Question

A firm produces a good q and receives a price p = 10 for the good. The marginal private cost of producing the good is MC = 2q. The production of each unit causes marginal external damage of 2 monetary units. What are the efficiency gains from implementing liability laws if the implementation has no cost?

Answer 1

Let's first calculate how much the firm will produce when there is no liability laws in place.

The firm will produce quantity q such that it maximizes their profit.

And we know the profit maximization condition is as follows,

MR = MC

MR = marginal cost

MC = marginal cost

We have MC as 2q now let's calculate the marginal revenue and the MR as 10 since the firm sells each unit for price 10.

Putting in the values,

2q = 10

q = 10/2

q = 5

So the firm will produce 5 units in absence of liability laws. And we know the external damage is equal to 2 momentary units for each units, so the total external damage will be equal to,

= 2 × q

Putting q = 5

= 2 × 5

= 10

So the total external damage is equal to 10.

Now what happens if the liability laws are implemented, in that case the government would impose a tax on firm equal to 2 per unit q. So the new marginal cost of firm becomes,

= 2q + 2×q

= 4q

So let's at this marginal cost how much firm is going to produce.

Again putting MC =MR we get,

4q = 10

q = 10/4

q = 2.5

So the after the implementation of liability law the firm is only going to produce 2.5 units.

And we know the external damage per unit q us equal to 2. So the new total external damage will be equal to,

= 2.5 × 2

= 5

So the new total external damage is equal to 5.

And the government gets tax of 2 per unit of output q, so there total revenue will be equal to,

= 2 × q

= 2 × 2.5

= 5

And please this revenue can be used to correct the damage which is being caused by the production.

Now to see how much efficiency gains that we got through the implementation of liability laws we need to compare the total external damage before and after the implementation.

New external damage = total external damage before implementation of law - total external damage after the implementation of law - government revenue form liability taxation

New external damage = 10 - 5 - 5

New external damage = 0

So the efficiency gains from the implementation of liability laws is 100% or in other words the liability is able to reduce to external damage to practically 0 in monetary units. Since the firms its self reduces half of the damage and the other half can be corrected by the government from the revenue it gets from liability tax. So after liability law the system is 100% efficient and gains from liability law implementation is of 100%.

I hope I was able to help you, if you still have any doubts please ask me through the comment section I'll get back to as soon as possible. Thank you