Similarly, Jane must have valued her house at less than $800,000, otherwise she would not have been willing to accept this amount. Suppose she would have sold it for no less than $790,000. Then she benefits $10,000 from the sale.
So, the total benefit of the transaction to Kiwis is $20,000, split evenly between the buyer and the seller.
Now suppose instead that a foreigner, Fritz, had out-bid Kiwi John. To do this, he must have paid at least $810,001 since, by hypothesis, John was willing to spend up to $810,000. What is the benefit to New Zealanders in this case?
John is where he started, still with his $800,000 and without Jane's house. He gets no benefit from the sale of Jane's house to Fritz. But Jane's benefit has risen from $10,000 to at least $20,001. Which means the total benefit to New Zealanders has increased by at least $1. (In reality, the net gain will usually be in the thousands.)
Mr Key does not need to look at data about how many Auckland houses are sold to foreign buyers to know that banning such sales is a bad policy. Foreign buyers make New Zealanders altogether better off. The more the better.
Of course, foreign buyers do not make all New Zealanders better off. If foreign Fritz had been banned from bidding, Kiwi John could have bought Jane's house for $800,000 and received a $10,000 benefit.
But that doesn't make the ban a good policy. We have already noted the most obvious reason. The ban provides this benefit for John by imposing a greater cost on Jane. He gets $10,000 and she loses at least $10,001. That may be OK with John and his mates. But it should not be OK with politicians who have no reason to care more about John than Jane.
The second reason should be obvious to both Labour and National politicians given their self-publicized concern for social justice. This way of providing John with a $10,000 benefit is unfair. It imposes the entire cost of a social policy on an arbitrarily selected group of people.
If the government wants to subsidize Kiwi home buyers, why not fund this subsidy from general taxation? This is the approach taken to funding most social policies.
Tertiary education subsidies are not extracted from those selling tertiary education. Healthcare subsidies are not extracted from people selling healthcare. Why should the cost of subsidizing Kiwi home buyers fall just on Kiwis who now own homes?
And on foreigners.
In my simple example, the benefit to New Zealanders is $20,000 when Kiwi John buys Jane's house and $20,001 when foreign Fritz buys it at his lowest possible price. But that is not the total benefit when Fritz buys because we have not counted his consumer surplus. Fritz must value the house at more than the $810,001.
If you count only New Zealanders, the ban is harmful. But if you count everyone, including foreigners, the policy is even worse. The ban would deny Fritz the consumer surplus he otherwise would have gained.
The policy is not racist, as some have suggested; a ban on foreign buyers would impose costs on people of all races. But it is xenophobic. It aims to fund a subsidy for a group of New Zealanders by imposing a cost on people for no reason except that they are foreigners.
Demand for Auckland residential properties and, hence, their price could be reduced by any material restriction on the people allowed to buy it. Ban grandparents. Ban women. Ban anyone over 180cms tall.
No politician would suggest such a thing. But why not? What is the relevant difference between foreigners and these arbitrarily chosen groups of Kiwis?
The answer is simple if ugly. Grandparents, women and tall Kiwis can all vote in New Zealand. Foreigners cannot. And, except in extreme cases, Kiwi voters don't care if our government harms foreigners. Xenophobic policies that appear to benefit Kiwis will always be attractive to vote seeking politicians.
Or pragmatic politicians, as they like to call themselves.
Jamie Whyte is a former leader of the Act Party and is managing director of
Whyte & Associates