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Unformatted text preview: ) a (tx2 )b = tabout technology.)bFirstt a+bwilltx1 , tx2 ); assume0that technologies are
A( x1 ) a ( x2 = we f ( generally t >
monotonic: if you increase the amount of at least one of the inputs, it
should be possible to produce at least as much output as you were proSo
ducing originally. This is sometimes referred to as the property of free
If the production function has the form f (x1 , x2 ) = Axa xb , then we sayif the ﬁrm can costlessly dispose of any inputs, having extra
• if Cobb-Douglas production function. This 2 just likearound can’t hurt it.
a + b < 1 returns to scale are decreasing; inputs the
that it is a
functional form for Cobb-Douglas preferences that we studied earlier. The will often assume that the technology is convex. This means
• magnitude 1 the utility function was not important, so we set
numericalif a + b = of returns to scale are constant; that if you have two ways to produce y units of output, (x1 , x2 ) and (z1 , z2 ),
A = 1 and usually set a + b = 1. But the magnitude of the then their weighted average will produce at least y units of output.
• if a + b > 1 returns allow these parameters to take One argument for convex technologies goes as follows. Suppose that you
function does matter so we have toto scale are increasing; arbitrary
values. The parameter A measures, roughly speaking, the scalehave a way to produce 1 unit of output using a1 units of factor 1 and a2
of producThe Cobb-Douglas isoquants used the same nice, well-behaved shape that the Cobb-Douglas indiffertion: how much output we would get if wehave one unit of each input.
The parameters a have; measurethe case amount of output responds to Cobb-Douglas production function is about the
ence curves and b as in how the of utility functions, the simplest example of well-behaved isoquants. 7...
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- Summer '13