MacroeconomicsProblem set 2Due date: Tuesday, November 3. Your group must submit the problem set by the beginning ofthe class.You must provide explanation for your answers. Please write clearly. If your answer is notclear, I cannot give you the credits for the questions.Simplified Romer Model (Answer the questions 1 and 2 below based on the model wediscussed in the class);1. An economy is on a balanced growth path in the Romer model.
Suppose that, a country istrying to encourage knowledge/idea production sector. To represent this policy in a simple way,letâ€™s assume that, in the year 2020, ̅ rises immediately and permanently to the new level ̅ . (4points)(a) What are the new growth rates of knowledge and output per person? Explain in words aswell.(b) Make a graph of output per person over time using a ratio scale. Do we observe the
economygrow at a higher rate? Explain.̅2. Now suppose that the parameters of the model take the following values: ̅̅̅ =80, =0.08,̅, and ̅ =2000. (4 points)(a) What is the growth rate of output per person in this economy?(b) What is the initial level of output per person? What is the level of output per person after 200years?3. Consider the following variation of simplified Romer model:̅̅̅̅There is a simple change. Donâ€™t be intimidated by the change. Just solve the model in steps andsee what you observe.(A) Solve this variant Romer model in detail. You need to show all the necessary steps to derivethe solutions (5 points). After that, answer the following questions:a.
What is the growth rate of knowledge in this economy? (2 points)b. What is the solution for the level of output per person? What is the growth rate of output perperson in this economy? (3 points)c. Suppose we have two economies — letâ€™s call them country 1 and country
2. The economy ofcountry 2 is described by the variant Romer model above.Country 1 is identical with the country 2 except that the production process of output in thiscountry 1 is described by the following production function (as we discussed in the class):These two economies are so far apart that they donâ€™t share ideas, and each evolves as a separateeconomy. On a single graph (with a ratio scale), plot the path of per capita GDP of country 1 andcountry 2 over time. Explain in words as well. (4 points)
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