Answer:
900 or 9 hundred
Explanation:
Given that :
the supply curve = P = 5 + 0.1Q
the Demand curve = P = 20 – 0.2Q
The relation of both above yields the equilibrium price and quantity .
SO;
5 + 0.1Q = 20 – 0.2Q
5 - 20 = -0.2Q - 0.1Q
-15 = -0.3Q
Q = -15/-0.3
Q = 50 hundreds of unit per day
Q = 5000 per day
So;
P = 5 + 0.1Q
P = 5 + 0.1 (50)
P = 5 + 5
P = $10
Therefore; the equilibrium price is $10
the equilibrium quantity is 5000
Similarly; the portable radio imposes $2.70 per day in noise costs on others.
∴ in order to deduce the social marginal cost curve ,w e need to shift the private marginal cost curve up by $2.70 for every unit.
Now; the social marginal cost curve will be ;
P = (5 + 2.7) + 0.1Q
P = 7.7 + 0.1Q
In order to determine the social optimum ; we relate the social marginal cost with demand curve as follows:
7.7 + 0.1Q = 20 - 0.2Q
0.1Q + 0.2Q = 20 - 7.7
0.3Q = 12.3
Q = 12.3/0.3
Q = 41 hundred unit per day
Q = 4100 per day
Recall :
P = 7.7 + 0.1Q
P = 7.7 + 0.1(41)
P = 7.7 + 4.1
P = $11.8
Finally; the equilibrium number of portable radios rented is 5000 - 4100 = 900 or 9 hundred
