A bee keeper raises bees next to a strawberry farm. The bee keeper sells honey a
ID: 1211523 • Letter: A
Question
A bee keeper raises bees next to a strawberry farm. The bee keeper sells honey at pB=¥100 a liter and has cost function cB=B^2 , where B is the number of liters of honey. The strawberry farm can sell crates of strawberries for pR=¥200 a crate and has cost function: cR=2R^2 (1/2)*B^2 .
a. If the strawberry farmer and bee keeper make separate production decisions, what quantity of their products will each choose to produce?
b. What is the Pareto efficient quantity of each product?
c. If the government decides to use a perunit subsidy to reach the Pareto efficient outcome, who should they subsidize and how much should the subsidy be? d. Now imagine that there is no government subsidy but the two businesses negotiate with each other to try and reach the Pareto efficient quantity. What is the minimum amount of money one firm would have to provide the other to make the other firm produce the efficient quantity? Would the paying firm be willing to pay that much money?
Explanation / Answer
Ans- a.-The bee keeper sells honey at pB=¥100 a liter and has cost function cB=B^2 , where B is the number of liters of honey.
When profit is maximum then,MR=MC
TR=100B MR=100.
TC=B2 MC=2B.
When profit is maximum,then
MR=MC
100=2B
B=50. This is the quantity what bee keeper will produce.
On the otherhand, The strawberry farm can sell crates of strawberries for pR=¥200 a crate and has cost function: cR=2R^2 (1/2)*B^2 .
MR=200. MC=4R
When profit is maximum then,MR=MC
200=4R R=50. The strawberry farmer will choose to produce 50 strawberries.
As strawberry farmer produces honey also,then,
TR=100B MR=100. TC=2R2-1/2B2 MC=B.
When profit is maximised then,MR=MC 100=B This honey produced for strawberry farmer.
b. Pareto efficiency is said to occur when it is impossible to make one party better off without making someone worse off.Pareto efficiency will occur on a production possibility frontier. When an economy is operating on a simple production possibility frontier, it is not possible to increase output of goods without reducing output of services.
Pareto Optimality is used heavily in political economics as a means to distribute resources in a more efficient manner to increase overall social utility. As it is the stated goal to promote the general interest of the public, Pareto Improvements are desirable to government officials seeking to act in the name of the electorate. Another practical uses include managers seeking to make decisions for investors, the company and consumers that serves everyone’s interests. Pareto Optimality has even been used in the engineering field in recent years.
1-when bee keeper has all honey and strawberry farmer has all strawberry.
2-When strawberry farmer has all honey and all strawberry.
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