1.
You are a farmer and you must choose between growing strawberries or corn. Your goal is
to maximize the present discounted value of your proFts. The interest rate is 7%. The
world exists in the year 2013 and 2014 and then ends. Here are some relevant data:
Strawberries
Corn
Price per unit in 2013 and
in 2014
8
5
Gallons of water needed
for growing each unit of
crop
4
1
Labor needed to pick each
unit of crop
1
1.1
1.
The price per gallon of water is $1.5 in 2013 and is expected to be $p in the year 2014
and the market price of labor is $.5 in 2013 and 2014.
Solve for p so that the farmer is just indi±erent between growing only Strawberries
versus only Corn.
2.
Suppose that the farmer has 100 acres of land and can only grow 500 units of either
crop per acre. If the price of water is expected to be $1.8 in 2014, how much water
does this farmer consume?
3.
Building on the informa²on provided in ques²on #2, now suppose the farmer can
purchase a water savings device for $3000 in 2013. This device reduces the amount of
water the farmer uses to .4 gallons per strawberry and .1 gallons per unit of corn. Does
this farmer buy this device? If “yes”, how much does water consump²on change by?
4.
You have enough land to grow one tree. The height of your tree (in feet) equals
100*(square root of age of the tree) ! The cost of cu³ng down the tree is $0. The
interest rate is 4%, and the price of one foot of the tree is $16.
a. What is your op²mal cu³ng strategy? Your goal is to maximize the PDV of proFts.
b. Ecotourists from Berkeley are willing to pay you $X dollars each year to look at your tree.
Write out an equa²on for X so that you are indi±erent between: 1) having the ecotourists
visit and 2) harves²ng the tree and sacriFcing the ecotourism payment.