Question

Consider a worker that ranks combinations of employee benefits (B) and wages (W) according to the utility function: U(B, W) = B αWβ , where α and β are positive constants and U is the satisfaction level. If firms do offer benefits, wages must be reduced by 95 cents for every dollar of benefits offered, in order for the firm to continue to break even. Suppose that a firm currently offers a compensation package of $40 in benefits and $60 in wages. Assume that an individual’s preferences are such that α = 1 and β = 2 (i.e.: they give more weight to wages than to benefits in the process of ranking compensation packages).

1. Why might such a weighting occur?

2. What is the utility level associated with the firm’s current compensation package?

3. How much wage would this individual be willing to give up for a $20 increase in benefits? What would such an increase in benefits cost the firm? By how much would the firm cut wages? Would the worker be made better off by such an increase in benefits? Suppose that workers preferences are now such that α and β are both given an equal weight of one.

4. Given the original compensation package, how much wage would the individual be willing to give up for a $20 increase in benefits? What would such an increase cost the firm? By how much would the firm cut wages? Would the worker be made better off by such an increase in benefits?

Answer 1

It is a problem where firm is providing compesation package consists of benefit (B) and wages (W).Utility of a customer is expressed by the understated utility function-

Here Alpha and beta are weight factor. satisfaction from each dollar of B is alpha times and from W is beta times. As per problem, alpha is 1 and betais 2. So wage is providing double satisfaction than one dollar benefit.

2. Current package is providing B of $40 and W of $60. So current utility is-

3. An idividual is willing to give up for each dollar of utility to the extent of MU from such B. MU is the partial derivative of TU function with respect to B. It is -

           

For each dollar B he can sacrifice MU of $3,600. So for $20 B he will sacrifice $72,000.

3. If $20 B is increased, then wages will be sacrificed to the extent of $20x0.95=$19. So if B is $40+20=$60 then W is $60-19=$41. Then his total utility is

It is less than previous benefit of $144,000.

For providing such benefit firm is paying a package of $60+$41=$101. Previously it is paying $40+$60=$100. So there is $1 increase in wages pack.

Firm has cut $19 wages

Worket has not benefitted from this package.

If alpha and beta both are 1 then utility of worker before such change was-

After such change it is-

So worker is now benefitted by $60.

4 . The answer for this question is covered in the 3rd point.