Three Essays on Applied Microeconomic Theory

This dissertation consists of three essays on Applied Microeconomic Theory.The first chapter studies investment incentives in a dynamic random search environment where a seller can make unobservable and selfish investments to reduce his production cost before searching for buyers. In the unique steady state equilibrium, although sellers make positive investments, equilibrium payoffs and the social welfare are a) constant given any search friction and b) equal to the values that would be created if there were no investment. These results hold even in the limit, with the investment strategy converges to the first best and the stationary investment distribution converges to a point mass at no investment.The second chapter demonstrates how sorting conditions change in search frictions, in a dynamic random matching environment where heterogeneous buyers have private types and heterogeneous sellers make take-it-or-leave-it offers. We first establish the existence ofsteady-state equilibrium and then characterize sorting conditions under two extremesearch frictions. Positive (negative) assortative matching requires the production function to be log-supermodular (log-submodular) with maximal search frictions. When search frictions vanish, the condition forpositive (negative) sorting returns to supermodularity (submodularity).The last chapter examines how patents influence firms' allocation of resources over a portfolio of projects with different non-obviousness. We consider the situation where two identical firms have the replicas of two projects. One is known to be good and the other is risky but is more innovative conditional on being good. Compared to the allocation of resources without any patent, the total amount of resources allocated on the risky project is more efficient. However, the competition for the patent of the safe project also induces firms to inefficiently delay experimenting the risky project. Overall, the welfare effect of patents might be negative