Suppose a firm producing roof shingles imposes a negative externality on the surrounding area due to the noxious fumes emitted from the plant.The private marginal cost,social marginal cost and marginal benefit associated with the production of the shingles are given by the following equations: MCP = 5 + 2Q MCS = 10 + 3Q MB = 50 - Q
The allocatively efficient level of output is ________ units.

Question

Quizplus · Accepted Answer

The allocatively efficient level of output occurs where the Social Marginal Cost (SMC) equals the Marginal Benefit (MB). We can find the SMC by adding the external cost (noxious fumes) to the private marginal cost (MCP). Therefore, SMC = MCP + External cost = 5 + 2Q + External cost. 
Since the problem gives us no information about what the external cost is, we cannot find the exact value of SMC. 
However, we can find the equilibrium point where MCP = MB, which is where the market would be if there were no externalities. 
Setting MCP = MB, we get: 
5 + 2Q = 50 - Q 
Solving for Q, we get Q = 15 
Therefore, the equilibrium level of output is 15 units. 
Since the socially efficient equilibrium occurs when SMC = MB, we can find the socially efficient level of output by setting: 
SMC = MB 
5 + 2Q + External cost = 50 - Q 
Solving for Q, we get Q = 10 
Therefore, the allocatively efficient level of output is 10 units.

Suppose a Firm Producing Roof Shingles Imposes a Negative Externality