The inverse demand for energy-efficient refrigerators is P = 2,000

Question

The inverse demand for energy-efficient refrigerators is P = 2,000 - 10Q, where Q measures refrigerators per month. The inverse supply of energy-efficient refrigerators is P = 10Q. Suppose the use of an energy-efficient refrigerator reduces carbon dioxide emissions, generating an external marginal benefit of $100. The socially optimal quantity of energy-efficient refrigerators is ____.
A) 130
B) 115
C) 105
D) 95

Quizplus · Accepted Answer

To find the socially optimal quantity of energy-efficient refrigerators, we need to account for the external marginal benefit (EMB) of $100 due to reduced carbon dioxide emissions. The inverse demand equation, which reflects the private benefit, is P = 2,000 - 10Q. To incorporate the external benefit, we adjust this equation to P = 2,000 - 10Q + 100, effectively shifting the demand curve upward by $100. However, since the external benefit is constant and does not depend on Q, we can simply add it to the price when equating demand and supply for social optimality. Thus, we solve for Q using the adjusted demand equation (including EMB) and the supply equation.Adjusted demand (including EMB): P = 2,000 - 10Q + 100 becomes P = 2,100 - 10Q when considering the external benefit.Supply: P = 10Q.Setting the adjusted demand equal to supply for social optimality: 2,100 - 10Q = 10Q.Solving for Q: 2,100 = 20Q => Q = 105.Therefore, the socially optimal quantity of energy-efficient refrigerators, considering the external benefit, is 105 units per month.