Suppose we have a individual worker whose utility function is u(w,r)w+1/r2. Ther
ID: 1116979 • Letter: S
Question
Suppose we have a individual worker whose utility function is u(w,r)w+1/r2. There are four types of jobs available to the worker with the following wage-risk characteristics: job 1 - (25,1/2); job 2 (23, 1/3); job 3- (12, 1/4); and job 4- (3,1/5), where the first number in a pair is wage and the second one is risk level (say, probability of a injury). (a) Given the worker's utility function, what job does the worker choose? (b) If government mandates all jobs to have the same level of risk. T-1/4, does the worker lose or gain in utility? What is the loss/gain?Explanation / Answer
u(w,r) = W + 1/r²
Utility if taking job 1 = 25 + 1/(1/2)²
= 25+2²
=29
Utility if taking job 2 = 23 + 1/(1/3)²
= 23+ 3²
=32
Utility from job 3 = 12+ 1/(1/4)²
= 12 + 4²
=28
Utility from job 4 = 3 + 1/(1/5)²
= 3+5²
=28
Since a rational consumer aims to maximize his utility, the individual will take up the job which gives him the highest level of utility. Here, the individual will take job 2 since the utility derived from job 2 is 32 while that from job 1, 3 and 4 is 29, 28 and 28 respectively.
(b) if the government mandates all jobs to have the same level of risk r= 1/4 and the consumer still sticks to job 2, his utility will change to
23+ 1/(1/4)² i.e. 39. Thus, his utility increases by 7 units from 32 to 39.
Thus, he faces a utility gain of 7 units.
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