Question

Use the accompanying table to answer the following questions.$$ \begin{array}{cccc} \text { Quantity } & \begin{array}{c} \text { Private } \\ \text { Cost } \end{array} & \text { Social Cost } & \text { Benefit } \\ \hline 1 & \$ 2 & \$ 4 & \$ 12 \\ 2 & \$ 6 & \$ 10 & \$ 22 \\ 3 & \$ 12 & \$ 18 & \$ 30 \\ 4 & \$ 20 & \$ 28 & \$ 36 \\ 5 & \$ 30 & \$ 40 & \$ 40 \\ \hline \end{array} $$a. What is the external cost per unit of output? b. What level of output will be produced? c. What level of output should be produced to achicve economic efficiency? d. What is the value to society of correcting the externality?

Short answer

Answer: The value to society of correcting the externality in this scenario is an increase in net benefit of \$10.

Step-by-step solution

a. Calculating the external cost per unit

For each unit, subtract the private cost from the social cost. 1: 4 - 2 = \$2 2: 10 - 6 =\$4 3: 18 - 12 =\$6 4: 28 - 20 =\$8 5: 40 - 30 =\$10 The external cost per unit of output increases by \$2 for each additional unit.

b. Level of output produced

Find the point where the private cost is equal to the benefit. At output level 3, private cost (\$12) equals the benefit (\$30). Therefore, the level of output produced is 3 units.

c. Level of output for economic efficiency

Find the point where the social cost is equal to the benefit. At output level 4, the social cost (\$28) is closest to the benefit (\$36), but not greater than the benefit. Therefore, the level of output that should be produced for economic efficiency is 4 units.

d. Value to society of correcting the externality

Compare the net benefit under both the current output level (3 units) and the economically efficient output level (4 units). At output level 3: Private Benefit = Benefit - Private Cost = \$30 - \$12 = \$18 At output level 4: Social Benefit = Benefit - Social Cost = \$36 - \$28 = \$8 The value to society of correcting the externality is the difference in net benefit between the current output level and the economically efficient output level: \$8 - \$18 = -\$10. This means that society gains \$10 in net benefit by correcting the externality and producing 4 units instead of 3.

Key concepts

Economic Efficiency

When we talk about economic efficiency, we're referring to a scenario where resources are allocated in a way that maximizes total surplus. Total surplus includes both producer and consumer surplus, and reflects the overall benefit to society. In simpler terms, it means getting the most bang for our buck.

To achieve economic efficiency in the context of externalities, we must consider not just the private costs incurred by producers but also the 'invisible' costs borne by third parties, which are the external costs. In our example, the economically efficient output was determined by finding the quantity where the social cost (private cost plus external cost) is closest to, but not exceeding, the societal benefit. That point ensures that resources are being used in a way that provides the highest net benefit to society, considering all costs and benefits.

Social Cost versus Private Cost

Understanding the distinction between private and social costs is crucial for grasping the concept of externalities. Private cost is the cost that a producer of a good or service incurs in the production process. It's what shows up on the company's financial statements and affects their bottom line directly. On the other hand, social cost takes a broader perspective. It includes the private cost as well as any additional costs that society bears—for example, pollution from a factory that affects the health of nearby residents.

In our textbook exercise, the social cost of each additional unit of production was higher than the private cost, indicating the presence of an externality. For each unit, as production increased, so did the external costs, illustrating how externalities can escalate if left unaddressed. The critical lesson here is that when externalities exist, private markets may fail to produce the socially optimal quantity of goods, necessitating intervention for correction.

Externality Correction Value

The value of correcting an externality is essentially the net gain in economic welfare that society enjoys once an externality has been addressed. In our exercise, this was shown by the change in net benefits when moving from the level of output produced privately to the level of output that is socially efficient. An externality correction can involve various methods such as taxes, subsidies, or regulation, and aims to align private incentives with the social good.

When a correction is made, as was the case in moving from three to four units of output in our example, there is an increase in total surplus and thus a gain to society. The value to society of correcting the externality was a $10 net benefit — a significant illustration of why understanding and managing externalities is critical for public policy and economic well-being.