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1. (30 points) Consider an economy that is described by the Solow growth model. The output is produced with the following production function: Yt= K351i (AtLt)3 where Kt Is the amount of capital and L: is the amount of labour used In production In period 75. A: Is the labouraugmenting productivity that grows at rate 9 = 0.02, while the population grows at rate 71 = 0.01. Capital depreciation rate is equal to 5 = 0.1. (a) Suppose the savings rate is equal to 3. Find the steady state in this economy. What happens to the capital per capita, output per capita and consumption per capita in the steady state? (b) Find the golden rule level of capital per effective worker. Find the savings rate that would lead to this level of capital per effective worker in the steady state, 39. (c) Suppose that the economy starts in the steady state that corre- sponds to 8 = .39, but a large natural disaster destroys 10% of the total capital stock. What will happen in the short and the long run? (d) To speed up the recovery, the government is considering a plan that would increase the savings rate by 10%. Is this a good idea? Explain