Australian Mother of Pearl (MOP) Industry, 1910

Output: MOP shellscarved into buttons, piano keys and boxes, similar to ivory.

Inputs

• Capital: Luggers (i.e., pearl boat), diving suits, pumps,…

• Labor: divers, tenders, pumpers,…

Mechanical & hand pumps

Tenders needed to keep the lifeline taut to help stabilize divers but not so taut to impair them from picking up shells. They were usually experienced divers.

Divers limited their time underwater and ascended in stages because of the bends

The West Australian Pearlers’ Association “was not a united organization,” being composed of “big operators” and “one-boat captains,” who “bid against each other to obtain the best divers” and “undercut” each other as suppliers to MOP markets.

Big operator: Burns, Philps & Co (BP) owned 2 dozen luggers

One-boat captain: Federick Everett (FE)

• Competitive labor market… voluntary exchange

• Competitive output market

Federick Everett’s Short-Run Demand for Labor

Assume: • FE’s Goal: max π• Two inputs, capital and labor• Labor is variable, capital is fixed• Labor and product markets are competitive

Marginal Product of Labor (MPL): the additional output produced by an additional worker, holding the amount of capital constant.

𝑀𝑃 𝐿=∆𝑄∆ 𝐿

Labor (# per lugger)

Mother of Pearl(tons per season)

MPL(tons per worker)

01234567

000479

1010

0

0 4 3 2 10

Diminishing Marginal Returns: must eventually decline as each additional worker has a smaller share of capital to work with.

Assume: laborers are identical, which is not quite true.

Marginal Revenue Product of Labor (MRPL): the additional revenue from employing one additional laborer

𝑀𝑅𝑃 𝐿=𝑀𝑃 𝐿 ∙𝑀𝑅¿ {𝑃𝑖𝑓 𝑜𝑢𝑡𝑝𝑢𝑡𝑚𝑎𝑟𝑘𝑒𝑡 𝑖𝑠𝑐𝑜𝑚𝑝𝑒𝑡𝑖𝑡𝑖𝑣𝑒

𝑀𝑅 𝑖𝑓 𝑛𝑜𝑡

Price of MOP in 1910 ≈ ₤ 150 per ton

0 1 2 3 4 5 6 7 80

50100150200250300350400450500550600650700

FE’s Short-Run Demand for Labor

Labor(# per season)

Wage(₤ per season)

Demand

Suppose the wage was ₤75 per season in 1910

0 1 2 3 4 5 6 7 80

50100150200250300350400450500550600650700

FE’s Short-Run Demand for Labor

Labor(# per season)

Wage(₤ per season)

Demand

Suppose the wage was ₤75 per season in 1910

𝑳𝝅

𝒘=𝟕𝟓

Market Demand = horizontal summation of the labor demanded of individual firms.

Short-run Employment Decision

• A firm that hires labor and sells its output in competitive markets will hire labor on the until it reaches (& is falling)

• This does not imply that “the firm should set W equal to MRPL” A competitive firm takes their W as given or pre-determined, implying that “a competitive firm should hire until MRPL = W”

Input Market Structure

Competitive Monopsony

Competitive

Monopoly

Output Market

Structure

Long-run Employment DecisionCapital Stock, K, and labor, L, are both variable

Isoquant: all combinations of K & L that produce the same Q.

“It was a well-known fact that a fleet (even a small fleet) worked much more steadily and consistently when it has a schooner to service it. The luggers could work further away from port and did not need to return so often.”

Big operators

One-boat captains

Schooners, mech. pumps

manual pumps

Slope = capital labor ratio

Q = 10 tons

Q = 15 tons

Q = 200 tons

Q=10 tons

Q=13 tons

Capital

Labor

A

One-boat captain: (FE)

Properties of Isoquants

• isoquants are downward sloping• isoquants do not intersect• higher isoquants are associated with

higher levels of Q• isoquants are [strictly] convex to the

origin

Q=10 tons

Capital

Labor

A

“There was no such thing as a standard lugger. They were built to multiple designs in shopyards in Fremantle and Broome, Singapore and Sydney, in the back yards of home builders, and next to cattle sheds in the Kimberleys.”

B

Point B—older lugger that takes more crew time to maintain it.

∆𝐾 <0

∆ 𝐿>0

𝑀𝑃𝐾 ∙ ∆𝐾(–)

Loss in Q due to less K

𝑀𝑃 𝐿 ∙ ∆ 𝐿(+)

Gain in Q due to more L

+¿ ¿0

Rearranging,

∆𝐾∆ 𝐿=−

𝑀𝑃 𝐿

𝑀𝑃𝐾

Q=10 tons

Capital

Labor

AB

∆𝐾 <0

∆ 𝐿>0

∆𝐾∆ 𝐿=−

𝑀𝑃𝐿

𝑀𝑃𝐾

slope of isoquant

ratio of MP with the MP of the input on the horizontal axis in the numerator.

Marginal rate of technical substitution (MRTS)

Isoexpenditure Curves:(aka isocost curves)

K

L

𝑤 ∙𝐿+𝑐 ∙𝐾=𝑇𝐸wage price of capital

(user cost)

total expenditures on inputs

Solving for K

𝐾=(𝑇𝐸𝑐 )−(𝑤𝑐 ) ∙𝐿

Vertical intercept

slope =

K

L

ratio of input prices with P of the input on the horizontal axis in the numerator

(𝑇𝐸𝑐 )𝑠𝑙𝑜𝑝𝑒=−(𝑤𝑐 )

all combinations of K & L that cost the same.

Higher ones represent more costly input bundles, e.g., what happens to vertical intercept if TE’ > TE

Q=10 tons

Capital

Labor

R

𝐿𝑅

𝐾𝑅

𝑠𝑙𝑜𝑝𝑒=−𝑤𝑐

𝑠𝑙𝑜𝑝𝑒=−𝑀𝑃 𝐿

𝑀𝑃𝐾

(𝑇𝐸𝑅

𝑐 )

Suppose Federick Everett (FE) wants to collect 10 tons of MOP. He can do it by spending TER on LR and KR.

Would he want to do this?

At R,

𝑀𝑃𝐿

𝑀𝑃𝐾>𝑤𝑐

Rearranging,

𝑀𝑃𝐿

𝑤 >𝑀𝑃𝐾

𝑐

ΔQ per $ spent on L > ΔQ per $

spent on K

Labor is giving you more “bang for the buck”

Better off ΔL>0 & ΔK<0

Q=10 tons

Capital

Labor

R

𝐿𝑅

𝐾𝑅

𝑠𝑙𝑜𝑝𝑒=−𝑤𝑐

𝑠𝑙𝑜𝑝𝑒=−𝑀𝑃 𝐿

𝑀𝑃𝐾

(𝑇𝐸𝑅

𝑐 )

Minimize Costs of Producing Q=10 tons

T

(𝑇𝐸𝑇

𝑐 )

𝐾 𝑇

𝐿𝑇