Question

The LoJack car recovery system allows the police to track stolen cars. As a result, they not only recover 90 percent of LoJack-equipped cars that are stolen but also arrest many auto thieves and shut down many “chop shops” that rip apart stolen vehicles to get their parts. Thus, LoJack provides both private benefits and positive externalities. Should the government consider subsidizing LoJack purchases?

Short answer

Yes, the government should provide subsidies to consumers to encourage purchases of the LoJack car recovery system.

Step-by-step solution

Step 1. Private benefits and positive externalities of the LoJack car recovery system

Private benefits occur when a market transaction directly affects one of the involved parties in a positive way.

For example, when a car owner buys a LoJack recovery system, it helps the owner recover his/her car after being stolen. This is the purpose of the good and helps the buyer directly.

Positive externalities occur when the consumption of a good helps a third party external to the market transaction by providing some benefits that he/she has not paid for.

For example, the LoJack recovery system helps the police officers to track down the stolen cars for the owner of the car and the buyer of the recovery system but also helps to catch auto thieves and prevent future robberies of cars without the recovery system. Thus, it helps other car owners too who did not buy or consume the LoJack recovery system.

Step 2. Underconsumption of LoJack car recovery system as a reason to provide subsidy

The presence of positive external benefits implies that the market is under-producing or under-consuming a good. This under allocation of resources to produce good results in efficiency loss as given below in the diagram by the shaded region.

The market equilibrium is reached when the demand curve (DL) intersects the supply curve (SL) of the LoJack recovery system at point “a”. At this point, the equilibrium quantity produced is Q. The DL curve shows the demand of only consumers who are receiving private benefits. The total external benefits are not included in this. Hence, the equilibrium level of output is not optimal from society’s point of view.

The market equilibrium is reached when the demand curve (DL) intersects the supply curve (SL) of the LoJack recovery system at point “a”. At this point, the equilibrium quantity produced is Q. The DL curve shows the demand of only consumers who are receiving private benefits. The total external benefits are not included in this. Hence, the equilibrium level of output is not optimal from society’s point of view.

Step 3. Encouraging LoJack car recovery system purchases and consumption by providing subsidies 

A new demand curve D’L (includes both private and external benefits) should be considered while choosing the allocation of resources to produce the good. The intersection of D’L and SL at point “b” will give the efficient level of output.

One way to achieve this new demand curve is by providing subsidies that affect the market incentives. If the consumers are getting subsidies in purchasing the recovery system, they can increase the consumption at the same price as before. To increase the consumption level, the government can provide subsidies equal to ab, encouraging purchases by shifting the demand curve from DL to D’L.

The new optimal and efficient output level Qe provides the maximum welfare to the society without any efficiency loss.