凹函数

       如果函数f(x)在区间I上二阶可导，则f(x)在区间I上是凹函数的充要条件是f''(x)>=0;f(x)在区间I上是凸函数的充要条件是f''(x)<=0;

　　不过补充一下，中国数学界关于函数凹凸性定义和国外很多定义是反的。Convex Function在国内的数学书中指凹函数。Concave Function指凸函数。在国内涉及经济学的很多书中，凹凸性的提法和国外的提法是一致的，也就是和单纯的数学教材是反的。很头大的问题。

　　另外，国内各不同学科教材、辅导书的关于凹凸的说法也是相反的。一般来说，可按如下方法准确说明：

　　1、f(λx1+(1-λ)x2)<=λf(x1)+(1-λ)f(x2) ， 即V型，为"凸向原点"，或"下凸"（也可说上凹），（有的简称凸有的简称凹）

　　2、f(λx1+(1-λ)x2)>=λf(x1)+(1-λ)f(x2) ， 即A型，为"凹向原点"，或"上凸"（下凹），（同样有的简称凹有的简称凸）

　　凸/凹向原点这种说法一目了然。上下凸的说法也没有歧义

The Combination of Market Prices and Public Health-Insurance [HT]

The book Bring Market Prices to Medicare argues that it can through a competitive bidding process to improve health care. The authors want beneficiaries to face the true price differentials between the lowest cost plans and less efficient plans, regardless if the plan is Medicare FFS or an MA plan. Another issue focuses on regional adjustments. Living in New York is expensive and health care is more expensive in New York than in rural Mississippi. However, should Medicare subsidize New Yorkers because their health care is more expensive. The authors argue no.  [HT]

● Bring Market Prices to Medicare: Essential Reform at a Time of Fiscal Crisis (AEI Studies on Medicare Reform), Robert F. Coulam, Roger Feldman, Bryan E. Dowd

The Effects of Entry and Exit (Turnover)

The dynamics of firms' entry and exit (if turnover rate and retention rate can be calculated like in a firm) will influence the competition, innovation, diffusion of advanced technology, and productivity. However, "The health care market exhibits important differences as compared to other markets, including various forms of market failure and, as a consequence, extensive market regulation. Thus, the economic effects of entries and exits in health care markets are less obvious. "

It is a very interesting topic to examine the economic effects of entry and exit in health care market. Martin in this paper attempted to establish a framework to study the impacts on the public-private and GP-specialists relationships. 

Source: Entry and Exit of Physicians in a two-tiered public/private Health Care System

预防医疗不省钱

It is well established that preventive care reduces the prevalence of disease and helps people live longer, healthier lives. Analysis of the cost-effectiveness of preventive care can guide policy-makers to allocate scarce resources. This synthesis reviews the evidence on the cost-effectiveness of clinical preventive care. Key findings include: although many preventive services are a good value (defined as costing less than $50,000 to $100,000 per Quality Adjusted Life Year), only a few, such as childhood immunizations and counseling adults on the use of low-dose aspirin are widely regarded as cost-saving. Costs to reduce risk factors, screening costs, and the cost of treatment when disease is found can offset any savings from preventive care. Prevention can reduce the incidence of disease, but savings may be partially offset by health care costs associated with increased longevity. Whether these additional competing risk costs outweigh the savings from avoiding the targeted disease depends on how healthy people are during the added life years. Given that so few preventive services save money and that these services are already in wide use, it is unlikely that prevention can reduce health care spending. The authors question whether the emphasis on savings is appropriate and suggest it is better to focus on high value preventive care, taking into account increased longevity and quality of life.

Source: Cost Savings and Cost-Effectiveness of Clinical Preventive Care

    Thus we must pay attention to the differences between cost-effectiveness and cost-saving of cares.

My favorite four HEALTH ECONOMISTS

Guy David, genius, I love his research.

David Meltzer, technically he is not so much young, but is still. Both Dav have particular interests in specialization. 

Almond, I have been attracted by issues with health shock and big famine. 

Chandra, so brilliant, "malpractice" expert, and be good at almost every field of health economics.