6.h. A subsidy versus a Voucher
Public schools are financed with government subsidies. Primary schools normally receive a 100% subsidy, which reduces the price p rice paid by students to zero. Public universities receive a partial subsidy, which normally leaves the th e student paying a reduced price, but still a positive price. If education were not subsidized, students (or their parents) would purchase education on the private market, using their own money. mone y. But with publicly funded education, the government pays f or or the student’s education, using tax dollars that were paid by the student. The average student pays pa ys for his education either way, either with direct fees paid to a private school, or with tax dollars paid to a public school. But with public education, the student’s choices are limited to the schools provided by the government. Simple economic logic tells us that nobody nobod y will spend someone else’s money as carefully as they spend their own, so we would naturally expect that a system of government-run schools will be inferior to what privately-operated schools would provide. We might observe, for example, that public schools will be run more for the benefit of teachers than for students. Public financing of education is normally justified on the grounds of helping those students who are too poor to pay for an education. If there were no public schools, then poor people might save a little on their taxes, but would probably have to spend much more on private schools. Educational vouchers are sometimes proposed as a compromise measure between the inefficient, one-size-fits-all public school system, and a system of private schools that would be of higher quality, but unaffordable to the poor. Suppose, however, the government said to you: “If you relieve us of the expense of schooling your child, you will be given a voucher, a piece of paper redeemable for a designated sum of money, if, and only if, it is used to pay the cost of schooling your child at an an approved school.” The sum of money might be $2000, or it might be a lesser sum, say $1500 or $1000, in order to divide the savings between you and the other taxpayers. But whether the full amount or the lesser amount, it would remove at least a part of the financial penalty that now limits the freedom of parents to choose. (Friedman, Free to Choose, 1979, p. 150.)
y
y
Figure 6.h.1
Figure 6.h.2
270 voucher=$100 No Subsidy
170
170 C
yB Subsidy=$100
B
$100 Subsidy
A yD
$100 voucher
A
No voucher
D xB
x (Education)
x (Education)
The political issues surrounding educational financing are tangled a nd controversial, but some of the economic issues are straightforward enough that they can be described in a standard consumer choice diagram. In figure 6.h.1, a student who gets no subsidy to his education reaches a consumer’s optimum at a point like A. Paying a subsidy to education would make education cheaper, so the budget line would rotate outward as shown, leaving the student at a new optimum at point B. The diagram gives a handy way to find the amount of money the government spends on the subsidy. Note that at point B, the student is consuming XB units of education, and YB units of other goods Y. If the student had tried to consume XB units of education without the subsidy, he would have only been able to afford YD units of other goods Y. Thus, the distance from B to D (i.e., YB -YD) represents the number of units of y the government spends on the subsidy. If we assume that Y is a numeraire good, meaning Py =$1, and if we arbitrarily say the government is spending 100 units of y on the subsidy, then we can say that the government spends $100 subsidizing this student’s education. Figure 6.h.2 shows what would happen if the government spent the same $100 on a voucher, rather than a subsidy. A voucher that is redeemable for $100 worth of education is much like a cash gift of $100. For example, suppose that the students could have afforded, at most, 170 units of y without an y government help. A $100 cash gift would have increased the vertical intercept of his budget line from 170 to 270, as shown. The difference between a voucher and a cash gift is that the voucher cannot be spent on anything but education. So if the student could afford, at the most, 170 units of Y without the voucher, he is still limited to 170 units of Y with the voucher. This means that the voucher budget line can go no higher than the horizontal line at 170. In this case, the voucher moves the student’s optimum from point A to point C, the same as a cash gift.
y
Figure 6.h.3
270 $100 voucher 170
C
yB Subsidy= voucher=$100
B
$100 Subsidy
A yD
D xB
x (Education)
Figure 6.h.3 allows us to compare a subsidy with a voucher. As before, a $100 subsidy to education flattens the budget line, causing it to rotate outward as shown, and allowing the student to reach a new optimum at point B. But if the same $100 had instead been spent on a voucher, the budget line would have shifted up by $100 without changing its slope. This means that the voucher budget line shown must pass through point B, since we already know that B is $100 above the point D, on the original budget line. Note that the voucher budget line cuts through the indifference curve at point B, and allows the student to reach a higher indifference curve at point C. In other words, the student will always prefer a $100 voucher to a $100 subsidy! But since the voucher leaves the student consuming less education than the subsidy (C is to the left of B.), we would expect teachers to oppose vouchers, since the voucher would lead to less demand for teachers.
y
Figure 6.h.4
270 $100 voucher A
C
170 yB
B
$100 Subsidy
Subsidy= voucher=$100 yD
D xB
x (Education)
A voucher does not always leave the student consuming less education. Figure 6.h.4 shows the case of a student who, with no government assistance, chooses to consume no education. On the original, unsubsidized budget line (passing through points A and D), this consumer’s highest indifference curve is reached at point A, with the student consuming no education. This kind of optimum is known as a corner solution. A subsidy to education will cause the budget line to flatten as shown, but in this case the subsidy leaves the student at point A, still consuming no education in spite of the subsidy. The voucher, however, makes a higher indifference curve attainable at point C. In this case, it is the voucher that is more ‘effective’, in the sense that it causes the student to consume more education than the subsidy.
