生產者理論知識(ppt 55頁)

主要內容
Overview...
Moving on from the optimum...
How it works...
The firm as a “black box”
black box problems
The solution to the first-stage problem ...
Yields minimised cost as a function of exogenous variables...
...optimal input demands as a function of exogenous variables
conditional input demand function
Take the conventional case...
the conditional demand curve
Points to note
What about the non-convex case...?
Nonconvex Z : jumps in z*
The demand correspondence
Let us set this difficulty aside...
Assume the existence of a conditional input demand function
Remember this...?
...yes, it's Shephard's lemma
Now let's differentiate this...
And now for a simple result:
Second derivatives commute...
The economic meaning...
Because the cost function is concave in prices:
The conditional demand curve slopes downwards
For the conditional demand function...
The second -stage problem
(our second response function)
Note what happens below Average Cost...
Supply curve
Production function with local IRTS
For the supply function...
Now put together the two stages of the optimisation process
(our third response function)
input-price fall: substitution effect
input-price fall: total effect
The ordinary demand function...
A Special Case
The short run...
With side condition(s)
The solution now involves the short run cost function
By definition...
Average cost in the short and the long run
Marginal cost in the short and the long run
The supply curve is steeper in the short run
So too is the conditional demand curve
You must remember this...
And they all hook together like this

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