The private marginal benefit for commodity X is given by 10-X, where X is the nu

Question

The private marginal benefit for commodity X is given by 10-X, where X is the number of units consumed. The private marginal cost of producing X is constant at $2. For each unit of X produced, an external damage of $3 is imposed on members of society. What type of externality is this? In the absence of any government intervention, how much X is produced? What is the social efficient level of production of X? What is the gain to society involved in moving from the inefficient to the efficient level of production (please quantify)? Suggest an approach that the government could take that could lead to the efficient level. How much would such an approach cost or benefit government in the form of increased government tax revenues or increased government costs?

Explanation / Answer

In the question, these numbers are given,
Private Marginal Benefit = 10 - X
Private Marginal Cost = $2
External Cost = $3

Without government intervention, PMB = PMC;
10-X=2
X = 10-2 = 8 units

Social efficiency implies PMB = Social Marginal Costs = $2 + $3 = $5
So, X = 10-5 = 5 units

Gain to society is the area of the triangle whose base is the distance between the efficient and actual output levels, and whose height is the difference between private and social marginal cost.
So, the efficiency gain is ½ *(8 - 5)*(5 - 2) = 1

Govt will benefit from a tax addition to the private marginal cost the amount of the external cost at the socially optimal level of production.

Here a simple tax of $3 per unit will lead to efficient production.
This tax would raise 3*5 units = 15 in revenue

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.