Answer to Question #276877 in Microeconomics for wilz

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

Hypothetical market for MSW management service:

Demand (D) : MPB = 18.35 – 2Q

Supply ( S ) : MPC = 2 + Q

DEMAND = SUPPLY for equilibrium

18.35 – 2 Q = 2 + Q

16.35 = 3 Q

3 Q = 16.35

Q = 5.45

Equilibrium quantity is Q = 5.45 at price

P = 18.35 – 2 Q = 18.35 – 2 (5.45)

P = 18.35 – 10.9 = 7.45

P = 7.45

The above equilibrium is when externality is not incorporated in supply function.When we consider the cost of externality supply function is S| = MPC + MEC

2 + Q + 0.25 Q

Demand = S|

18.35 – 2Q = 2 + 1.25 Q

16.35 = 3.25 Q

3.25 Q = 16.35

Q = 16.35/3.25

Q1 = 5.03

When cost of externality is considered, output reduced to Q1= 5.03

Resource mis allocation or 1 unit extra will be provided in the market if negative externality is not considered.

ii) Flat fee pricing system is when a flat fee is charged for waste generated irrespective of quantity Therefore marginal private cost of additional waste management service is zero.

MPC = 0

Equilibrium is where MPB = MPC

18.35 – 2 Q = 0

2Q = 18.35

Q2 = 9.175

Resource mis allocation is 9.175 – 5.45 = 3.725.units extra service demanded and supplies in case of flat fee pricing system.

B. Waste and charge is a free charged at the time of disposal of waste.It is used based on the quantity of waste generated.To restore efficiency,dollar value waste – end charge should be equal to MPC + MEC at the socially optimum level of output so it comes both private cost of waste + cost of externality. Socially optimum level of output is Q1= 5.03 marginal social cost at this output is PE = 8.2875 . Therefore fee of $ 8.28/unit .