Demonstrate a theoretical understanding of production functions. Empiricallyestimate a simple health production function and use this to derive policy recommendations. You are welcome to work with others, but should each turn in your own assignment.1.Before we begin working with a theoretical model or actual data, let’s use some hypothetical numbers to demonstrate how to construct an infant health production function from raw data.To be technically efficient, one must use input into production in such a way that at the next level the input (from low levels to higher levels) the marginal product is as large as possible.Imagine that we are choosing hospitals in the US in which to build intensive neonatal care units.In this context, some groups and locations are at higher risk of experiencing infant mortality than others. Imagine the consequences of putting an intensive neo-natal care unit in different hospitals are as follows.[I made these numbers up]

Hospital A: Placing a neo-natal care unit in a poor urban hospital in the Northeast saves 5 infant lives per 5000 births.

Hospital B: Placing a neo-natal care unit in a poor rural hospital in South Carolina saves 9 infant lives per 5000 births.

Hospital C: Placing a neo-natal care unit in a southern urban hospital in Alabama saves 6 infant lives per 5000 births

.Hospital D: Placing a neo-natal care unit in a hospital in downtown New York saves 3 infants lives per 5000 births.

Hospital E: Placing a neo-natal care unit in a hospital in a middle class town in upstate New Yorksaves 4 infant lives per 5000 births.

Hospital F:Placing a neo-natal care unit in a hospital on the island of Hawaii (Hawaii is known forbeing a state where the quality of life is exceptionally good) saves 1 infant life per 5000 births

.Hospital G: Placing a neo-natal care unit in an already crowded hospital that is operating overcapacity and lacks the expertise to handle this type of care, increases infant mortality by 2 deathsper 5000 births

a). Draw and clearly label the associated Health Production Function (HPF) where the number of hospitals with a neo natal care units is the input. (Assume efficiency and that the groups are otherwise identical.). Does this HPF exhibit diminishing marginal returns?

b) If the government can only build 3 neo-natal care units which hospitals should get these units? Show and label this point on the production function. How many lives are saved per 5000 births?