The Long-run Supply Curve for Higher Education

In one of his many random thoughts, Tom Sowell wonders [h/t to Hispanic Pundit],

If the government gave a $5,000 subsidy to anyone who buys an automobile, do you doubt that the price of automobiles would go up -- perhaps by $5,000? Why then does no one see any connection between government subsidies to college students and rising tuition?

This is a good question for introductory economics students.

Cross your fingers and hope they don't give Sowell's "perhaps" answer, which implies vertical long-run supply curves for both automobiles and higher education. There's no perhaps about it; the price would not rise by $5000 in the long run because additional resources would flow from other activities into producing automobiles or higher education.

At the same time, if we believe in scarcity, we know the prices would rise by some amount. Contrary to our textbook assumptions of "constant cost industries", long-run supply curves are upward sloping; and so if demand increases, the equilbrium price must rise, even in the long-run. But surely not by $5000.