Production theory with convex labor friction : foundation of an optimal non-market-clearing economy

This paper provides a general framework for the supply side when a firm employing multiple workers faces convex search friction. It also provides analytical scheme for non-steady states. Convex search friction makes the path outside of unbounded steady states possess greater significance than mere transition, since any level of output can be supported as a steady state equilibrium depending on the state of expectation. The marginal profit value of labor is always strictly positive, which results in persistent excess demand in the labor market as well as excess supply in the goods market. However, the fact that convex search friction makes immediate adjustment of employment suboptimal induces further hiring to depend on coordination of expectation. It raises non-market-clearing equilibrium in terms of long-run without price- nor wage-rigidity in competitive markets.