White Smile Inc. has two plants at which it produces electronic toothbrushes. Factory workers at each plant have the same characteristics (e.g., skills, alternative employment opportunities, level of income, risk aversion, etc.). The quality of a toothbrush produced is easy to supervise but the effort exerted by a worker is not. Thus, White Smile Inc. pays its factory workers according to a piece-rate contract. More precisely, each worker at plant 1 is paid I =a1+b1 X, where a1 is the base salary and b1 a piece rate ($ per unit produced) and X is the number of units produced by a worker. Similarly, each worker at plant 2 is paid I=a2+b2 X. Statistical data shows that the probability that the machines used by each worker in the production process break down - due to factors beyond the worker's control - is higher at plant 1 than at plant 2. This is the only difference between the two plants. Based on this information, what should a properly designed piece-rate contract for workers at these plants exhibit?