Question

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

 

                                   MPB   =         25 − 2Q          

                                   MPC    =          4 + Q

                                   MEC    =         0.5Q,

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

A.     Quantitatively determine the effect of the resource misallocation due to: (12 marks)

a.     the presence of the negative externality, and

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

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

Answer 1

A)

Markel for MSW management services.

Demand (D): MPB = 25 - 2Q

Supply (S): MPC = 4+Q

Demand = supply for equilibrium

$25-2Q = 4+Q\\ 21 = 3Q\\ Q = 21 / 3 \\ = 7$

equilibrium quantity is Q = 7 at price

$P = 25-2(7) = 25-14 = 11$

The above equilibrium is when externality is not incorporated in supply function. When we consider the cost of externality, supply function is, $ = MPC + MEC = 4+Q+0.50Q

Demand = S'

$25-2Q = 4 +1.5Q\\ 21 = 3.5Q\\ Q₁ = 6$

when cost of output reduces externality s considered, to Q₁ = 6 i (socially optimum output )

 Resource misallocation 1 unit extra will be provided in the market negative externality is not considered.

flat fee pricing system is when a flat fee is charged for waste generated irrespective of quantity. Therefore marginal private cost ve cost is of additional зего ... waste MPC = 0 management service

equilibrium is where MPB = MPC

$25-20 M O\\ 2Q = 25\\ = 12.5$

Resource mis allocation is 12.5-7 = 5.5 unit extra service demanded & supplied incase of flat fee pricing system. 

B)

waste end charge is a fee charged at the time of disposal of waste It is based the amount / quantity go of waste generated to restore efficiency ,dollar value of MPC + MEC at the socially optimum level of output so that it covers both private cost of waste + social cost cost of externality. socially optimum level of output is Q₁ = 6 marginal social cost at this output is PE = 13 . Therefore fee of $13 / unit.