Suppose the demand faced by a labor monopsony is W = 20,000 – 50l, where W is the annual wage and l is the number of workers hired. The labor supply is given by W = 5,000 + 75l. How many workers will the firm hire?
Question
Suppose the demand faced by a labor monopsony is W = 20,000 – 50l, where W is the annual wage and l is the number of workers hired. The labor supply is given by W = 5,000 + 75l. How many workers will the firm hire?
Solution
To find out how many workers the firm will hire, we need to set the demand equation equal to the supply equation and solve for l (the number of workers).
The demand equation is W = 20,000 - 50l and the supply equation is W = 5,000 + 75l.
Setting these two equations equal to each other gives us:
20,000 - 50l = 5,000 + 75l
Solving for l, we first combine like terms:
20,000 - 5,000 = 75l + 50l
15,000 = 125l
Then, divide both sides by 125 to solve for l:
l = 15,000 / 125
l = 120
So, the firm will hire 120 workers.
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