NOTE: it is a monopsony question

Happy Hospital uses nurses (N) to produce treatments for its patients. It chooses its staffing of nurses to minimize personnel costs, and its capital is fixed in the short run. Nurses are willing to work at a wage, w=2N. Hospitals production of treatments (T) is given by T=40N+10, and treatments are priced at $1 each

Write down Happy Hospital optimization problem. How many nurses will the hospital hire? How much will nurses earn in wages? Plot the market demand curve for treatments, the inverse labor supply curve and the firm's marginal cost curve for nurses and mark the equilibrium nurses hired, wages paid, and shade the region of deadweight loss. Explain why the marginal cost curve lies above the inverse labor supply curve. Why might the inverse labor supply curve for nurses slope up? What would the equilibrium be under perfect competition and how could policymakers achieve that equilibrium?