Farmer Jones and Farmer Smith graze their cattle on the same field Answer

Farmer Jones and Farmer Smith graze their cattle on the same field. If there are 20 cows grazing in the field, each cow produces $4,000 of milk over its lifetime. If there are more cows in the field, then each cow can eat less grass, and its milk production falls. With 30 cows on the field, each produces $3,000 of milk; with 40 cows, each produces $2,000 of milk. Cows cost $1,000 apiece.
a. Assume that Farmer Jones and Farmer Smith can each purchase either 10 or 20 cows, but that neither knows how many the other is buying when she makes her purchase. Calculate the payoffs of each outcome.

Each
farmer has 2 strategies-buys 10 or buy 20, so that we have 4 possibilities

 Both buy 10. Total profits=10*( 4000 – 1000)=
30000. Each farmer gets 30000 as profit

Both
buy 20. Total profits= 20*(2000 – 1000)= 20000. Each farmer gets 20000 as
profit

One buys 10 and other
buys 20 then total profits=10*(3000-1000) =20000.and 20*(3000-1000) = 40000
respectively.

                                                                jones

Smith

b. What is the likely outcome of this game? What would be the
best outcome? Explain.

If
smith buys 10 cows then jones will buy 20

 If smith buys 20 cows then jones will buy 20

Buying
20 cows is the dominant strategy for Jones

If
Jones buys 10 cows then Smith will buy 20

 If Jones buys 20 cows then Smith will buy 20

Buying
20 cows is the dominant strategy for Smith

The
Nash equilibrium is that both buy 20 cows

The socially
optimal/best outcome is with 10 cows each as they both earn more than 20000

c. There
used to be more common fields than there are today. Why?

Common fields lead to overgrazing, that results from lack of
property rights. This is referred to as the tragedy of the commons -a situation where a good is used
collectively and gets overused, so that in the long run the benefit to each
user declines. It was
first explained in an article in Science in 1968 by Garrett Hardin. The users
are guided by self interest which does not factor in the effect on the group as
a whole. Take a green are where cows love to graze. If the land was public
property, all cows would be let loose by the cattle owners in the self interest
of feeding their cows well. They do not realize that if all cows graze it leads
to overgrazing and the grass quality suffers leading to lower milk production
that lowers profits for all  In the end
all farmers end up with lower profits.

To counter this
problem fields are privatized where grazing rights are well defined in the
interest of all farmers involved.

Looking for a Similar Assignment? Order now and Get 10% Discount! Use Coupon Code "Newclient"