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

explanation: doctrine of respondeat superior is a legal doctrine that is commonly used in tort. this principle makes an employer or principal legally responsible for the wrongful acts done by an employee or agent, if such acts occur within the scope of the employment or agency.