Question

Pricing and demand will be taken as exogenously determined. Your goal is to efficiently use the inputs. This starts with what might be termed the short short-run, where all inputs are fixed, but they can be reallocated to different purposes. It then moves to the short-run, where some inputs (e.g., labor) is variable, but other inputs (e.g., capital) are fixed. It concludes with the long-run, where all inputs are variable.

Part A: The ‘short short-run’

The 4-A clinic consists of four workers (Sam, Ann, Trey, and Lina) who share some or all of the following tasks: performing a medical procedure, follow-ups, and tests. The data below gives their time per task, in minutes. Assume that each can work up to six hours per day (e.g., 360 minutes) at these tasks, but no more. ‘N/A’ means that the individual isn’t qualified to perform the medical procedure.

Individual	Medical procedures	Follow-ups	Tests
Sam	21	10	5
Ann	15	9	6
Trey	N/A	20	8
Lina	N/A	18	6

Each patient seen will ultimately need one medical procedure, two routine follow- ups, and three routine tests.

1. Calculate the number of ‘patient-equivalents’ that can be handled during a workday. If you have 4 medical procedures, 8 follow-ups, and 12 tests, that counts as four patient-equivalents, so your answer would be 4. In solving for this, you must use whole numbers; no partial patients are allowed. Some staff may be partially idle. You are reporting the aggregate for the four workers. Your score on this question will be based on how close you are to the correct answer without going over.

Reallocating the labor:

2. If each worker is assigned to tasks so that total group output is maximized, how many ‘patient equivalents’ can be seen per day? Use whole numbers when assigning tasks. Your score on this question will be based on how close you are to the maximum possible number of patients. Setting this up in Excel to keep track of total patients and minutes used is highly recommended. You will want to use the concept of comparative advantage.

Answer 1

Using concept of comparative advantage. Ann has a comparative advantage over Sam in Medical procedure (The opportunity cost of doing a medical procedure is missing out on 1.67 followups or 2.5 tests as compared to Sam Who has an opportunity cost of 2.1 followups or 4.2 tests) So we begin by assuming Ann does all medical procedures unless more can be covered by followups and tests in which case sam will also do some (Or reduce in the case where even those covered by Ann cannot be covered by followups and tests from others)

Similarly Lina has a comparative advantage in Tests (Missing out on 1/3rd followups as compared to Trey whose opportunity cost is 0.4 followups for every test conducted) So we assume Lina does all tests unless more are needed in which case Trey or sam will also do some.

With these assumptions, we can start and correct along the way

1) Ann can do 360/15= 24 Medical procedures in a day. This will require 48 followup routines and 72 tests to complete 24 patient equivalents

2) Lina can do 360/6= 60 tests. That leaves 12 tests and 48 followups remaining.

3) Out of Sam and Trey, Sam has comparative advantage in followups (Opportunity cost of 2 tests as compared to 2.5 for Trey) So Sam will do all followups= 360/10=36 followups

4) This leaves Trey to cover 48-36= 12 followups and 12 tests. He can do it as follows. Use 240 minutes to do 240/20= 12 followups and out of the remaining 120, use 96 to do 96/8=12 tests.

So we got a total of 24 patient equivalents as follows: Ann does 24 medical procedures exhausting the 360 minutes.

For the tests: Lina does 60 out of the 72 tests as she has comparative advantage in tests over the other 2. This exhausts her 360 minutes. Remaining 12 are done by Trey as he has comparative advantage over sam in tests.

For followups: Sam does 36 followups exhausting the 360 minutes as he has comparative advantage in it over the other 2. Remaining 12 are done by Trey. Trey sits itle for the remaining 24 minutes that remain.

So the answer to 1) is 24

Now assuming 2) asks us to find maximum patient equivalents in a work day after assigning tasks to each person. Thus everyone continues what they have a comparative advantage in but Trey is assigned only to followups and so he can't do tests. Now Ann can do 24 Medical procedures. Sam and Trey can do a combined 48 but Line can do only 60 tests, so the total number of patient equivalents is limited by this to 60/3=20 patients.

We can't increase this further, changing medical procedures so that Sam does them won't help because then Sam can only do 17 medical procedures. SImilarly we still need 40 followups so Sam and Trey both will have to do it.

Answer in the case where everyone is assigned tasks is 20 as Trey is assigned followups

Hope it helps. Do ask for any clarifications if required.