4. Consider the following educational production function Q = P0.50.5 where P is the average quality...

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4. Consider the following educational production function Q = P0.50.5 where P is the average quality of one's peers (i.e., the other students in the same classroom) and A is one's own ability. Assume there are 100 students in the grade, five teachers, 40 high ability students (with AH = 36), and 60 low ability students (with A = 16). (a) What is the (expected) level of student achievement, Q, for high and low ability students if the school randomly assigns 20 students per classroom? What is the average level of student achievement for the entire grade? (b) What is the (expected) level of student achievement, Q, for high and low ability students if the school intentionally places all the high ability students among two classrooms and all the low ability students among the remaining three classrooms? What is the average level of student achievement for the entire grade? (c) Assess the impact of tracking on the distribution of student achievement in the grade. What does this imply about a possible equity-efficiency tradeoff reagrding policymaking decisions concerning tracking? 5. Let's re-consider the previous question, but now assume the educational production function is given by where |A P 10.5 0.5 1+|A-PI Q = [ + A P| is the absolute value of the difference between one's own ability and the average quality of one's peers. (a) Re-answer questions (a) -(c) in the previous question. (b) Give one possible explanation for why the production function in the previous question may be more realistic, and one for why the production in this question may be more realistic. 4. Consider the following educational production function Q = P0.50.5 where P is the average quality of one's peers (i.e., the other students in the same classroom) and A is one's own ability. Assume there are 100 students in the grade, five teachers, 40 high ability students (with AH = 36), and 60 low ability students (with A = 16). (a) What is the (expected) level of student achievement, Q, for high and low ability students if the school randomly assigns 20 students per classroom? What is the average level of student achievement for the entire grade? (b) What is the (expected) level of student achievement, Q, for high and low ability students if the school intentionally places all the high ability students among two classrooms and all the low ability students among the remaining three classrooms? What is the average level of student achievement for the entire grade? (c) Assess the impact of tracking on the distribution of student achievement in the grade. What does this imply about a possible equity-efficiency tradeoff reagrding policymaking decisions concerning tracking? 5. Let's re-consider the previous question, but now assume the educational production function is given by where |A P 10.5 0.5 1+|A-PI Q = [ + A P| is the absolute value of the difference between one's own ability and the average quality of one's peers. (a) Re-answer questions (a) -(c) in the previous question. (b) Give one possible explanation for why the production function in the previous question may be more realistic, and one for why the production in this question may be more realistic.