Sluggish factors

Definition

Sluggish factors: factors that cannot move freely across uses (sectors)

For sluggish factors, price differs between its usages (since thee factor cannot move freely across usages)

So we can use a CET function to allocate it to different usages given the relative price.

For example: consider capital as the sluggish factor here, with transformation elasticity as ETRAE:

Supply allocation

From the CET function (mathematically equivalent with the solutions of producers' behavior from CES function), we have:

The derived allocation of endowments is:

Where:

• QOES: quantity of the sluggish variable (es) used by sector p
• QO: quantity of the sluggish variable
• REVSHR: cost share of sector-specific use the sluggish variable
• PMES: price of the sluggish variable by sector
• ETRAE: transformation elasticity (can be indexed with es)

Its linearized form is:
EQUATION ENDW_SUPPLY
# This equation distributes the sluggish endowments across sectors(HS4) #
(all,i,ENDWS_COMM)(all,j,PROD_COMM)
qoes(i,j) = qo(i) - endwslack(i) + ETRAE(i) * [pm(i) - pmes(i,j)] ;

Market clear condition

Then the market clear condition for sluggish input is:

Level form

For each sector, the allocated sluggish input to that sector = the conditional demand of sluggish input in that sector

Linearized form

And the price index of the sluggish factor (calculated from the price of the sluggish factor by sectors) is:

Note

• Here mobility refers to the ability to move across uses (not between regions)

Example

• land in livestock vs. crops
• specialized labor
• specialized machinery and equipment