2. A competitive refining industry produces one unit of waste (X) for each unit
ID: 1117607 • Letter: 2
Question
2. A competitive refining industry produces one unit of waste (X) for each unit of refined output (Q). That is, X = Q. The industry disposes of the waste by releasing it into the atmosphere. The inverse demand and supply functions for the refined product are (Inverse Demand) pD = 24 – Q. (Inverse Supply) pS = Q, where the supply price is also the marginal private cost (MCP). The marginal external cost (i.e., the marginal cost to others that is caused by pollution) is (Marginal Cost to Others) MCO = 2Q A. Identify the equilibrium price and quantity (p*, Q*) in a free market. B. How much waste should the market supply at the social optimum (QE = XE)? C. Use a graph to identify the efficiency loss due to the extermality (i.e., the DWL associated with the externality). D. Suppose the government imposes a Pigovian tax of t dollars per unit of waste. Determine the value of t that will induce the industry to produce the socially efficient level of output (t*).
Explanation / Answer
a) If there is no correction for the externality, the equilibrium will occur at the point where the marginal benefit curve, P=24-Q, intersects the marginal private cost curve, MPC= Q . This occurs at
24-Q=Q
Q= 12
At Q= 12, P= 12
b) At the social optimum marginal benefit, P=24-Q , will equal marginal social cost, MSC= MPC+ MCO
24-Q= Q+ 2Q
4Q=24
Q= 6;
Thus, the social optimum is to produce Q =6 .
c) At the uncorrected equilibrium, the marginal social cost is MSC= 3Q = 3*6= 18. Thus, the deadweight loss will be
= .5 *(12-6)* (18-12)
= 18
d) The emissions fee of $T should be set to shift the MPC curve so that it intersects the marginal benefit curve at Q =6, the socially optimal quantity. At Q = 6 the marginal benefit is P =18 and the marginal private cost is MPC= 6. Therefore, the optimal tax is T= 18-6 = 12.
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