Producer Price Index Manual: Theory and Practice ... - METAC

17. Economic Approach
the numerators is expressed by the fact that the
revenue line through C lies below the parallel
revenue line through D. Now, if the producer’s period
0 output production possibilities set were
block- shaped with vertex at q 0 , then the producer
would not change production patterns in response
to a change in the relative prices of the two commodities
while using the period 0 technology and
inputs. In this case, the hypothetical vector q 0*
would coincide with q 0 , the dashed line through D
would coincide with the dashed line through C,
and the true output price index, P 0 (p 0 ,p 1 ,v 0 ), would
coincide with the ordinary Laspeyres price index.
However, block shaped production possibilities
sets are generally not consistent with producer behavior;
that is, when the price of a commodity increases,
producers generally supply more of it.
Thus in the general case, there will be a gap between
the points C and D. The magnitude of this
gap represents the amount of substitution bias between
the true index and the corresponding
Laspeyres index; that is, the Laspeyres index generally
will be less than the corresponding true output
price index, P 0 (p 0 ,p 1 ,v 0 ).
17.25 Figure 17.1 also can be used to illustrate
the inequality (17.5) for the two-output case. Note
that technical progress or increases in input availability
have caused the period 1 output production
possibilities set S 1 (v 1 ) ≡ {(q 1 ,q 2 ) : [q 1 ,q 2 ,v 1 ] belongs
to S 1 } to be much bigger than the corresponding
period 0 output production possibilities set S 0 (v 0 ) ≡
Figure 17.1. Laspeyres and Paasche Bounds to the Output Price Index
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