The price per gallon of water is $1.5 in 2013 and is expected

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 profits. 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 indifferent 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 information provided
in question #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 consumption 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 cutting 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 optimal cutting strategy? Your
goal is to maximize the PDV of profits.
b. Ecotourists from Berkeley are
willing to pay you $X dollars each year to look at your tree. Write out an
equation for X so that you are indifferent between: 1) having the ecotourists
visit and 2) harvesting the tree and sacrificing the ecotourism payment.

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