The utility of a worker is a function of their consumption and the amount of effort they supply at work. In particular, the individual's utility function is given by (c,e)=-2 The output of an individual is given by y = r. The firm does not observe the effort of the individual, but does observe her output. The firm offers wage compensation that is given by W(v) = w+fy where w is the "base wage," paid independently of the worker's output, and is the piece-rate, which is the compensation per unit of output produced. The price of output is p = 10. (a) Find the optimal wage contract offered by the firm. (b) Write down a utility function for the worker such that the firm will offer a positive base wage w