A contract pays

if the outcome is a "failure" and

if the outcome is a "success", so that each point in the quadrant is a possible contract. The Demonstration shows the regions of contracts that are:

(i) incentive compatible but not individually rational (green);

(ii) individually rational but not incentive compatible (blue); and

It also shows the optimal least-cost contract and, implicitly, the expected cost.

The green negatively sloped line represents the locus of contracts that just satisfy individual rationality; that is, the agent receives exactly his reservation utility. The blue positively sloped line represents the locus of contracts that just satisfy incentive compatibility; that is, the agent is indifferent between choosing

and choosing the minimum effort,

. The purple line represents a locus of contracts that cost the principal the same amount.

These change as the disutility of effort

, reservation utility

, and degree of relative risk aversion

, change. Where

is the agent's wage and

is the disutility of his effort, the agent's utility is given by

.

The expected cost of the contract is directly proportional to the intercept of the purple line. Pay attention to the values on both axes and the size of the region. Notice what happens to the purple and green lines as the degree of relative risk aversion approaches 0; also notice that everywhere,

.

The model assumes that

and

. The agent's utility is square-root utility (his utility equals the square root of his wage) so that

; the degree of relative risk aversion is

.