Suponha que o tempo é continuo e que os preços p_t se ajustam de maneira proporcional ao excesso de demanda Z_t com constante de proporcionalidade k. Isto é, p_t = kzt. Assumindo que as ofertas e demandas são lineares: q^s_t = c + dp_t, q^d_t = a - bp_t, respectivamente, julgue a seguinte afirmativa, se as constantes k,a,b,c e d são estritamente positivas:

Item 2 - O estado estacionário !$ \overline p !$ é sempre positivo;

Something new to cheer

WHEN Charles Miller, son of an English railway engineer posted to Brazil, returned to São Paulo from a British boarding school in 1894, he brought back a football—and popularised a game that would help define Brazilian identity. Miller’s other sporting import, rugby, had less appeal. It was played at a few posh boarding schools and almost nowhere else. But now rugby is beginning to find a mass audience.

Asked which sport would grow most, more Brazilians picked rugby than any other in a survey conducted in 2011 by Deloitte, a consultancy. Since then its popularity has shot up as if propelled by a well-taken conversion kick. Some 60,000 Brazilians are thought to play rugby, far fewer than the 30m who play football or the 5m-10m who take part in volleyball—but up from 10,000 five years ago. The national team, the Tupis, named after a family of indigenous peoples, draw audiences of 10,000 to stadiums and 7m to television screens. (The league is still amateur.) Highlights from European games pop up on the São Paulo metro’s in-train television.

Rugger’s return to the Olympics at the Rio de Janeiro games last August, after a 92-year hiatus, spurred interest. The sport’s good governance helps win fans in a country beset by corruption scandals. The Brazilian Rugby Confederation (CBRu), which replaced an amateurish association in 2010, is run like a business. Its chief executive, Agustin Danza, holds an MBA and answers to a 12-member board. In November last year a non-profit group gave the CBRu Brazil’s first sport-governance trophy. The volleyball federation has sent five scouts to learn its management tricks.

Sponsors have taken note. The Tupis now have two dozen, including Unilever, a consumergoods giant, and Bradesco, a Brazilian bank. The CBRu’s budget has swelled from 1.3m reais in 2011 to 18m reais ($6m). Mr Danza has used the money to lure coaches from rugby powerhouses like New Zealand and Australia. His objective is to qualify for the World Cup in 2023.

It will take plenty of training. Brazilian women came a respectable ninth in the Olympic seven-a-side tournament, but the men came last. They are ranked 36th in the world.

Argentina, Brazil’s rival in all things sporting and otherwise, is ninth. Mr Danza (himself Argentina ) is banking on support, and cash, from the sport’s global governing body. He is hoping that World Rugby will soon name Brazil as one of its priority markets. With more exposure and money, the amateur league could turn professional.

The CBRu is trying broaden the sport’s appeal—and talent pool—beyond the upper class. “In my day the team was all pale posh guys,” recalls Jean-Marc Etlin, a financier and former Brazil forward. Thanks to programmes that promote the sport in state schools, his son’s team-mates on the under-19s national side now include players from poor backgrounds.

The biggest obstacle to rugby’s popularity remains Brazilians’ obsession with football. “Every other sport is peripheral,” sighs Mr Etlin. Mr Danza thinks football’s woes, including sleaze in the federation and the national team’s underwhelming performance (by Brazilian standards), give rugby an opening: “When the footballers disappoint, Brazilians start looking for someone else to cheer.”