We are interested in adapting the short run model of the rm to better understand how schools respond to changes in policy in the short run. A school can hire teachers (N) to produce student achievement (A). The more teachers the school hires, the smaller the class size, and the higher the average student achievement. Suppose that the school short run production function how hiring more teachers leads to higher average student achievement according to the production function A: 300N2f3_ 1. In a diagram measuring the number of teachers along the horizontal axis and average student achievement along the vertical axis draw the school's production function. What is the shape of this function? Most education scholars believe that the increase in student achievement from reducing class size is high when class size is high but diminishes as class size falls. Keeping in mind that the fewer the number of teachers the higher the class size, 2. Does the suggested production function agree with this belief? Justify your answer. As mentioned above, we assume that A is the average score on a standardized test. Now, suppose that the typical parent is willing to pay a price of p : 4 for each unit increase in their student's achievement. Suppose also that teachers' unit salar}r is w : 60,000 per school year. The school has 100 students. 3. Show that the school's yearly profit depends on the number of teachers (the school's variable input) according to the profit function Profitm) = 120,000sz3 60,000N Fixed Cost 4. By maximizing profit with respect to the number of teachers, nd the prot maximizing number of teachers. 5. What is the optimal average class size at this school? 6. What is an iso-proEit line? Why is the slope of an iso-prot line equal to w/p? 7. In your diagram, add an iso-prot Line and illustrate the school's optimal number of teachers along the horizontal axis and the optimal average student achievement along the vertical axis. Suppose that the department of education introduces a program that would reimburse 50% of the school's yearly capital investment costs for building upgrades. 8. How would this program affect the school's prot function? According to this model, would the program be successful in raising the average student achievement at the school in the short run