periods (like in the Solow Growth Model). Show your work for all of the following questions: 1. What is aggregate output in the first period? 2. Suppose that aggregate consumption in the first period is C = 25, and there are no government expenditures: G =0. How much aggregate investment is there in the first period? 3. What is the national savings rate in the first period? 4. How much capital stock will there be in the next period? 5. Suppose that the national savings rate is kept constant. Does the economy appear to be in a steady state? Why or why not? If your answer is no, then what is the steady state level of capital? 6. Recall that in equilibrium, the real wage is equal to the marginal product of labor. What then is the real wage in the steady state? 7. What is the gross domestic income each period in the steady state?2. Now, the aggregate investment rate, I Z (S X Y) Z Y - (v where S indicates the savings rate of the economy, whilst Y indicates the output of the economy. Y = KN = V25 x 100 = V2500 Now, 2 :30 . Thus, the aggregated investment within the domestic economy is: I : Y _ C' : :30 2:3 : 2:3 5 2 l - Y '20 _ 3. Thus, the national savings, E _ 0"). i.e. the savings is 50% or half of the consumption spendings of the economy. AkFifk _ \\ Ak: n J\\.' J\\" 25 25 :W_(l) W 4. The change in capital stock to the next year is: : 0 . Thus, the capital stock available in the next period will be the same as the initial period, i.e