(fLK (fK) - fLfKK) /fK2 dK + (fLLfK - fLfKL)/fK2 dL
Then divide through by dL, using the fact that dK/dL = -fL/fK along an isoquant, and
(f2LfKK + f2KfLL-2 fKfLfLK ) /(fK)3
Observe that the above condition is negative if th
The power of steam was initially used by Richard Trevithick for running carriages on the roads.
Later in 1804, he became the first person to utilize steam power to run locomotives on the rail
track. Later, George Stephenson, an engineer in the mining indu
The atmospheric engine worked on the principle of creating a partial vacuum by condensing
steam under a piston, within a cylinder. It was largely used for pumping out water from the
mines. Later on, James Watt improvised on the engine, thus, making it tec
The water frame was a spinning frame that worked with the use of water. It provided more
power to the spinning frame than manually operated ones. Hence, not only did it reduce the
amount of labor required, but it also increased the spindle count, and prov
The invention of the reaper machine made it easy for farmers to reap their crop. The reaper was
able to do the work of five men alone, thus, making the process cheaper and less laborintensive. Thus, manual work was eventually replaced by machines.
The invention of the power loom was a great breakthrough in the weaving industry. It was a
mechanized loom that used a rotating shaft for power transmission. The power loom used water
as the source of power instead of steam, thus, making the weaving proce
3. Appendix: Separable Utility and the Grouping of Goods. One shortcoming of general utility
theory is that it says relatively little about demand relationships between goods. Other than the
result that net substitution effects are symmetric, virtually an
But this desire may have to wait to be satisfied by a second expedition with a dedicated
drill ship, the Joides Resolution. The JR can bore hundreds of metres into the seabed,
increasing the chances of capturing an unabridged view of the past. A firm book
MeBo's drill cores are now back in Bremen. A week ago, the cylindrical liners containing
some 60m of ocean-floor material were being X-rayed at a local hospital to precisely
determine their internal structure. And in the past few days, the task began of s
The paper said this investigation had centred on one former CIA operative but there
was not enough evidence to arrest him. He now lives in another Asian country.
In 2012, an official at China's security ministry was arrested on suspicion of spying for
However, others were somewhat worried that overtly trying to force the issue might be
the wrong approach, given the temperamental nature of the current US president.
"I think pressure may well be the wrong tactic right now," said Elliot Diringer, a Clinto
The new White House, in case you missed it, takes a very different view on climate
change to a majority of countries in the world.
The Donald Trump-era perspective is that climate change is essentially an exaggerated
threat, that coal, oil and gas are tre
In my experience, "Japanese corporate culture" is often used as a scapegoat for a
whole raft of business problems. As a consultant, I often hear CEOs in Japan,
Japanese and non-Japanese, whether running Japanese companies or nonJapanese companies, blame s
1. The smarter way: Some teams get help from technologies like
telescopic conveyors, which can stretch inside the containers for faster
and easier unloading. Man-lifters also make it easy for the teams to
reach shipments at the top of tall containers. As
Arsenal need the spending power of a billionaire such as Alisher Usmanov in
order to move to the next level, says Gunners legend Ian Wright.
Uzbek-born Russian Usmanov has made a 1bn bid to take full control of the Gunners,
but majority shareholder Stan K
His travel ban, in the name of protecting the US against terrorism, also specifically
targeted all Muslim-majority countries, a move that was derided by Muslims
everywhere, including in the Middle East.
That ban was the work of Miller, a 31-year-old aide
Despite a growing shift towards protectionism in Europe and America, public
policies in Asian countries continue to embrace greater globalization.
Greater global connectedness often goes together with higher levels of
innovation and economic productivity,
Still, another source says Obama would "take his call and try to help" if Trump were in a
jam and needed advice.
However, the story says the bulk of the Obamas' time is spent focusing on the Obama
Presidential Center, to break ground in Chicago in 2018, a
Whatever we call it, this is Chinese President Xi Jinping's pet project, launched in
2013. Xi will host a BRI summit in Beijing on May 14 and 15 amid great fanfare
about trade and infrastructure achievements and prospects. But what is the BRI,
and is it a
In his inaugural address on May 10, Moon said, "I will do whatever I can for
peace on the Korean Peninsula" and added that he is prepared to visit Pyongyang
"under the right circumstances." He backed up his words by nominating Suh
Hoon, a key player behin
Usmanov said in April that Kroenke must "bear huge responsibility" for the club's
failures on the pitch.
The Gunners' London rivals Chelsea won the Premier League this season - the fifth
time they have done so under the ownership of billionaire Roman Abra
The smarter way: Some teams get help from technologies like The launch
drew international condemnation and forced Moon to take a more resolute tone.
"I promised to do all I can to settle peace on the Korean Peninsula," he said.
"Despite my promise, I deep
"Contouring" - using contrasting shades to create a more defined, threedimensional look - is rapidly catching on across the nation, particularly among
Masako Miyamoto, a 21-year-old student in Tokyo, is thrilled with it. "I'll never
The Ministry of Health, Labor and Welfare proposes banning smoking in all
eateries, except for small bars and similar establishments under 30 sq. meters, a
move geared in part toward the 2020 Tokyo Olympics. Since the World Health
Organization and Interna
For the three months ended March 31, the Fort Myers, Florida-based cancer genetic testing firm
recorded $61.7 million in total revenues, slightly above the consensus Wall Street estimate of $61.4
million, and up from $59.7 million in the year-ago period.
It was the summer of 1986 when 5-year-old Lisa showed up outside Katherine Deckers
mobile home at a trailer park in Scotts Valley, Calif. While her father worked as a
handyman, Lisa played for hours with Deckers young grandson, yearning for everything
As with all things Trump, the figure is likely an exaggeration, because it reportedly
includes major offers made during the Obama administration. But it is a huge deal
nonetheless, said to include a THAAD missile defense system, armored personnel
Standing on the steep rocky shores of Lake Tanganyika at sunset, looking out at fishermen
heading out for their nightly lamp-boat fishing trips, it's easy to imagine this
immense 32,900km2 body of water as serene and unchanging.
Located in the western bra
But the far-flung getaway has recently caught the eye of craft beer enthusiasts too,
thanks to the work of the island's first craft brewery.
Said to be the first women-run beer operation in the Philippines, Palaweo Brewery -located in Puerto Princesa, the
A Strategy for
Designing a House
Minimize plumbing runs
A Strategy for
Designing a House
Working on the computer
Playing with pets