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Ag Ec/ERRE 429
In-Class Exercise
Week 4
Private Property and Open Access
This week’s exercise explores how private property rights affect resource use. You will
need to use Solver.
1) Suppose that you own a plot of land that is good for grazing cattle. The total pounds
of beef that can be produced on this land depends on the number of cattle that are grazed
there. Let B equal the pounds of beef produced each year. Let H equal the number of
head of cattle stocked. The production function for beef is given by
B = 400*H - 5*H2
It costs $80 to buy one head and put it onto the pasture. You can sell your beef for $0.50
per pound.
Create a spreadsheet to determine the stocking level that maximizes the economic rents
generated by your land. Each row of the spreadsheet should have a different level of
stocking, from 0 to 60 by 1 (i.e. there will be 61 rows of numbers in the spreadsheet).
Columns in the spreadsheet should be
# cattle stocked
lbs of beef produced
Marginal Physical Product (how much extra beef you will produce if you
add one more head to the land)
Marginal Revenue Produce (how much extra revenue you will receive if
you add one more head to the land = MPP*P)
revenues from beef sales
total costs of stocking
economic rent generated
a) What is the level of stocking that maximizes economic rents? This is the economically
efficient level of stocking. How much rent is generated by the pasture?
b) At that stocking level, what is the relationship between Marginal Revenue Product and
the cost of adding one more cattle?
2) Now suppose that the pasture is open to any farmer who wants to graze cattle. You
must decide how many of your cattle to put on the pasture, given the total number of
cattle stocked by other farmers.
Create a new spreadsheet. Assume that all other farmers together stock 21 cows, and that
you stock 3 cows (put these two numbers into separate cells - we will vary them later).
For these specific stocking levels, calculate the
- total number of cattle stocked
- the total pounds of beef produced
- the average production of beef per cow (APP)
- the average revenues received per cow (ARP)
- the average profit per cow
- the total amount of rents generated by the pasture, to all farmers
Check that this matches up with what you got for question 1.
Assuming that all cows grow equally well, each cow will generate the average level of
profit. For your cows only, calculate
- your revenues
- your costs
- your profits (your share of the rents generated)
a) What level of rents do you receive if you stock 3 cows, and everyone else stocks 21?
What is the total amount of rents generated by the land to all farmers?
Now, use solver to determine how many cows you should stock to maximize your profits,
given that all other farmers together stock 21.
b) Compare this answer to the answer in part a. Do you stock more or less cattle than is
economically efficient? Are your rents higher or lower than in part a? Are total rents
higher or lower than in part a?
c) Now suppose other farmers are free to adjust their stocking levels. Without solving
anything, do you expect them to increase their stocking level, decrease, or keep it the
same? Why?
d) Where would this stop? What is the equilibrium stocking level, if each farmers is
allowed to stock as many cattle as they want? What are the total rents generated at the
equilibrium? You should not have to do any new calculations to answer this question
(hint – use the worksheet you constructed for question 1).
e) Why did the first fundamental theorem of welfare economics break down (which
assumption was violated)?