Answer:
See explaination
Explanation:
Demand for paper is given below:
P(Q)=60-Q,
Number of paper mills=20
The cost curve for firm is given below:
C(Q)=10Q2
The external cost in terms of pollution down river by production of paper is given below:
EC(Q)=10Q2
a. The optimal level of paper production by market can be calcuated by equating MC=P
20Q=P
Q=P/20
b. The optimal level of paper production by market can be calcuated by equating MC=P.
MC=20Q
60-(20Q)=20Q
Q=60/40
Q=1.5
Total quanity by 20 firms will be 1.5*20=30
c. The socially efficient level of paper output is calcuated below:
MC+EC'=20Q+20Q
60-(20Q)=40Q
Q=60/60
Q=1
Total quanity by 20 firms will be 1*20=20
The price will be P=60-20=40
d, The deadweight loss occurs as market price increases and quantity decreases due to the external cost . The deadweight loss is calcuated below:
DWL=(1/2)*change in price* change in quantity
=(1/2)*10*10=50
e. 20 firms merged into one firm to make monopoly firm. The cost function for the monopoly is given below:
Cm(Q)=20*10(Q/20)2
The marginal cost for the monopoly firm will be
MCm=Q
The marginal revenue for the firm is 60-2Q
For optimal output MR is equated to MC
60-2Q=Q
Q=20
P=40.
The monopoly outcome is below the perfect competition outcome and price is higher in comparison to perfect competition. The monopoly outcome is same as socially efficient outcome.
The total surplus for this outcome is sum of consumer surplus and producer surplus and subtraction of external cost
TS=CS+PS-EC
=(1/2)*20*20+(1/2)*40*20-10(20)2
=600-4000=-3400
Due to the external effects the total surplus to the society is negative. In perfect competition this effect is not considered and output produced is high therefore, the external cost will be higher with higher output leading to higher negative social surplus. Generally the monopoly outcome reduces the total social surplus but in case of externality, the monopoly total surplus is higher than the perfect competition.
