Question

Suppose a hospital only needs one input, nurses, to treat their patients. A public insurer reimburses each treatment at $10 and suppose that the hospital needs to hire L nurses to provide T = 5L − 1/20 ∗L^2 treatments. Hospitals pay their nurses a wage W and suppose that 5 + W/2 nurses are willing to work at the hospital for a wage W.

Imagine that the hospital acts as a monopsonist in the labor market (monopoly in employment). What is the profit maximizing employment level and what would be the corresponding wage? Quantify the deadweight loss.

Answer 1

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50-wL finchion 50 labur demand

find the ou oul Phanjina Pabanie 2 Tot T.E R2 0 w TE ME Pangin enat = T£)= d {221o) Minnt Product ia to Mg ind expenae erenu p.T Tot 1-15 PSL- produnt= T-P (pir-^) rarenu = r(5-) 50- L 605L 56 Aimation 3P

e 3& Jraph no Deadweight1oss pOrfeycom7 etihv e nar ket in giren Finding 5tw S0- 2 3-1 Labir whih this onant ou, or L 1a S+w ts7 M Shown

Labur demand le manjind abenе Eе сopuilibinn Peint Fi monopionis 5о (h, 3а) чо 35 E 3 о iад1 5 5 Зо во о

Deuua t (a x ) T-h3 Are a (3&14) (20-2) odead