An analytical model of search and bargaining with divisible money

We propose a standard search and bargaining model with divisible money, in which only the random matching market opens and the generalized Nash bargaining settles each trade. Assuming fixed production costs, we analytically characterize a tractable equilibrium, called a {\it pay-all equilibrium}, and prove its existence. Each buyer pays all the money holding as a corner solution to the bargaining problem and each seller produces a positive amount of goods as an interior solution. The bargaining power parameter affects the distribution of the money holdings and possibly induces economic inefficiency. We propose a redistributional monetary transfer that adjusts the bargaining outcome and improves the allocation efficiency. Moreover, we analyze a temporary expansion of the money supply that increases social welfare through a redistribution.