2.) (30 points) Consider a beekeeper that is deciding how much honey to produce.

Question

2.) (30 points) Consider a beekeeper that is deciding how much honey to produce. The beekeeper gains a benefit from producing honey, represented by the marginal benefit function and which is given by: MB = 300-6Q where Q is barrels of honey. In addition, she has a marginal cost function, which reflects her cost of producing honey; this is given by: MC = 40 + 4Q The beekeeper's total profit function is given by: = 2600-50° pollinate a neighboring apple orchard. Thus, in addition to the private benefit accruing to the beekeeper herself, there is also a marginal external benefit to the apple orchard, which is given by: MEB = 100-2Q And a total external benefit to the apple orchard given by: TEB = 100Q-Q2

Explanation / Answer

Answer:

a.  social marginal benefit (SMB) = MB + MEB

SMB = 300 - 6Q +  100 - 2Q

= 400 - 8Q.

In case of self interest

MC = MB

40 + 4Q = 300 - 6Q

So, Q = 26

In case of social optimal

MC = SMB

40 + 4Q =  = 400 - 8Q.

S0, Q=30

b. Total External benefit for q =30 and q = 26

TEB= 100Q - Q^2

= 100*30 - 30^2

= $2100

For Q=26

TEB= 100Q - Q^2

= 100*26 - 26^2

= $1924

So additional benefit $2100 - 1924

= 176 is the maximum amount orchad owner willing to pay

Additional cost to beekeeper for producing extra 4 units

= 56

c. No as it is less then what beekeeper will accept

d.The associated efficiency loss = 5*(300 - 6*5 -(40 + 4*5))

= 210

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