Midterm 2 Optimal Rate Question

For questions 1 through 3 consider the case where you have available to you four equally
productive workers. Since each has been on the job for a different amount of time, they earn
different daily wages:

. Larry = \$6 per day
. Moe = \$7 per day
. Curly = \$3 per day
. Shemp = \$5 per day

There are also five tasks, each requiring only one worker, that can only be done today
that provide you with a financial benefit:

. Iron Pants = \$10
. Blend Scotch = \$8
. Serve Dinner Guests = \$6
. Unpack the Mummy = \$4
. Save the Queen = \$2

There is no financial benefit if you perform these tasks tomorrow. Consider the optimal
allocation of tasks. As in class, please treat ties in favor of production.

1. Which worker will remain unemployed?

(a) Larry
(b) Curly
(c) Shemp
(d) Moe
(e) Other, i.e., more than one or none.

Solution:

To solve this problem we need to first organize all the information. We start by making a column of the workers in ascending order based on wage (the cheapest worker is at that top). Then we organize the tasks by making a column of their respective financial benefits in descending order(most profitable at the top). Finally we make a column of the net financial benefit from assigning a laborer to a task.

 Laborer Task Net finacial benefit Curly=\$3 Iron Pants=\$10 \$7 Shemp=\$5 Blend Scotch=\$8 \$3 Larry=\$6 Serve Dinner Guest = \$6 \$0 Moe=\$7 Unpack Mummy=\$4 -3\$

Now that we have this table we hire the laborers as long as we have a positive net financial benefit. We simply look at the table and see that Moe provides a negative net financial benefit so we do not hire him.

2. Which of the following tasks will remain undone?

(a) Iron Pants
(b) Blend Scotch
(c) Unpack the Mummy
(d) Serve Dinner Guests
(e) All will be done.

Solution:

Again we look at the table at see that unpacking the mummy will not get done because it provides a negative net financial benefit.

3.What is your net benefit of optimally employing the Stooges?
(a) \$9
(b) \$7
(c) \$10
(d) None of the above

Solution:

We take the sum of the non-negative net financial benefits. This comes to \$10