Question

Consider two firms with the following marginal abatement costs (MAC) as a function of emissions (E): MAC_1 = 4 - 2E_1 MAC_2 = 8 - E_2, and assume marginal external damages (MED) from aggregate emissions from the two firms (E_Agg) is: MED = E_Agg. The socially efficient level of aggregate emissions is ____

Answer 1

The socially efficient level of aggregate emissions is
`\(E_{\text{Agg}} = 3\).`

Step-by-step explanation:

To determine the socially efficient level of aggregate emissions
`(\(E_{\text{Agg}}\))`, we need to find the point at which the sum of the marginal abatement costs (MAC) across firms equals the marginal external damages (MED). Mathematically, this is expressed as:

`\[MAC_1 + MAC_2 = MED\]`

Substituting the given MAC functions and MED, we get:

`\[4 - 2E_1 + 8 - E_2 = E_{\text{Agg}}\]`

Now, we can substitute
`\(E_2 = E_{\text{Agg}} - E_1\)` into the equation to have a single variable:

`\[4 - 2E_1 + 8 - (E_{\text{Agg}} - E_1) = E_{\text{Agg}}\]`

Solving for
`\(E_1\)`, we find
`\(E_1 = 1\)` and consequently
`\(E_2 = 2\)`. Therefore,
`\(E_{\text{Agg}} = E_1 + E_2 = 3\).`

In economic terms, this result represents the optimal level of emissions that balances the cost of reducing emissions (MAC) with the societal cost of environmental damages (MED). In this case, for firms 1 and 2, emitting a total of 3 units is socially efficient. This approach aligns with the goal of minimizing the overall cost to society associated with emissions and environmental damages.