RIU.Cost

Production and Cost
The Example: RIU

We will now use the university as an example to illustrate the important production and cost relationships. In this example output will be the number of students and input will be the number of faculty. All the $ figures are in $1,000s. In the first table and set of graphs we are looking at the production relationships and in the second we are looking at the cost relationships. What you will note is these curves look very much like those in the textbooks and the other example.

Production Relationships

The table below contain data pertaining to RIU. Output is measured by the number of students and the variable input is the number of faculty. What we are looking for is the relationship between the two. Below the table you will have examples worked out for each column. What you will notice with the graph is the university does exhibit diminishing marginal product. Marginal product peaks at 700 faculty and after that the marginal product of the faculty decreases.

The Tables

Inputs and Outputs: Production Relationships
all $ figures in 1,000s

Faculty	Students	AP	MP	MRP
500	6700	13.40
550	7300	13.27	12	$121.20
600	8000	13.33	14	$142.80
650	8775	13.50	15.5	$155.00
700	9800	14.00	20.5	$202.95
750	10125	13.50	6.5	$63.70
800	10400	13.00	5.5	$53.35
850	10625	12.50	4.5	$43.20
900	10800	12.00	3.5	$33.25

500 / 6,700 = one potential size of the faculty and the number of students that could enroll with this size faculty
13.27 = Average product = students per faculty = output/input = 7300/550 = 13.27
14 = marginal product = output per additional faculty = D output/Dinput = (8000-7300)/(600-550) = 700/50 = 14
$63.70 this is marginal revenue product: you cannot figure this out until you have more information, specifically what price (tuition) would be at each student size. We will come back to this soon.
The Graphs

Total Product

Marginal and Average Product

Marginal Revenue Product

Cost Relationships

It is now time to look at the cost relationships implied by the production relationships. To make the connection between the two we need two pieces of information. The first is fixed costs and in this example fixed costs are $10,000,000 which shows up as $10,000 in the table. To get the variable cost figures, you need to know faculty salaries are $70,000 [this would appear as $70 in our calculations]. The variable cost for a university with 6700 would be calculated by multiplying the size of the faculty (500 from the previous table) times the $70 (given information). Variable cost would be equal to $70 * 500 = $35,000 [variable cost would be $35,000,000]. If we added to this the level of fixed costs ($10,000,000), we would get total costs of $45,000,000 that shows up as $45,000 in the table.

The Tables

Cost Relationships
all $ figures in 1,000s

Students	Fixed Costs	Variable Costs	Total Costs	Average Cost	Marginal Cost
6700	$10,000	$35,000	$45,000	$6.72
7300	$10,000	$38,500	$48,500	$6.64	$5.83
8000	$10,000	$42,000	$52,000	$6.50	$5.00
8775	$10,000	$45,500	$55,500	$6.32	$4.52
9800	$10,000	$49,000	$59,000	$6.02	$3.41
10125	$10,000	$52,500	$62,500	$6.17	$10.77
10400	$10,000	$56,000	$66,000	$6.35	$12.73
10625	$10,000	$59,500	$69,500	$6.54	$15.56
10800	$10,000	$63,000	$73,000	$6.76	$20.00

$10,000 = fixed cost = does not change as output changes (could be property tax, heat for buildings...)
$38,500 = variable cost = $70 times the 550 faculty needed to teach 7300 students (550*70=38,500)
$55,000 = total cost = fixed plus variable cost = $10,000 + $45,500
$6.17 = average cost = cost per student = total cost/ students = $62,500/10125 = $6.17: The cost per student at RIU is $6,170.
$15.56 = marginal cost = cost per additional student = D cost/ D students = (69,500-66,000)/(10625-10400) =(3500/225) = $15.56: The cost of expanding to 10,625 students costs $15,560 per student at RIU.
The Graphs

Total Cost Curves

Average Cost Curves

Marginal Cost Curves