Imagine that the government announces a new policy giving a $1,000 scholarship to every student who attends a local community college.
In order to calculate the MVPF of this policy, we begin by calculating the net cost of the policy, the denominator in the MVPF ratio.
Let’s imagine that 100 students were always planning on attending the community college next year, regardless of the scholarship opportunity.
The government pays $1,000 to each of those students to help with their tuition costs. That means the policy initially costs $100,000.
Now let’s imagine that scholarship also convinces 20 students to attend college. Those students were planning on stopping school after high school, but now decide to pursue more education.
So, the government also spends $1,000 on scholarships for those students and the cost of the policy rises from $100,000 to $120,000.
Now we’ve calculated the short-run costs of this policy, but the MVPF requires we calculate the long-run costs.
As the result of the scholarship, 20 new students have received an education that will pay off in the long-run.
Community college helps to increase wages. So, let’s assume that each new student now earns an additional $15,000 as the result of their additional education.
Summed across the 20 new students, the policy will raise wages by $300,000.
If those new students pay a 20% tax rate on their earnings, the government receive $60,000 in additional tax revenue from those students.
So, while the upfront cost of the scholarship is $120,000, the government recoups $60,000 in the form of taxes paid and the long-run costs are just $60,000.
That $60,000 cost is the number that goes in the denominator of the MVPF.
Now we have the denominator of the MVPF and we turn our attention to the numerator, the “willingness to pay.”
For the 100 students who were always going to attend college, the willingness-to-pay is simple. The government has given them $100,000 scholarship funds collectively and so their willingness-to-pay is $100,000.
For the 20 new students, we calculate the willingness-to-pay they would have after having realized the impact of the policy on their bottom-line. We discussed above that the policy increased student earnings by $300,000 before taxes.
After taxes, those students walked away with $240,000.
So, we say that their willingness-to-pay is $240,000. When we add their willingness-to-pay with the willingness-to-pay of initial 100 students, we get that total willingness-to-pay is $340,000.
Now we’re ready to calculate the MVPF of this policy
We calculated that willingness-to-pay was $340,000. We calculated that costs were $60,000. Putting that together, we get an MVPF of approximately 5.67.
In other words, this scholarship program provides nearly $5.67 in benefits for each $1 the government spends on the program.
As you might expect, calculating the MVPF in the real world is a bit more complicated. Calculating costs or willingness-to-pay can take many more steps.
Moreover, all MVPF estimates come with statistical uncertainty that needs to be incorporated.