In: Economics
a)
Set MC=P for profit maximization in case of perfectly competitive market
15+2Q=300-3Q
5Q=285
Q=285/5=57
P=300-3Q=300-3*57=$129
Without regulation, profit maximizing price is $129 and quantity is 57 units.
b)
In this case
MSC=MPC+MEC=15+2Q+Q=15+3Q
Set MC=P for profit maximization in case of perfectly competitive market
15+3Q=300-3Q
285=6Q
Q=285/6=47.50
P=300-3P=300-3*47.50=157.50
Socially efficient price is $157.50 and quantity is 47.50 units.
c)
Marginal private cost will increase by $0.80 for each in this case
MC'=15+2Q+0.80=15.80+2Q
Set MC'=P for profit maximization in case of perfectly competitive market
15.80+2Q=300-3Q
284.20=5Q
Q=284.20/5=56.84
P=300-3Q=300-3*56.84=$129.48
New equilibrium price is $129.48 and quantity is 56.84 units. We can see that output is quite different from socially efficient combination. So, tax policy does not achieve the goal of socially efficient allocation of resources.
d)
In case of monopoly, socially efficiency cannot be achieved as P is not same as MSC. Monopolist chooses the output level such that MR=MSC.
However monopolist maximizes its profit by selecting output level such that MR=MSC
Given P=300-3Q
Total Revenue =TR=P*Q=(300-3Q)*Q=300Q-3Q2
MR=dTR/dQ=300-6Q
Equate MR=MSC for profit maximization in case of monopoly.
300-6Q=15+3Q
285=9Q
Q=31.6667
P=300-3Q=300-3*31.6667=$205
But this is not socially efficient output and price combination.