Yunnan is a province in Southwest China. The province spans 394,000 square kilometres and has a population of 48.300 million. The capital of the province is Kunming also known as Yunnan; the province borders the Chinese provinces Guangxi, Guizhou and the Tibet Autonomous Region, as well as the countries Vietnam and Myanmar. Yunnan is China's fourth least developed province based on disposable income per capita in 2014. Yunnan is situated in a mountainous area, with high elevations in the northwest and low elevations in the southeast. Most of the population lives in the eastern part of the province. In the west, the altitude can vary from the mountain peaks to river valleys by as much as 3,000 metres. Yunnan has the largest diversity of plant life in China. Of the 30,000 species of higher plants in China, Yunnan has 17,000 or more. Yunnan's reserves of aluminium, lead and tin are the largest in China, there are major reserves of copper and nickel; the Han Empire first recorded diplomatic relation with the province at the end of the 2nd century BC.

The area was controlled by the Sino-Tibetan-speaking kingdom of Nanzhao, followed by the Bai-ruled Dali Kingdom. After the Mongol invasion of the region in the 13th century, Yunnan was conquered by the Ming dynasty. From the Yuan dynasty onward, the area was part of a central-government sponsored population movement towards the southwestern frontier, with two major waves of migrants arriving from Han-majority areas in northern and southeast China; as with other parts of China's southwest, Japanese occupation in the north during World War II forced another migration of Han people into the region. These two waves of migration contributed to Yunnan being one of the most ethnically diverse provinces of China, with ethnic minorities accounting for about 34 percent of its total population. Major ethnic groups include Yi, Hani, Zhuang and Miao. Yunnan Province has been identified as "the birthplace of tea...the first area where humans figured out that eating tea leaves or brewing a cup could be pleasant."

"Yunnan" acts as a place name. In Tang Dynasty, Xuanzong canonized Piluoge, the chief of Nanzhao to be the "King of Yunnan"; because of Nanzhao was originated from Yunnan county. Along with the powerful and prosperous of Nanzhao, "King of Yunnan" controlled more areas. "Yunnan" became the common name of this area. Therefore, Yuan Dynasty set "Yunnan Province"; the province name "Yunnan" continues to this day. Han Dynasty literature did not record the etymology of "Yunnan", so people have many conjectures. Conjectures are "south of colorful clouds" and "south of Yunling Mountains"; some annals in Ming Dynasty, for example Dian Lüe and Yunnan General Annals record the first conjecture. But modern historian Tan Qixiang disagree with this, he said, a superficial explanation of the literal meaning, it is wrong for the second conjecture because the name "Yunling Mountains" first appeared in Tang Dynasty literature, but "Yunnan" first appeared in Han Dynasty. "Yunnan" has been a place name before "Yunling Mountains".

Modern research gives more conjectures. You Zhong said "Yunnan" means "south of the mountain with clouds". Wu Guangfan said "Yunnan" might be a Bai language name; the Yuanmou Man, a Homo erectus fossil unearthed by railway engineers in the 1960s, has been determined to be the oldest-known hominid fossil in China. By the Neolithic period, there were human settlements in the area of Lake Dian; these people constructed simple wooden structures. Around the 3rd century BC, the central area of Yunnan around present day Kunming was known as Dian; the Chu general Zhuang Qiao entered the region from the upper Yangtze River and set himself up as "King of Dian". He and his followers brought into Yunnan an influx of Chinese influence, the start of a long history of migration and cultural expansion. In 221 BC, Qin Shi Huang extended his authority south. Commanderies and counties were established in Yunnan. An existing road in Sichuan – the "Five Foot Way" – was extended south to around present day Qujing, in eastern Yunnan.

In 109 BC, the Han dynasty invaded Dian during its southern expeditions. Under orders from Emperor Wu, General Guo Chang was sent south to Yunnan establishing the Yizhou commandery. By this time, agricultural technology in Yunnan had improved markedly; the local people used bronze tools and kept a variety of livestock, including cattle, sheep, goats and dogs. Anthropologists have determined, they lived in tribal congregations, sometimes led by exiled Chinese. During the Three Kingdoms, the territory of present-day Yunnan, western Guizhou and southern Sichuan was collectively called Nanzhong; the dissolution of Chinese central authority led to increased autonomy for Yunnan and more power for the local tribal structures. In AD 225, the famed statesman Zhuge Liang led three columns into Yunnan to pacify the tribes, his seven captures of Meng Huo, a local magnate, is mythologized in the Romance of the Three Kingdoms. In the 4th century, northern China was overrun by nomadic tribes from the north. In the 320s, the Cuan clan migrated into Yunnan.

Cuan Chen named himself king and held authority from Lake Dian known as Kunchuan. Henceforth the Cuan clan ruled eastern Yunnan for over four hundred years. International trade flowed by din of Yunnan. An ancient overland pre-Tang

In economics, the isoelastic function for utility known as the isoelastic utility function, or power utility function is used to express utility in terms of consumption or some other economic variable that a decision-maker is concerned with. The isoelastic utility function is a special case of hyperbolic absolute risk aversion and at the same time is the only class of utility functions with constant relative risk aversion, why it is called the CRRA utility function, it is u = { c 1 − η − 1 1 − η η ≥ 0, η ≠ 1 ln ⁡ η = 1 where c is consumption, u the associated utility, η is a constant, positive for risk averse agents. Since additive constant terms in objective functions do not affect optimal decisions, the term –1 in the numerator can be, is, omitted; when the context involves risk, the utility function is viewed as a von Neumann-Morgenstern utility function, the parameter η is the degree of relative risk aversion. The isoelastic utility function is a special case of the hyperbolic absolute risk aversion utility functions, is used in analyses that either include or do not include underlying risk.

There is substantial debate in the economics and finance literature with respect to the empirical value of η. While high values of η Template:Mehra & Prescott; this and only this utility function has the feature of constant relative risk aversion. Mathematically this means that − c ⋅ u ″ / u ′ is a constant η. In theoretical models this has the implication that decision-making is unaffected by scale. For instance, in the standard model of one risk-free asset and one risky asset, under constant relative risk aversion the fraction of wealth optimally placed in the risky asset is independent of the level of initial wealth. Η = 0: this corresponds to risk neutrality, because utility is linear in c. Η = 1: by virtue of l'Hôpital's rule, the limit of u is ln ⁡ c as η goes to 1: lim η → 1 c 1 − η − 1 1 − η = ln ⁡ which justifies the convention of using the limiting value u = ln c when η = 1. Η → ∞: this is the case of infinite risk aversion. Isoelastic function Constant elasticity of substitution Exponential utility Risk aversion Wakker, P. P.

Explaining the characteristics of the power utility family. Health Economics, 17: 1329–1344. Closed form solution of a consumption savings problem with iso-elastic utility

Ancher Nelsen, was an American politician who served as the 34th Lieutenant Governor of the state of Minnesota and an eight-term congressman. He was born near Minnesota, to Danish parents. Nelsen attended elementary school in Brownton and graduated from Brownton High School in 1923. In 1924 he began operation of his 280-acre diversified farm at McLeod County. In 1929 he married Ilo Zimmerman of Brownton, he was a member of the Minnesota Senate, 1935–1949. He was elected the 34th Lieutenant Governor of Minnesota in 1952, he served less than one year. He resigned to become administrator of the Rural Electrification Administration Program, in Washington, D. C. 1953–1956. United States Congress. "Ancher Nelsen". Biographical Directory of the United States Congress. Minnesota Historical Society biography Minnesota Legislators Past and Present A film clip "Longines Chronoscope with Ancher Nelsen" is available at the Internet Archive