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Question: juan is uninsured and he just started to live in...

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Juan is uninsured and he just started to live in Boston. In order to stay healthy, he needs to visit a primary care physician on a regular basis. In Boston, primary care physicians charge on average Py dollars per visit. Juans monthly income is m dollars and he has to split his income between visits to the doctor and paying rent. We will denote X the number of times Juan visits a primary care physician (per month) and Y the number of square feet he decides to rent each month. Juan is trying to figure out how big his apartment should be. Clearly, he has to face some trade-offs because the bigger the apartment he rents, the less money he will have to go see a doctor on a regular basis. The rental price per square foot in Boston is on average Py dollars per square foot. However, his final decision also depends on his preferences. Suppose Juan preferences over consumption bundles of health care and housing are captured by the following utility function U(X,Y) 2XY a) b) Write down Juans utility maximization problem subject to his budget constraint. What are the two conditions that must be satisfied in order for Juan to be maximizing his utility subject to his budget constraint How much health care is he going to consume as a function of the prices he faces Px,Py and his monthly income m? How big is his apartment in the end as a function of the prices he faces Px , Py and his monthly income m? In other words, derive the demand function for health care and housing for Juan: X(Px ,Py ,m) and Y (Px ,Py ,m) Graph the demand for health care services X(Px.Py ,m) in a plane where the vertical axis is labeled Px (dollars per visit) and the horizontal axis is labeled (quantity demanded of good X or number of visits per month). An approximate graph is okay c) d) e) What percentage of this income is Juan spending on health care? f) What is the elasticity of demand X(Px, Py ,m) with respect to its own price Px g) Suppose Juan gets an insurance plan and we denote his coinsurance rate algebraically by the variable co. For example, in class we saw an example with the following coinsurance rate co 1/2. Derive Juans demand for primary care physician visits now that he has coverage. Your answer should be in terms of the prices faced by Juan, his income and the coinsurance
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