Suppose a hospital is planning about how many patients to treat over the next two years. One key factor the hospital needs to consider in its planning is that hospitals that see many patients in one year have lower costs of care in subsequent years. Let p be the price of hospital care, let 91 be the number of patients the hospital treats in year one, let q2 be the number of patients the hospital treats in year two, and let c₁ and c₂ be the hospital's per-patient cost in years one and two. The hospital's profits over the two year period are: II = (pic₁)91 + (p2 - c2)92 The hospital takes p1 and p2 as fixed and they choose q1 and q2 to maximize profits, II. (1) 1. Suppose, as a warm up exercise, that there is no learning by doing, and that the unit cost functions are as follows: c₁ = 21 and c2 = 92. Is the cost of caring for patients increasing or decreasing in the number of patients seen? Derive the supply function in periods one and two for the hospital. [Hint: Substitute the unit cost functions into the profit functions and take the derivative of II with respect to 91 and 92].

In some circumstances, individuals reproduce better when the population size is large, and fail to reproduce when the population size is small (the Allee effect introduced in Exercise 46). Suppose that per capita production is an increasing linear function with λ(0) =−2 and a slope of 0.01. Find λ(b) and the differential equation for b. Is b(t) increasing when b = 100? Is b(t) increasing when b = 300?

The Grossman model states that health is a capital good that can be carried over from one period to the next. With this in mind, which of the following is most likely true about how the individual will value health in a lifecycle context compared to a one-period model? Individuals tend to value health less in the life cycle context compared to the one period model Individuals tend to value health more in the life cycle context compared to the one period model. not change the emphasis they put on health.

Medicare recipients can purchase supplemental private insurance (known as Medigap insurance) to fill the gap in coverage left by Medicare. This gap includes copayments, deductibles, and prescription drug expenses not covered by Medicare. Several years ago, the government enacted regulations that specify minimum standards for items that Medigap policies must cover. This made the policies more expensive, and as a consequence, about 25 percent of the elderly who would have purchased some Medi-gap insurance purchased none at all [Finkelstein, 2004]. Consider an individual who consumes two goods, "insurance" and "all other goods." The cost of a unit of Medigap insurance is $1, as is the cost of a unit of all other goods. Sketch a budget constraint and set of indifference curves that are consistent with the following scenario: In an unregulated market, an individual with a $30,000 income purchases $5,000 worth of Medigap insurance. The government then puts mandates on Medigap policies that…