Gun Buybacks and Firm Behavior: Do Buyback Programs Really Reduce the Number of Guns?

Abstract

We suppose that guns or firearms are subject to an anticipated future buyback program undertaken by the government. A simple linear demand durable-goods monopoly model is then analyzed where the durable-good manufactured is a firearm that lasts for two-periods. The model is calibrated so that buyers are indifferent between selling (participating in the buyback program) or holding the gun in the future period. This allows us to focus solely on the firm''s behavior. We find, among other things, that if the firm can credibly commit to its current buyers the anticipated buyback has no impact on the future stock of guns. In this case, the firm simply increases its production of new firearms after the buyback, and offsets all the units collected and destroyed by the government. However, in contrast, we show that if the seller cannot commit to these buyers, the future stock is indeed reduced (but by only one-half of the buyback program level). Thus, any anticipated (repeated) buyback's impact on future stock levels of firearms depends critically on the commit ability of the durable-goods manufacturer, independent of the buyers' reselling and arbitrage activities. Moreover, regardless of commitment ability, the model suggests the imperfectly competitive firms may, at least partially, counteract the buyback program, making any governmental buyback less effective at reducing future firearm stocks than expected.