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Environments with fixed adjustment costs such as transaction costs or \lqmenu costs\rq$ $ are widespread within economic systems. The presence of fixedminimal adjustment costs produces adjustment stickiness so that agents mustchoose a sequence of points at which time to perform their actions. This paperperforms an analysis of the effect of transaction costs on agent behaviourwithin a dynamic optimisation problem by way of introducing the theory ofincentive design to optimal stochastic impulse control. The setup consists ofan agent that maximises their utility by performing a sequence of purchases ofsome consumable good over some time horizon whilst facing transaction costs anda Principal that chooses the agent's transaction costs. This results in adynamic Principal-Agent model in which the agent uses impulse controls toperform adjustments to their cash-flow process. We address the question ofwhich fixed value of the transaction cost the Principal must choose to induce adesired behaviour from the agent. We study the effect of changes to thetransaction cost and show that with an appropriate choice of transaction cost,the agent's preferences can be sufficiently distorted so that the agent findsit optimal to maximise the Principal's objective even when the agent'scash-flow is unobserved by the Principal.

Optimal Selection of Transaction Costs in a Dynamic Principal-Agent Problem