Answer to Question #276817 in Microeconomics for jeshmita

Question

1.     Consider the following model of a hypothetical market for MSW management services:

 

                                   MPB   =         18.35 − 2Q     

                                   MPC    =          2 + Q

                                   MEC    =         0.25Q,

           where Q is the number of trash containers per household per month.

A.     Quantitatively determine the effect of the resource misallocation due to:  

                                           i.           the presence of the negative externality, and

                                          ii.           the use of a flat fee pricing system in the presence of a negative externality.

B.     Determine the dollar value of a waste-end charge that would restore efficiency to this market. Explain your answer intuitively.  

Answer 1

a).

i)

For equilibrium: Demand = Supply

Therefore, 18.35 − 2Q = 2 + Q

16.35 = 3Q

Therefore, Q= 5.45

Equilibrium quantity is 5.45 at price p

p = 18.35 + 2 (5.45)

p = 29.25

The above equilibrium is when externality is not incorporated nin the supply function.

When we consider the cost of externality the supply function will be

S' = MPC +MEC

S '= 2 + Q + 0.25Q

Demand = S'

18.35 − 2Q = 2+ 1.25Q

Therefore, Q' = 5.0308

When externality is considered, the output reduces to 5.0308.

When negative externality is not considered, resource misallocation of 0.4192 will be provided to the market.

ii).

Flat fee system is a system when a constant fee is applied irrespective of quantity.

Therefore, MPC ie the cost of additional waste management service is zero

MPC = 0

under Equilibrium MPB = MPC

18.35 − 2Q = 0

Q =9.175

Therefore, resource misallocation is 9.175 - 5.45 =3.725

b)

Waste end charge is the cost charged at the time of waste disposal and it is dependent on the quantity of waste generated. To restore efficiency, dollar value of waste minus end charge should be equal to MPC -MEC at a socially optimum level of output. to cover both the private cost of waste plus the cost of externality. Socially optimum level of output is 5.0308. Marginal social cost at this point is 8.2884. Therefore, the fee should be 8.2884 per unit.