No Class on Monday 3/24; Homework due that night

UC

UB

Wage

Probability of Death

pZ

pY

PB

wA – wNA

wNA

wA

Determining the Market Compensating Differential

The supply curve slopes up because as the wage gap between the Arctic voyages and non-Arctic ones increases, more and more whalers are willing to sign on for the Arctic voyages. The demand curve slopes down because …

The market compensation differential equates supply and demand, and gives the premium required to attract the last whaler to sign on to the Arctic voyage.

Number of Arctic Seamen (AS)

S

P

D

wA - wNA

Market for Arctic Unskilled Seamen

(wA – wNA)e

ASe

Empirical Tests of Compensating Wage Differentials

Detailed data must be available

1. Individual Characteristics: age education, union status, etc.

2. Job Characteristics: attractive and disagreeable aspects of jobs—it is often difficult to measure characteristics such as the riskiness of a job.

Theory must be applicable (negative results where there is little possibility of getting positive ones aren’t very interesting or publishable.)

1. Workers have good information—on the characteristics of jobs and the alternatives.

2. Workers have mobility—they have the opportunity to choose other alternatives

Press gangs (impressment)

. – For our estimates of compensating wage

differentials to be valid…..• workers maximize utility.• workers know job attributes and competing job offers.• workers are mobile.• Held other factors constant…

Blubber heads… Green…

Contracts using specified the whaling ground (Arctic versus non-Arctic)

New Bedford newspapers reported on the average catch and length of voyage of all vessels returning to New Bedford

Losses of vessels was big news

Full Information:

Worker Mobility

Press gangs (impressment)

iiiiiii uArcticIndianAtlanticthVoyageLengwagewage 543210 )var(

10723 labor contracts of unskilled seamen over the years 1840-1858

Monthly wage (mean = $8)

Equals one if (hunting ground) destination is

Calculated using ships returning in year t-1 from the destination whaling ground

Wage premium holding the financial risk and voyage length constant.

= 5.43

In the mid-19th century, whaling vessels from New Bedford, Massachusetts sailed all over the world in search of sperm and bowhead whales. While sperm whales provided higher quality oil, only bowheads provided whalebone (a flexible bonelike screen) which was an important input into a variety of products ranging from corsets to umbrellas. The two types of whales were found in different areas of the World's oceans: bowheads were found primarily in the Arctic while sperm whales were found in the Atlantic, Indian and Pacific Oceans. Whaling was a risky occupation, particularly for sailors working in the Arctic. Over the years 1816 to 1905, 3.5 percent of the Arctic fleet was lost each year along with 2.5 percent of the non-Arctic fleet. Economic historians have estimated that the annual earnings of unskilled sailors on whaling vessels was roughly $2,870 (2008 $) for non-Arctic voyages and $3,125 for Arctic voyages, holding the length of voyages and financial risk of voyages constant.

What is an estimate of the value that unskilled sailors placed on a statistical life?

𝑤 𝐴=$ 3125

𝑤𝑁𝐴=$2870

𝑟 𝐴=3.5 per 100

𝑟𝑁𝐴=2.5 per 100

𝑤 𝐴=$ 3125

𝑤𝑁𝐴=$ 2870

𝑟 𝐴=3.5 per 100

𝑟𝑁𝐴=2.5 per 100

Suppose the Rotch Whaling Company (RWC) has a fleet of 40 whaling ships and 1000 sailors that will be sent either to the non-arctic in search of sperm whales or the arctic in search of bowheads.

DestinationExpected Number

of DeathsTotal Wage Bill

Arctic 35 $3,125,000

Non-Arctic 25 $2,870,000

Difference 10 $255,000

Rotch Whaling Company

Widows, Orphans & Survivors

January 1, 1845

25,500Twenty-Five Thousand and Five

Hundred

William Rotch Jr. One arctic death

Value of a Statistical Life𝑉𝑆𝐿=

𝑤 𝐴−𝑤𝑁 𝐴

𝑟 𝐴∗   −𝑟𝑁 𝐴

∗ risk per sailor

¿$ 3125 − $ 28700.035 −0.0 25

“What value of statistical life does EPA use?”

“EPA recommends that the central estimate of $7.4 million ($2006)…be used in all benefits analyses that seek to quantify mortality risk reduction benefits regardless of the age, income, or other population characteristics of the affected population.”

http://yosemite.epa.gov/ee/epa/eed.nsf/pages/MortalityRiskValuation.html#whatisvsl

Value of a Statistical Life𝑉𝑆𝐿=

𝑤 𝐴−𝑤𝑁 𝐴

𝑟 𝐴∗  −𝑟𝑁 𝐴

∗¿

$ 3125 − $ 28700.035 −0.0 25

19th Century America

21th Century America

Life was cheap in the 19th Century

Suppose the government of Massachusetts was considering requiring whaling companies to adopt safety measures that would reduce the fatality rate of Arctic to the levels of non-Arctic ones. Under what assumptions would this increase efficiency and under what assumptions would it erode efficiency. Illustrate and explain your answer.

U0Wage

Probability of Death

wA

2.5 3.5

p0 = 0

wNA

U1

U0

Wage

Probability of Death

wA

2.5 3.5

p0 = 0

wNA

U1

AB

wAReg

No Reg

= R