9781118041581

chronic complaint of many low-income people is poor teeth and gums.

Indeed, poor teeth can be a visible “marker” of poverty and low

educational attainment.

In what sense, are the uninsured poor caught in a vicious circle? Is their

medical plight due to personal decision failure, or market failure, or both?

Spreadsheet Problem

S1. Suppose that the gross profit generated by a particular worker is given by

1,000e u, where e denotes the worker’s effort (measured as an

index between 0 and 50) and u is a random variable with a mean of zero

and a positive standard deviation. Thus, profit depends not only on the

worker’s effort but also on random factors beyond his control. The

worker’s disutility associated with effort is given by D 10e^2. The

employer compensates the worker with an incentive contract of the form

P W b, where W is a fixed wage component and b is the worker’s

profit share. For concreteness, let e 30, and suppose that the contract

calls for W $10,000 and b  .3. Then the expected gross profit

attributable to the worker is $30,000. The employer’s expected wage

payment is 10,000 (.3)(30,000) $19,000, and the employer’s

expected profit is 30,000 19,000 $11,000. In turn, the worker’s

expected profit (net of any disutility) is $19,0000 10(30)^2 $10,000.

Under an incentive contract, the variability in the worker’s wage

(i.e., the risk) increases with the profit share b. A risk-averse worker will

discountthe expected profit listed earlier by a risk premium to account

for the burden of risk. To be precise, we suppose that the risk premium

takes the form R 10,000b^2. The maximum premium, $10,000, occurs

under 100 percent profit sharing (b 1). Of course, for b 0, the wage

is fixed, so there is no risk and no risk premium. For b  .3, the

premium is $900, so the worker’s risk-adjusted profit is 10,000  900 

$9,100. In general, the worker’s risk adjusted profit is given by:

a. Create a spreadsheet similar to the example given. For the contract

with W $10,000 and b  .3, find the worker’s optimal level of effort.

(Hint:Use the spreadsheet’s optimizer to maximize the worker’s risk-

adjusted profit in cell E12. Alternatively, adjust the worker’s effort

until MW1000b 20e in cell E17 is exactly equal to zero.)

b. Find the worker’s optimal effort levels for sharing rates of .4, .6, .8,

and 1.0. What pattern do you detect?

c. Using the optimizer, find the sharing rate and level of effort that

together maximize the employer and worker’s total profit. (Hint:

Adjust cells C7 and D7 to maximize cell C17 subject to the constraint

WWb(1000e)10e^2 10,000b^2.

622 Chapter 14 Asymmetric Information and Organizational Design

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