LECTURE 14
Today is Thursday, October 7, 2010.
The price of gold is $1,335 per troy
ounce.
SUN DEVIL MINING COMPANY
Shaft # 212
THE PRODUCTION FUNCTION, CONTINUED
AGAIN, OUR GOAL IS TO MAXIMIZE PROFIT EACH WEEK THAT WE
OPERATE THE MINE.
THIS IS THE ONLY GOAL THAT WE HAVE, AND
THE ONLY REASON THAT WE DECIDED TO OPERATE OUR ARIZONA
GOLD MINE.
We create our production function empirically.
We hire doses of labor and
capital (N&K) and set them to work mining gold.
One dose of N&K is one
worker, plus the optimum physical amount of capital the worker needs to
efficiently mine gold from our mine shaft, working one four-hour shift per
week.
First, we apply one dose of K&N to our fixed mine shaft each week, to
determine the output of gold produced.
The result is .375 ounces of gold per
week (3/8 of one ounce).
Mathematically, to produce one ounce of gold per
week should take 2 2/3 doses of K&N per week.
When we apply 2 2/3 doses
of K&N per week to our mine shaft, we produce one ounce of gold per week.
We then tell our crew, "Apply increasing doses of K&N to our mine shaft each
week until production is running at 2 ounces per week; then 3 ounces per
week; then 4 ounces per week, and so on.
Keep increasing weekly output by
increasing our variable inputs, K&N, until we produce 14 ounces of gold per
week.
And be sure to record your data."
The first two columns of Table 13-1, below, (which was first discussed in
Lecture 13) record our production data, and, empirically, show our production
function.
The first two columns, (1) "Output in ounces per week", and the (2) "Labor
and capital required to produce those levels of output", again, are empirical
propositions.
We simply apply varying amounts of K&N to our fixed mine
shaft until we observe the desired levels of output.
1
1
There are no restrictions.
We could have asked our crews to produce and record half-ounces, or quarter-
ounces of gold produced each week, and recorded the necessary doses of K&N required.
For simplicity we