Public School Teacher Salaries, Class Size and Private School Markets: In exercise 14.10, we noted that private schools that charge tuition operate alongside public schools in U.S. cities. There is much discussion in policy circles regarding the appropriate level of public school teacher salaries (which are set by the local or state government) as well as the appropriate number of public school teachers (that determines class size in public schools).
A: Suppose again that private schools face U-shaped long-run AC curves for providing seats to children and that the private school market is currently in long run equilibrium.
(a) Begin by drawing two graphs — one with the long run AC curve for a representative private school and a second with the demand and (short run) aggregate supply curves (for private school seats) that are consistent with the private school market being in long run equilibrium (with private school tuition p on the vertical axis).
(b) Now suppose the government initiates a major investment in public education by raising public school teacher salaries. In the market for private school teachers (with private school teacher salaries on the vertical and private school teachers on the horizontal), what would you expect to happen as a result of this public school investment?
(c) How will this impact private school tuition levels, the number of seats in private schools and the overall number of children attending private schools in the short run?
(d) How does your answer change in the long run as private schools can enter and exit the industry?
(e) Suppose that instead of this teacher salary initiative, the city government decides to channel its public school investment initiative into hiring more public school teachers (as the city government is simply recruiting additional teachers from other states) and thus reducing class size. Assuming that this has no impact on the equilibrium salaries for teachers but does cause parents to feel more positively about public schools, how will the private school market be impacted in the short and long run?(f) How will your long run answer to (e) be affected if the government push for more public school teachers also causes equilibrium teacher salaries to increase?
B: As in exercise 14.10, assume a total city-wide demand function x(p) = 24, 710 − 2500p for private school seats and let each private school’s average long run cost function be given by AC (x) = 0.655x1/3 + (900/x). Again, interpret all dollar values in thousands of dollars.
(a) If you have not already done so, calculate the initial long run equilibrium size of each school, what tuition price they charge and how many private schools there are in the market.
(b) If you did B(a) in exercise 14.10, you have already shown that this AC (x) curve arises from the Cobb-Douglas production function x = f (ℓ, k) = 35ℓ0.5 k0.25 when w = 50 and r = 25 and when private schools face a fixed cost of 900. If you have not already done so, use this information to determine how many teachers and how much capital each school hires.
(c) Suppose that the increased pay for public school teachers drives up the equilibrium wage for private school teachers from 50 to 60 (i.e. from $50,000 to $60,000 per year). What happens to the equilibrium tuition price in the short run?
(d) What happens to school size and class size?
(e) How will your answers on school size, tuition level and class size change in the long run? (You can use the cost function given in equation (13.35) of exercise 13.5 to derive the AC function — just make sure you keep track of the fixed cost of 900!)
(f) How many private schools will remain in the market in the long run?