A small city has only one hospital, which is the only employer of nurses in the city. The hospital's marginal revenue product for nurses is 110 - 2L, where the marginal revenue product is measured in dollars per hour and L is measured in thousands of hours per year. (So, for example, if the hospital's nurses are currently working 20,000 hours in total, the marginal revenue product of the next hour worked by a nurse would be 110 - 2(20) = $70.) The labor supply of nurses is , where w is the wage in dollars per hour and L is again measured in thousands of hours per year. Holding all other inputs constant, what wage would the hospital offer to nurses to maximize profit? How many nursing hours would be worked at this wage? What would happen instead if this were a competitive labor market for nurses? What wage would be offered and how many hours would be worked if the labor market were competitive? How does that compare to what this hospital does to maximize profit?