Healthcare Economics: Sweetwater nursing home has 150 beds. Its cost and volume data are as follows

Question

Sweetwater nursing home has 150 beds. Its cost and volume data are as follows. Calculate its average and marginal costs for volumes ranging from 100-140. What patterns do you see?

 

Residents      Costs
80               $10,000
100             $11,000
120             $12,000
140             $13,000

Answer 1

The easiest way to solve this problem is to set up a spreadsheet matrix

calculating average cost as the number in the cost column divided by the number in the residents column

calculating the marginal cost as the (difference between two adjacent rows in the cost column) divided by (difference between two adjacent rows in the residents column)

to yield:

residents costs avg cost marginal cost
80     $10,000  $125
100   $11,000  $110  $50
120   $12,000  $100  $50
140   $13,000    $93  $50

 

Marginal cost beyond 80 residents is a constant of $50/resident which is lower than the average cost per resident.  As the nursing home expands the average cost per resident will drop toward the marginal cost.  Realistically at some point the marginal cost will rise when the nursing home needs to upgrade existing facilities to house more residents.