A executive can either slack (effort e = 0)or work hard (e = 1)on behalf of shareholders. If she slacks,the firm earns a gross return of 1,000 for sure. If she works hard,there is an even chance of the gross return being 10,000 or 80,000. Her overall utility equals her utility from wage income (of the form w^1/2,where w is the wage)minus the disutility of work (simply d),or in other words U = w^1/2 -d. If she slacks,she experiences no disutility of work (d = 0)but if she works hard,the disutility of work is d = 50. Assume that U = 0 in her next best available job. What is the optimal wage contract that shareholders would offer if they can observe the effort of the executive? A)A flat wage w = 0 and no requirement to work hard. B)A flat wage w = 50 and a requirement to work hard. C)A flat wage w = 2,500 and a requirement to work hard. D)A share of 50% of the profits and a requirement to work hard.

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If the executive slacks, the firm will earn a gross return of 1,000. Therefore, the shareholders' expected profit will be 1,000 for sure, regardless of the wage offered. The executive's utility from the wage income will be w^1/2 = w/2, and her overall utility will be U = w/2. If the executive works hard, the firm's expected profit will be (10,000+80,000)/2 = 45,000. Therefore, the shareholders' expected profit will be maximized if they offer a wage that leads the executive to work hard. The optimal wage should satisfy two conditions: 1. The expected utility from working hard should be higher than the expected utility from slacking: w/2 -50 >0 w> 100 2. The wage should also ensure that the executive prefers this job to her next best available job, which offers zero utility: w^1/2 -d > 0 w/2 -50 > 0 w > 100 Therefore, the optimal wage is w = 2,500, and the shareholders should require the executive to work hard to maximize their profits. The expected profit of the shareholders will be (1/2)($10,000 - $2,500) + (1/2)($80,000 - $2,500) = $43,750.

A Executive Can Either Slack (Effort E = 0)or Work