RIU_Price

Output, Price, and Profit

The Example: RIU

How many students should RIU have if the goal of the administration is maximization of profit? 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 'real world' the university would likely have some goal other than profit maximization and a measure of output other than the number of students, but we will ignore this problem for now. The table below contains all of the revenue, cost, and profit data for the University. The decision variable for the university is the number of students. RIU administrators must decide on their output level - the size of student enrollment.

Because we are assuming profit maximization, the university will be guided by the decision rule, MR = MC. The university will continue to expand as long as MR > MC. As we saw earlier, the university could have also used the guide of marginal profit and continued to expand as long as marginal profit was greater than 0. Finally, if the profit data existed, you could look at the profit column and find out what size gave RIU the largest profit.

And there is no surprise that the result is the same regardless of the criterion that you used. The optimal size of the university is 9,800 students. You can see this in the table, or you can look at the graphs derived from the table. At 9,800 students:

the gap between TR and TC is maximized
the profit graph is at its maximum value
that marginal revenue = marginal cost
that marginal profit = 0.

{Actually the marginal graphs tell us the optimal level of output is higher, but this is simply due to the approximation. What we do know is that MR > MC at 9,800 and MR < MC at 10,125. Somewhere between there we would have had MR = MC and that would have been the profit maximizing size of the university.

Profit, Cost and Revenue Relationships: A Tabular Approach

The University's Finances: Revenue, Cost, and Profit

Students	Tuition	Total Revenue	Marginal Revenue	Total Cost	Average Cost	Marginal Cost	Total Profit	Marginal Profit
6700	10.2	68340		45000	6.72		23340
7300	10.1	73730	8.98	48500	6.64	5.83	25230	3.15
8000	10	80000	8.96	52000	6.50	5.00	28000	3.96
8775	9.9	86873	8.87	55500	6.32	4.52	31373	4.35
9800	9.8	96040	8.94	59000	6.02	3.41	37040	5.53
10125	9.7	98213	6.68	62500	6.17	10.77	35713	-4.08
10400	9.6	99840	5.92	66000	6.35	12.73	33840	-6.81
10625	9.5	100938	4.88	69500	6.54	15.56	31438	-10.68

Examples of some calculations:

$9.9 = at a tuition rate of $9,900, RIU will have 8,775 students
$80,000 = $80,000,000 total revenue when there are 8,000 students paying tuition of $10,000 each
$8.94 = $8,940 = marginal revenue of moving from 8775 to 9800 students = Drevenue/Doutput = ($96,040-$86,873)/(9800-8775) = (9,167/1025) = 8.94
$55,000 = $55,000,000 total cost of a university with 8775 students
$6.32 = $6,320 = average cost = cost per student of a university with 8,775 students = $55,500/8775 = $6.32
$4.52 = $4,520 = marginal cost of moving from 8000 to 8775 students = ($55,500-$52,000)/(8775-8000) = (3500/775) = $4.52
$35,713 = $35,713,000 total profit at 10,125 student = total revenue-total cost
$5.53 = $5,530 = marginal profit = (marginal revenue - marginal cost) = ($8.94 - $3.41) = $5.53

Profit, Cost and Revenue Relationships: A Graphical Approach

Total Cost, Revenue, and Profit

Marginal and Average Revenues, Costs, and Profit

Bottom Line: Any firm that wants to maximize profit should choose an output level - or a price for their product - in such a way that the follow the Optimal Choice Rule

Marginal Revenue = Marginal Cost

* in this example we would continue to expand as long as marginal revenue > marginal cost since this would mean profit would be increasing (revenue rising more than costs). In this simple example we would stop expanding the size of the school at 9800 students (when you look at the marginal analysis you see that it is at a size greater than 9,800 and less than 10,125)