Saturday, December 09, 2023

What is the price elasticity of demand for au pairs in Massachusetts?

See Cost of Hiring Au Pairs Could Double: Under Biden Administration Proposal New formula for foreign nannies would take into account state and local minimum wages by Michelle Hackman of The WSJ. Excerpts:

"A popular child-care option would be put out of reach for some families under a new Biden administration proposal that could double the cost of hiring an au pair.

The proposed policy change, released this fall by the State Department, would require au pairs—foreigners brought to the country to work as nannies—to be paid using a new formula that takes into account state and local minimum wages, in a bid to ensure that they are paid fairly."

"In 2019, a federal appeals court required that au pairs in Massachusetts be paid the state’s minimum wage. In 2020, the required weekly stipend rose from $195.75 to $528.63, a 170% increase. As a result, by 2022, the number of new au pairs heading to Massachusetts fell by 68%, while the program grew in all other unaffected states by 4% in the same time frame, according to a paper published by the Cato Institute, a libertarian think tank that favors increased immigration and reducing other government regulations."

Price elasticity of demand-It tells us how responsive quantity demanded (Qd)is to a change in price. That is, when price changes, will the change in Qd be large or small? The bigger the change in Qd  the greater will be the price elasticity of demand.

We will use Ed to stand for price elasticity of demand. Here is the definition

Ed = %DQd /%DP

where D (the Greek letter delta) means "change in."

Or  Ed = % change in Qd divided by % change in P

If we use this formula then for au pairs it would be 68/170 = 0.40. That means a 10% increase in the price of au pairs would reduce quantity demanded 40%.

But usually in a principles class we use the mid-point formula for elasticity. See Calculating Price Elasticities Using the Midpoint Formula from Lumen Learning for more information on how it works and why it is used.

But the formula simplifies to (Q2 - Q1)/(Q2 + Q1) times (P2 + P1)/(P2 - P1)

We have Q1, Q2, P1, P2 because their is a first quantity, etc.

For the au pairs we don't have a Q1 & Q2 but we know that quantity went down 68%. So I used Q1 = 100 and Q2 = 32. That is a 68% drop.

Then

(32 - 100)/(32 + 100) times (528 + 195)/(528 - 195) 

= -68/132 times 723/333

= -.515 times 2.017

= -1.12

We usually drop the negative sign since we know the relationship along the demand line is negative.

The midpoint elasticity is much higher than the one found earlier (0.40). An elasticity of 1.12 means that if price goes up 10%, then quantity demanded goes down 11.2%. That is a pretty strong response (although 4% is strong as well).

2 comments:

Anonymous said...

Please check the calculations. 68/170 = .4 ok but I don't think that gives a 40% change in quantity from a 10% change in price. It looks inelastic to me not elastic. Maybe I am missing something.

Cyril Morong said...

No, I am saying that if price goes up 10%, quantity would go down 4%. You are right, that is normally defined as being inelastic (less than 1). But it is still a big drop. Some au pairs would lose out