The question is as follows: The Happyland Hospital is a monopsonist employer of nurses in the small city of Happyland. The market supply function of nurses is $S(W) = 0.1W - 100$, where $W$ is the nurses weekly wage. What is the hospital's marginal expenditure, ME? If the hospital's marginal benefit of a nurse is $2,000 per week, no matter how many nurses it hires, what is the profit-maximizing number of nurses for the hospital to hire? What will the nurse's wage be? What is the deadweight loss?
And my work so far is as follows:
$Q_s = 0.01W - 100$
$0.01W = Q + 100$
Inverse Supply: $W = 100Q + 10,000$
$ME = W+(dW/dQ)Q = (10,000 + 100Q) + 100Q$
$ME = 10,000 + 200Q$
Profit Maximization - $MB = ME$
$10,000 + 200Q = 2000$
I first derive the Inverse supply curve then use that to derive marginal revenue. Now I'm setting $MB = ME$ as this is the profit maximizing point, but the Q it yields is negative. $(-40)$. Have a feeling this is a problem point. Am I going wrong here?