We show analytically that ensuring stable nominal wage growth is optimal monetary policy under fixed menu costs of adjusting goods prices, even when wages are completely flexible. This nominal wage targeting contrasts with inflation targeting, the optimal policy prescribed by the textbook New Keynesian model in which firms are permitted to adjust their prices only randomly (due to an exogenous Calvo friction). Menu costs, unlike the conventional model, induce state-dependent pricing and are less tractable to work with. We build an analytical, multisector model to show that optimal monetary policy is exactly nominal wage targeting for shocks that are not too small, and approximately so otherwise.

Monetary economics traditionally does not consider a market-based benchmark: when we study trade, we start with a benchmark of free trade; when we study monetary economics, however, we start with a benchmark of central banking. This paper aims to fill that gap. We study competition among unbacked, costless (“fiat”) moneys. First, under flexible prices, there is a first welfare theorem for money: When producers of such moneys have commitment technology — such as blockchain technology — then competition implements the optimum quantity of money. Second, under nominal rigidities where the competing moneys also serve as competing units of account, then competition can also implement the equivalent of “optimal monetary policy” to avoid macroeconomic fluctuations, if the competing moneys pay interest.

Inflation targeting is strictly suboptimal when economic actors have incomplete information about the state of the economy. Nominal income targeting is approximately optimal, and exactly optimal under certain parameterizations. We derive this result in a “Lucas islands” monetary misperceptions model built from, unlike prior work, explicit microfoundations. Agents have knowledge of local productivity and money supply conditions, but must perform a signal extraction problem each period to estimate the aggregate productivity shock and the aggregate money supply shock. Without full information, agents cannot perfectly distinguish between relative price shocks and aggregate shocks, causing monetary policy to affect the real economy. Since the model is built from agents optimizing from first principles, we are able to take a second-order welfare approximation and ask what monetary policy rule is optimal. In contrast to sticky price or sticky information models, inflation and price level targeting are always suboptimal, as price level variation provides useful information to agents. Under log utility, nominal income targeting is optimal.

We use a theory of apologies to analyze a nationwide field experiment involving 1.5 million Uber ridesharing consumers who experienced late rides. Several insights emerge. First, apologies are not a panacea: the efficacy of an apology and whether it may backfire depend on how the apology is made. Second, across treatments, money speaks louder than words - the best form of apology is to include a coupon for a future trip. Third, in some cases sending an apology is worse than sending nothing at all, particularly for repeated apologies. For firms, caveat venditor should be the rule when considering apologies.