Search and endogenous growth: when Romer meets Lagos and Wright

In this note, we develop a search-based monetary growth model to analyze the growth and welfare effects of inflation. We introduce endogenous growth via capital externality into a two-sector search model and compare the effects of inflation to those from a standard cash-in-advance (CIA) growth model. We �find two important differences between the two approaches. First, while the growth effect of inflation operates solely through endogenous labor supply in the CIA model, the growth effect of inflation operates through an additional consumption effect in the decentralized market in the search model. Second, we quantitatively evaluate the welfare cost of inflation and fi�nd that the search model exhibits a larger (smaller) welfare gain than the CIA model when we decrease the growth rate of money supply to achieve the Friedman rule (zero inflation). These contrasting results are due to a non-linearity in welfare as a function of inflation in the search model