What comes first to increase college tuition for all---increasing costs or increasing subsidies?

This graph shows the rise in cost of attending college, public and private, since 1980.  It is in the form of an price index where the year 1980 is 100. and currently we are at 359, which means there has been a 259% increase in the cost of college tuition to a public university.  Notice as we reach the 2000's the slope of the graph increases considerably, indicating the cost of college is increasing at an increasing rate. Why? Lots or reasons, but subsidies to students have grown considerably.

WSJ...""But the federal government gave out $28.2 billion in Pell grants to students in the 2009-10 school year, almost $10 billion more than the previous year. Pell grant numbers for the current school year are not yet available, but are expected to rise.
Federal grants, including Pell and veteran's benefits, accounted for 44% of the $94 billion in total grant money awarded to students in the 2009-10 school year, compared with 34% the previous year, according to the data. Ten years ago, federal grants represented 29% of the total. The other major sources of grants are colleges and universities, and employers...""

The writer quoted below is commenting on an excerpt from THIS WSJ article about rising college tuition. It reminds me of the chicken and egg conundrum of what comes first.

""From The Enterprise Blog: ""College tuition and fees climbed once again this year, but the burden was tempered for some students and their families by a big jump in federal aid…""

Correct me if I’m wrong, but couldn’t it just as easily have been written:

""Federal aid for college climbed once again this year, but the help was tempered for some students and their families by a big jump in college tuition and fees…""

Hypothetical: I have my own college and I call it "Hayward University" or as it is better known, "Hay, YOU!" (look at the photo above--yes, we are all about the athletics!).  In the short run, there are a fixed number of seats available for college students at my university to meet existing demand.  I currently have 5,000 seats and no plans to expand.  The Supply curve for the seats is vertical at 5000 seats. No matter what the tuition is, I ONLY have 5,000 seats to offer.  I am a captive of the Demand curve!

The Demand curve for those seats is downward sloping to reflect the inverse relationship between price and quantity demanded. The Demand curve intersects the Supply curve at $10,000 per year tuition for each of my 5,000 seats. See graph below that illustrates this equilbrium:

Assume my students become aware they are now eligible for additional student aid in the form of a $1,000 subsidy (Pell Grant et al). So, now instead of paying $10,000 tuition, each student now only has to pay $9,000.  At $9,000 the quantity demand for seats to my school is 6,000 (Point "B").  So, now my quantity demanded (6,000) exceeds my quantity supplied (5,000).  The lower the tuition, the more students want to come to my campus.  I am out of equilibrium.  As shown below, I NOW have a shortage of seats relative to the quantity demanded (Point "B").  How do market forces take care of this? 

The price will increase along the demand curve (as price increases, the quantity demanded decreases) from Point "B" back to Point "A".  Right where we started:

BUT, that is not the end of the story. We cannot forget about the $1,000 subsidy.  Well, I GET THAT TOO!  The market tuition returns to $10,000 PLUS the subsidy---$11,000 to attend my school:

What is true at $10,000 tuition and quantity supplied of 5,000 seats is going to be true at every tuition price and quantity demanded of seats RELATIVE to the original Demand curve. We find that the Demand curve shifts to the RIGHT:

Bottomline? Tuition in the end does not DECREASE and likely INCREASES,  nor do more students necessarily get additional access to college. Nice for me. I will start tuition rates NEXT year at $11,000 for subsidized students and non-subsidized students.

This comment from the article will not be to the liking of college administrators "like me"...

""But Patrick Callan, president of the National Center for Public Policy and Higher Education, said colleges and universities need to get tuition under control. He likened the trends in costs and federal aid to a treadmill, where prices rise, federal money gets pumped in, and costs increase again.
"Unless governors and legislatures stiffen their spines and not allow schools to pass so much of the cost on to families, we are never going to make a dent in access and affordability," said Mr. Callan, whose research group tracks higher-education issues. ""