A worker's job consists of operating a machine. If the worker operates the machine as

instructed (e = 1), then with probability 1/2 the level of output of 1 (s = H) and the

firm's revenue is z > 0, and with probability 1/2 output and revenue are zero (s = L).

Alternatively, the worker can choose to use the machine for her own private purposes

(e = 0), obtaining a private consumption value of

g= 1/2 from doing so. If she does

so, however, output and revenue are zero with certainty. The worker has utility

u(y) = y (1/2) y², where y is her disposable income, inclusive of any private value she

obtain from the machine, i.e. y(w, e) = w + (1 e)/2, where w is the wage received

from her employer and e: {0, 1} is an indicator of how she uses the machine (e = 1: as

intended; e = 0, for private purposes).

Employers operate under conditions of perfect competition, meaning that they must

break even in expectations (zero expected profit). So, if their expected revenue is E(v)

and the cost of using the machine is r, the expected wage paid, E(w), must be such

that E(v) r E(w) = 0. Assume z = 2 (1 + r). When e = 1, this implies

E(v) r = z/2 r = 1, making the zero-profit condition:

E(w) = 1.

(i) Suppose that firms can observe how a worker uses the machine, and offer a

contract (w(e = 1),w(e = 0)) where the wage paid is conditioned on how the

machine is used. Assuming w(e = 0) = 0 (firms pay a zero wage if they see

improper use of the machine), what is equilibrium the level of w(e = 1) (the level

for which firms break even)? (4 marks)

(ii) Suppose now that firms cannot observe how machines are used but that a project's

outcome is verifiable, implying that the firm can offer a wage contract (w_H,w_L)

where the wage paid depends on the outcome of the project, s: {H, L}.

Characterise wage contracts that induce