I need help with parts (a) through (f) in question 1 and part (a) in question 3.
Suppose that the production function for a city like Edinburgh is: Y=(AT)L1 where T is land, L is labour, and A is a variable called the efficiency of land, and reflects the city's technological knowledge in the use of land. So, the term AT measures the effective total land available. In this city, labour (workers' human capital) deteriorates at a rate but the city save a constant fraction of total income each year, s, to reinvest in workers' human capital: L=sYL a. Define output per effective land y (where y=ATY ) in terms of and labour per effective land l( where l=ATL). b. Assume that A grows at a rate of g, so AA=g. Derive the change in labour per effective land (l) in terms of all the parameters: ,s,,g and state l. (Hint: Note that l represents k in Solow's model) c. Solve for the steady state labour per effective land, l. d. Use a diagram to represent the city's steady state. Identify clearly all the functions included in the diagram and show the direction of movement of labour per effective land, l. e. Assume that the city increases the amount spend in worker's human capital, s. Would it has a higher steady state labour per effective land? Would it have higher growth in labour per effective land? f. By definition, L=ATl. At what rate does L growth? Q3. O-ring Theory, Empirics and Students Setting (35 points) a. Describe the O-ring theory. How does this model relate to the real world? [HINT. Think about stylized facts that you can relate to the theory] [5 points] b. There are 4 students of different "capacity" working together for a group exam based on 4 chapters of a book. The amount of the book each student can cover ranges from 0 to 1 and determine their grade. In this setting, each group member gets the same grade. Due to time constraints, no student can study more than 1 chapter. The list of students and their capacity to cover a chapter is the following: Assume that the grade production function is one in which each book chapter covers a different topic and so the amount of the book chapter covered by a particular student does not affect the groups' understanding of the chapters covered by other students. [6 points] i. Compute the group grade (HINT. If they covered 75% of the book, they get a grade of 75 ) ii. How much better is the group grade if students B is replaced by student E that covers 0.6 of chapter 2 ? iii. How much better is the group grade if student A is replaced by student F that covers 0.9 of chapter 1 ? Suppose that the production function for a city like Edinburgh is: Y=(AT)L1 where T is land, L is labour, and A is a variable called the efficiency of land, and reflects the city's technological knowledge in the use of land. So, the term AT measures the effective total land available. In this city, labour (workers' human capital) deteriorates at a rate but the city save a constant fraction of total income each year, s, to reinvest in workers' human capital: L=sYL a. Define output per effective land y (where y=ATY ) in terms of and labour per effective land l( where l=ATL). b. Assume that A grows at a rate of g, so AA=g. Derive the change in labour per effective land (l) in terms of all the parameters: ,s,,g and state l. (Hint: Note that l represents k in Solow's model) c. Solve for the steady state labour per effective land, l. d. Use a diagram to represent the city's steady state. Identify clearly all the functions included in the diagram and show the direction of movement of labour per effective land, l. e. Assume that the city increases the amount spend in worker's human capital, s. Would it has a higher steady state labour per effective land? Would it have higher growth in labour per effective land? f. By definition, L=ATl. At what rate does L growth? Q3. O-ring Theory, Empirics and Students Setting (35 points) a. Describe the O-ring theory. How does this model relate to the real world? [HINT. Think about stylized facts that you can relate to the theory] [5 points] b. There are 4 students of different "capacity" working together for a group exam based on 4 chapters of a book. The amount of the book each student can cover ranges from 0 to 1 and determine their grade. In this setting, each group member gets the same grade. Due to time constraints, no student can study more than 1 chapter. The list of students and their capacity to cover a chapter is the following: Assume that the grade production function is one in which each book chapter covers a different topic and so the amount of the book chapter covered by a particular student does not affect the groups' understanding of the chapters covered by other students. [6 points] i. Compute the group grade (HINT. If they covered 75% of the book, they get a grade of 75 ) ii. How much better is the group grade if students B is replaced by student E that covers 0.6 of chapter 2 ? iii. How much better is the group grade if student A is replaced by student F that covers 0.9 of chapter 1
