Question

Question: You are an industry analyst who specializes in an industry where the market inverse demand is $\text{P = 200 - 4Q}$. The external marginal cost of producing the product is ${\mathbf{\text{MC}}}_{\mathbf{\text{External}}}\mathbf{\text{= 6Q}}$, and the internal cost is ${\mathbf{\text{MC}}}_{\mathbf{\text{Internal}}}\mathbf{\text{= 12Q}}$.

a. What is the socially efficient level of output?

b. Given these costs and market demand, how much output would a competitive industry produce?

c. Given these costs and market demand, how much output would a monopolist produce?

d. Discuss actions the government might take to induce firms in this industry to produce the socially efficient level of output.

Short answer

Answer:

1. The socially efficient level of output is 9 units.
2. The competitive industry’s output produced is 13 units.
3. The monopolist's output is 10 units.
4. The government can impose an output tax of per unit, equal to the external marginal cost.

Step-by-step solution

Marginal Cost 

The society's marginal cost is the sum of the industry's internal and external marginal costs.It is the supplementary cost incurred by the society due to the economic activities, i.e., utilization and manufacturing by the entities like firms and users.

a.

Given values are

$$\begin{gathered} P=200-4Q \\ M{C}_{int}=12Q \\ M{C}_{ext}=6Q \end{gathered}$$

As a result, the social marginal cost remains the same as before:

$$\begin{gathered} \text{Marginalcost=ExternalMarginalcost+InternalMarginalcost} \\ P=M{C}_{ext}+M{C}_{int} \\ 200-4Q=6Q+12Q \\ 200=22Q \\ Q=9.09units \end{gathered}$$

Therefore, the socially efficient level of output is 9 uints.

Output Determination in Competitive Industry 

b.

A competitive industry would produce the following output:

${\text{P = MC}}_{\text{int}}$

To determine the output that a competitive industry would create, we equatethe internal marginal cost with price:

$$\begin{gathered} 200-4Q=12Q \\ 200=12Q+4Q \\ 200=16Q \\ Q=\frac{200}{16} \\ Q=12.5units \end{gathered}$$

Thus, output produced is 13 units.

Output determination in Monopoly

c.

A monopolist's output would be as follows:

To begin, we calculate the Total Revenue (TR), which is:

$$\begin{gathered} TR=P\times Q \\ =200Q-4Q^2 \end{gathered}$$

Then there's the Marginal Revenue (MR), which is calculated as follows:

$$\begin{gathered} MR=\frac{dTR}{dQ} \\ =200-8Q \end{gathered}$$

Finally, we simplify for Q by equating MR to :

$$\begin{gathered} MR=M{C}_{int} \\ 200-8Q=12Q \\ 200=20Q \\ Q=10units \end{gathered}$$

Hence, the output is 10 units.

Action by the Government 

d.

The government can levy a per unit of output tax, which is equal to the external marginal cost. The industry will be able to produce more efficient production with this strategy as it covers the difference between external and internal marginal cost. By creating an additional unit of good or service, a marginal external cost is imposed on third parties.