Question

Consider the "production" of education. For simplicity, assume that a given quality of education has two inputs: teachers (i.e., labor) and classroom technology (i.e., capital). A student is educated by 0.04 teachers (i.e., the student:teacher ratio is 25:1) at an annual cost of $2,400 per year (the teacher's salary is $65,000 per year, or $2,600 per student). Each student is also provided $600 worth of technology per year, for a total annual cost of $3,200 per student. a. Suppose that the teacher's union wins a new contract and that the teacher's salary increases to $75,000. What is the increase in per-student cost assuming that the school district continues to maintain a 25:1 student teacher ratio and purchases the same amount of classroom technology? b. Your answer from part a overestimates the increase in per-student cost if the school district chooses the student teacher ratio and level of classroom technology that minimizes cost. Explain why. c. Explain how the magnitude of the overestimate depends on the shape of the isoquants and the marginal rate of technical substitution between teachers and technology. (It may be useful to consider the cost-minimization problem under two extreme case of the production function: a perfect substitutes production function and a fixed-proportion production function. These are both discussed in the chapter on "Production.")

Answer 1

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a) Suppese the union wins clay the teacher seebery increased to $75,000 per year with respect to the mein tening natio of 25.1 aud the cloiss room technology is constant. so the increased per student cost will be - $75,000 25 - Bovo per student Total cost of Pew student = $servo + $ 600 = $3600 Por student. b) If the school thinks to minimize the cost then. they have to increase their ratio of studente will be 28:1 where school com minimize the cost from to 12.5% to soot, (i.e. the estimated cost currently with increased salary is 112.5% them the earlies which can be reduced to joor by increasing the ratio from 251 to 28:1 l.e. three child increase Pes teacher to justify the Sabry increase c) The isoquent curve is based the everestiwited increased of the technology and the salary. The graphical reporesentation is as follows. capite Ysoquent,