It is costly for an employee to put in full effort at work. The cost of full effort is C. The employee is tempted to shirk, in which case they only face the effort cost of (1 - S)*C, where S is the degree of shirking the employee chooses, expressed as a decimal between 0 and 1.

To incentivize the worker not to shirk, the firm offers an efficiency wage; that is, the employee receives a wage W_H from the firm whereas the competitive wage the employee could earn elsewhere is W_L.

The firm does random monitoring and the probability that the employee is found shirking and is fired is equal to its level of shirking squared: prob(fired) = S².

Assume the employee is risk-neutral and maximizes the expected wage net of effort costs. If the employee is fired they earn the competitive wage without any additional cost of effort.

If the cost of full effort is C = 20, the efficiency wage is W_H = 100, and the competitive wage is W_L = 50, what level of shirking does the employee choose?

Hint: The employee's payoff is their expected wage, net of effort costs. Form an equation for the payoff and maximize with respect to S.

Express your answer in decimal form with two decimal places.