OWN-PRICE VS. CROSS PRICE ELASTICITY BASICS
Elasticity = % change in quantity/% change in price
OWN-PRICE ELASTICITY
On demand side: percent change in quantity demanded of labor type i in response to a
1% change in wage rate for labor type i.
On supply side: percent change in quantity of labor supplied of labor type i in response
to a 1% change in wage rate for labor type i.
CROSS-PRICE ELASTICITY
On demand side: % change in quantity of labor demanded of labor type i in response to
a 1% change in wages for labor type j (or some other input into the production process–
could be capital).
Using doctors and nurses as an example, the question is whether they are substitutes
or complements in the production process from the point of view of the firm (i.e., the
demand side):
• If the cross price elasticity of demand is positive (that is, the quantity of nurses
demanded increases when the wages of doctors increase), they are substitutes.
o Logic: Price of doctors has increased and firm shifts toward lower cost
nurses, increasing the demand for nurses (substitution effect); the demand
for both doctors and nurses decreases because the cost of production has
gone up (scale effect), but because they are substitutes in the production
process, the substitution effect dominates so the demand for nurses
increases.
• If the cross price elasticity of demand is negative (that is, the quantity of nurses
demanded decreases when the wages of doctors increase), they are
complements.
o Logic: Price of doctors has increased and firm shifts toward lower cost
nurses, increasing demand for nurses (substitution effect); the demand for
both doctors and nurses decreases because the cost of production has gone
up (scale effect), but because they are complements in the production
process, the scale effect dominates so the demand for nurses decreases.
On the supply side: a % change in quantity of labor supplied of labor type i in response
to a 1% change in wages for labor type j. In this case, we are usually looking at members
of a household the trade off between goods and leisure made on a household basis.
Using wives and husbands as an example, the question is framed in terms of both
the consumption of goods and leisure and possible home production of goods.
• If cross price elasticity of supply is positive (that is, the hours of work
supplied by a wife increases when her husband’s wages increase), they are
complements.
•
o Logic: Wages of husband increases and it is assumed that he supplies
more labor (that substitution effect dominates for him as an
individual). Because the husband and wife are complements in the
home production process/consumption of leisure, the wife also
increases her labor supply.
If cross price elasticity of supply is negative (that is, the hours of work
supplied by a wife decreases when her husband’s wages increase), they are
substitutes.
o Logic: Wages of husband increases and it is assumed that he supplies
more labor (that substitution effect dominates for him as an
individual). Because the husband and wife are substitutes in the home
production process/consumption of leisure, the wife decreases her
labor supply and either produces more at home or consumes more
leisure.