Answer to Question #162095 in Microeconomics for adnand

Question

 

Farmer Jones and Farmer Smith graze their cattle in the same field. If there are 50 cows grazing in the field, each cow produces $50,000 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 70 cows in the field, each produces $85000 of milk; with 100 cows, each produces $1,10,000 of milk. Cows cost $1500 each.

 

a).        Assume that Farmer Jones and Farmer Smith can each purchase either 25 or 50 cows, but that neither knows how many the other is buying when she makes her purchase. Calculate the pay-offs of each outcome.

b).       Fill in the pay-offs in a 2 × 2 decision box.

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

d).        There used to be more common grazing land than there is today. Why? 

Answer 1

Answer:

a.

Case 1:-

Farmer Jones buys 25 cows 

Farmer Smith buys 25 cows.

Total cows are 25+25= 50

Therefore, Farmer Jones generated revenue = $50,000x25 = $1,250,000

And, Farmer Smith  generated revenue of $50,000x25= $1,250,000

When the price of cows is substracted we get,

Farmer Jones profit = $1,250,000 - (1500x25) = $1,212,500

Farmer Smith = $1,250,000 - (1500x25) = $1,212,500

Case 2:-

Farmer Smith buys 25 cows and Farmer Jones buys 50 cows.

The total number of cows will be 25+50= 75

Therefore, Farmer Jones generated revenue of $85,000x50 = $4,250,000

And, Farmer Smith generated revenue = $85000x25 = $2,125,000

When you substract the price of the cows, we get,

Farmer Jones profit is $4,250,000 - $1500x50 = $4,175,000

Farmer Smith profit is $2,125,000 - $1500x25 = $2,087,500

Case 3:-

Farmer Smith buys 50 cows and farmer Jones purchases 25 cows

The total number of cows will be 50+25 = 75

Therefore, Farmer Jones generated revenue of  $85,000x25 = $2,125,000

And, Farmer Smith generated revenue = $85000x50 = $4,250,000

When you substract the price of the cows, we get,

Farmer Jones profit is $2,125,000 - $1500x25 = $2,087,500

Farmer Smith profit is $4,250,000 - $1500x50 = $4,175,000

Case 4:-

Farmer Jones buys 50 cows 

Farmer Smith buys 50 cows.

The total number of cows on field will be 50+50= 100

Therefore, farmer Jones generated revenue of $110,000x50

And, farmer Smith generated revenue of= $110,000x50

When you substract the price of the cows, we get,

Farmer Jones profit = $5,500,000 - 150050 = $5,425,000

Farmer Smith profit = $5,500,000 - 150050 = $5,425,000

b.

c. From the calculations done in question (a), the highest profit will be achieved when both farmers have 50 cows each. In this case each farmer will make a total profit of $5,425,000.

d.

The grazing land was traditionally more common unlike today due to the explosion of population and urbanisation. A large proportion of land has been used up for settlement which used to be grazing land. This is the reason why grazing is no more practiced widely.