Normally the analysis of household decisions focuses on the consumption decisions, but equally important is the function of households in supplying labor and and other resource services. The analysis will be first for a single household and the extension to the entire market is merely a matter of aggregating over all households in the market.

Let the preferences of a household about supplying various types of labor and other services be represented by a Disutility function D(L,K) where L is the level of the resource under consideration and K is the vector of the levels of use of all other resource services. The objective of the household is to minimize the disutility the members experience in achieving a certain level of money income. When a household minimizes D(L,K) subject to the constraint r_LL + R_K·K = M, they supply resourse services such that

∂D/∂L = μr_L
 

The Lagrangian multiplier μ is such that dD/dM=μ. It is the marginal disutility of earning another dollar of income. (The first order conditions for the other resources are not relevant here.)

For an increase in resource use of dL the increase in disutility is given by:

dD = (∂D/∂L)dL = μr_LdL
 

But dD=(dD/dM)dM = μdM so the amount of money income equivalent to the increase in disutility experienced from an increase in the amount of resource service supplied is given by:

dD = μr_LdL = μdM
and thus
dM = r_LdL
 

The increase in income ΔM equivalent to the increase in disutility due to an increase in resource service supply from L to L+ΔL is given by the integral of the above relation over the range of L from L to L+ΔL; i.e.,

ΔM = ∫_L^L+ΔLr_LdL.
 

The supply function for a resource service for a household is the relationship between the quantity L supplied as a function of its price with all other factors held fixed; i.e,,

L = g(p_L)
and the inverse supply function is
r_L = g^-1(L)
 

Thus the previous integral expression is just the area under the supply curve with resurce servic price being expressed as a functio of the quantity of the resource service supplied.

The sum of the equivalent money incomes for all consumers as a result of the sum of their increases in resource supply is then the area under the aggregate market supply curve.