Check my work Check My Work button is now disabledItem 6Item 6 10 points Suppose the supply curve of portable radio rentals in Golden Gate Park is given by: P = 5 + 0.1Q, where P is the daily rent per unit in dollars and Q is the volume of units rented in hundreds per day. The demand curve for portable radios is: P = 20 – 0.2Q. If each portable radio imposes $2.70 per day in noise costs on others, by how much will the equilibrium number of portable radios rented exceed the socially optimal number?

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