Hi! Can anyone please help me with this problem of principal-agent problem? Thank you!

1. A worker can exert two effort levels , solid and sloppy, which cause mistakes with probability 0.25 and 0.90. Her utility function is 100 10/10 d, where d is 2 if effort is solid and 0 if it is SIOppy. Whether a mistake occurs is observable, but effort is not. Risk neutral employers compete for the worker, and her output is worth 0 if a mistake occurs and 20 otherwise. Except for (b), this problem requires little computation. a) Will the worker be paid anything if she makes a mistake?Explain briey. b) Will she be paid more if she does not? Explain (hint: check that there is a contract which induces high effort which she prefers to the best contract that induces low e'ort). c) What would the contract look like if a third category, \"slight mistake,\" with an output of 19, occurs with probability 0.1 if effort is SIOppy and proba- bility 0.0 if effort is solid? d) Suppose now that slight mistakes are not possible, but that a new third category, \"huge fortune,\" with output 100 occurs with probability 0.01 if effort is sloppy and probability 0.001 if effort is solid. Will the worker be paid more in case there is a mistake or a huge fortune