Question

Question 5: Consider a worker that ranks combinations of employee benefits (E) and wages (W) according to the utility function U = EW , where a and 8 are positive constants and U is the index of satisfaction. Suppose that firms are able to remain competitive (i.e., keep profits at zero) if they offer S90 in wages and no employee benefits. If they offer benefits, wages must be reduced by 75 cents for every dollar of benefits offered. Suppose that currently, the firm is offering a compensation package of $40 in benefits and S60 in wages. 1. Suppose an individuals preferences are such that a = 1 and 8 = 2 (i.e., they give more weight to wages than to benefits in the ranking process). Why might such a weighting occur? 2. What is the utility level associated with the initial compensation package? 3. How much would this individual be willing to give up for a $20 increase in benefits? What would such an increase in benefits cost the firm? Would the worker be made better off by such an increase in benefits? 4. Suppose that workers are now given more freedom over the choice of benefits so that and are both given an equal weight of one. Given the original compensation package, how much would the individual be willing to give up for a $20 increase in benefits? What would such an increase in benefits cost the firm? Would the worker be made better off by such an increase in benefits?

Answer 1

Questions: Answer: Given U = ECOWA Cetility function) → fins are competitive Cprofit is at zero), $90 = wages. No employee benefite - firms offer benefits, wages = geduced by 75 Cents forevery dollar Now if firm is operating a compensation package of $40 in benefits and 860 in wages. © If a=land ß = 2 (ie) give more weight to wages than to benefits in ranking process, such weighting occurs because > Here firm is providing compensation package consisting of benefit (B) and wages (w) Utility function of customer is expreffed of: (UCB, w) = BºwB.

. Here Alpha and beta are weight factor: Satisfaction from Each dollar of B is alpha times and from w is beta times. As given Q =), B=2 , wage is providing double Satisfaction than one dollar benefit @ utility level affociated worth the initial compensation package : » arrent package is providing Bof $40 and w of $60. 80 current utility 18: UCB,W) = 40 B'X 602 = 40* 3600 = $144,000 (3) Individual be cuilling to give up for $20 increate in benefit in this benefit cost the firm and better off to the worker or not: 2 An individual is willing to give up for each dollay

of the ability to the extent of My from such B "Mu is the partial derivation of to function with respect to B. les mug = du = 2 B9-WB = Bºw? 602 = ($3600 for each sollar B he can sacrifice MU of (8 3660] So for $20 he will sacrifice E$ 79000 lig (20x3606) 4) Encrease in benefits i8 $20 then; ĐIf $20 B is increased, then wages will be sacrificed to the extent of 820*0.75 = 815 So if B is 8404 $20 = 860 then . w is 800 $15= $45. total utility = 0: B'w2 = 60's* 452 = 60 * 2025 -121500

Hence this is less than the previous valve Cie (121500 – 144000) . for providing such benefit fim is paying a package of 860+ $45 = 18005) Previously it is paying $ not $ 60 = ($100] so there is an increase in 85 wage pack. Finns has cut $15 wages. workers had not benefited from this package. If & and p both are I then etility of worker before... such change wasi USBw = 40*60 = $ 2400 After such change: → Uz Bw = Go * 45 = 2700 2400) So cuorkers are now benefited ($300)