Variables aggregation

Good afternoon everyone,

I have a model where 3 firms compete with each other, and competitive input markets. Is it okay if I aggregate labor and capital as follows:

L= L(sector1) + L(sector2) + L(sector3)
K= K(sector1) + K(sector2) + K(sector3)

Since input markets are in perfect competition, wages and the rental price of capital equates in the three sectors.

Thank you.

Best regards

Without proper context, it is impossible to tell.

@jpfeifer basically I have three firms that produce from capital and labor inputs from a standard CES function.

Let say that I have an agriculture sector, industry sector and other industries sector. Each has a different amount of labor and capital inputs. My issue is with aggregation in total labor and total capital for market clearing. I wondered if I could sum the amount of inputs across sectors to have the total amount of labor and capital in the economy.

Wages and rental capital price are the same across sectors. There is no differentiation of labor or capital quality, so labor and capital across sectors are of same function and quality. Their prices are the same.

That means aggregate capital and labor are just the sums of the ones in the respective sectors. So the above is correct. The only complication may be the timing for capital: Timing of capital in two sector economy

@jpfeifer thank you very much.

If I want to code the model in intensive form, usually for a CES function we would have:

Is the last equation right ?

That looks mathematically correct.

1 Like

Good afternoon @jpfeifer ,

I have a hard time finding the steady state equation that determines this l1.

My households supply labor inelastically, so they do not choose endogenously labor. The three firms choose the sectoral split of labor, but I somehow cannot manage to find the SS equation for this split l1, l2 and l3 that are the labor share of the sectors in total labor. Is this split exogenous rather than endogenous ? My first hint would be that the split in endogenous as one sector can become bigger than the others and demand for a higher share of labor than the others that are declining.

Thank you

That split should be endogenous.