Suppose we want to choose an optimal level of heating for our classroom. However

Question

Suppose we want to choose an optimal level of heating for our classroom. However, the class is divided. Four people are often cold have an aggregate (cold) marginal benefit, MBC, from heating the room by T units of: MBC = 100 - T

Five people are often hot and have an aggregate (hot) marginal benefit from heating the room: MBH = 50 – 0.5T

The marginal cost to heat the room is: MC = 0.5T

a) How many units of heating will be implemented under a majority rules vote? (Assume that everyone votes.)

b) What is the efficient level of room heating?

c) What is the deadweight loss resulting from majority rules voting?

Explanation / Answer

Under majority rule, the preferences of people feeling hot will prevail, and thus the function for MBH=50-0.5T will be used.

Under optimal condition, MB = MC

Thus, 50 - 0.5T = 0.5T

Thus, T = 50 units of heating

The efficient level would be adding the MBH for both the people and then equating it to MC

Thus, 150 - 1.5T = 0.5T

150 = 2T

T = 75

Thus, T = 75 is the optimal level of heating

Deadweight loss = 1/2 * (reduction in heating units) * (reduction in MBH) = 1/2 * 25 * 12.5 = 156.5 utils

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