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What is the equilibrium weekly wage and quantity of


This is from a practical exercise. The answers are below BUT, I do not know how they came up with them. I'd like a step-by-step explanation of how they got the answers.

Practical Exercise 1:

Assume the demand for teachers (Ld) in a school is given by the following equation: W = 1700 - 2LD and the supply of teachers (LS) depends on whether the school is a public school or private school:

Public School Supply: W = 4LS + 800

Private School Supply: W = 4LS + 500

  1. What is the equilibrium weekly wage and quantity of teachers in each school?
  2. What is the pay difference between the two schools?
  3. If this was a perfectly competitive market, what should happen to the quantity and wage of private school teachers?
  4. If this was a perfectly competitive market, what should happen to the quantity and wage of public school teachers?

The book answers are as follows:

BOOK ANSWER:

  1. Public: W* = 1400; L* = 150 and Private: W* = 1300; L* = 200
  2. $100
  3. Quantity decreases and wages increase
  4. Quantity increases and wages decrease

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