Within the seminal cobweb model of Brock and Hommes, firms adapt their price expectations by a profit-based switching behavior between free näive expectations and costly rational expectations. Brock and Hommes demonstrate that fixed-point dynamics may turn into increasingly complex dynamics as the firms' intensity of choice increases. We show that policy-makers are able to manage rational routes to randomness by adjusting profit taxes. As suggested by our analytical and numerical analysis, policy-makers should increase (decrease) profit taxes if destabilizing expectations generate higher (lower) profits than stabilizing expectations to alter the composition of applied expectation rules and thereby to promote market stability. Our results are not restricted to cobweb models: a huge body of literature demonstrates that rational routes to randomness may emerge in many different markets.