Suppose Cayuga Medical Center (CMC) currently chooses to rent 250 hospital rooms (K) and use 400 workers (L) to produce its output of care to Q1 patients per year. Assume the production function for patient care yields a typically curved isoquant. The rental price of each hospital room (K) for a year is $16,000 and a worker (L) earns $40,000 per year.

a) (10 points) Demonstrate in a graph (using isoquant and iso-cost curves) CMCs choice of K and L that produces Q1. Put L on the horizontal axis and K on the vertical axis. Calculate the total cost to CMC of producing Q1 at these prices and choices of K and L. Also highlight the intercepts and the slope of the iso-cost line. Label both axes and CMCs choice clearly.

b) (10 points) Because of the inflow of new people moving to Ithaca CMC wants to expand and produce Q2, which is greater than Q1. To produce Q2 CMC would optimally choose 350 hospital rooms and 430 workers. What is CMCs total cost of producing Q2? On a new graph, draw CMCs optimal choice of K and L to produce Q2. Similar to part a, compute the value of intercepts and the slope of the iso-cost line.

c) (10 points) However, because New York State has what is called a certificate of need law the maximum number rooms that a hospital system can have is 275. With this restriction Cayuga Medical Center chooses to still produce the Q2 by using the maximum number of allowable rooms (275) and then needs to hire 480 workers to produce this output. What is the additional cost of producing Q2 because of the restriction on the number of rooms? Add to your graph from part c, the iso-cost for producing Q2 under this restriction. Clearly label all curves and points that represent CMCs choices.

d) (10 points) Labor cost has increased significantly in the post-COVID world. Suppose a worker is now earning a wage of $50,000 per year, and the maximum room policy (275 rooms allowed) is still effective. Show, in the diagram, the new iso-cost required to produce Q2. Clearly label all curves and points that represent CMCs choices