In this post, I'm going to use some fairly simple comparative statics to look at the probably effects of the two policy approaches. I'm putting aside the issue of whether there is a 'housing affordability crisis' at all (incidentally, I have an MBA student looking at that question at the moment - my take is that it depends on how you define 'crisis', hence the quotation marks), and let's assume that there is a crisis and it needs to be 'solved' somehow.
The policiesThe National government is proposing that "grants for first-home buyers will be increased from $10,000 to $20,000 for a couple buying a newly built home". This approach is a straight out subsidy, effectively being paid to the buyers (but which, of course, will be passed onto the firm selling the newly-constructed home). Subsidies are a market-based solution, because the government isn't intervening directly in the market but simply changing the incentives for buyers and sellers.
In contrast, the Labour opposition is proposing to "build 100,000 new, affordable homes over ten years and sell them at cost to new home buyers". This approach is a more direct intervention in the market for new housing, since the government would be constructing houses itself (or presumably, through some intermediary - likely drawn from the same set of large firms that would benefit most from the subsidy offered by National).
Let's start with National's housing subsidy, and for simplicity let's ignore that there is already a subsidy in place for new home buyers, and that this policy simply increases the existing subsidy. Before we lay out the comparative static results, we need to recognise an important feature of the market for housing. That feature is that the supply of housing is relatively less elastic than the demand for housing, especially in the short run. In other words, if the price of housing increases supply will not respond quickly and the number of new homes will not increase by a lot. This is because it takes a long time to develop new housing, get building permits, complete construction, etc. In contrast, the number of buyers wanting to purchases will decrease almost immediately if price rises (or increase immediately if price falls).
The effect of the (increased) housing subsidy is shown in Figure 1 below. Demand for new housing is initially D0, and the subsidy induces increased demand for housing - this isn't a 'true' increase in demand since it would not exist without the subsidy, so we show this with the new curve D+subsidy. The price of new housing is initially P0, but once the subsidy is implemented the price for sellers increases to PP, and the effective price for buyers (after subtracting the subsidy) falls to PC. The higher price for sellers induces them to provide more new housing, while the lower effective price for buyers encourages them to buy more new housing. Everyone wins!
Everyone, that is, except the taxpayer. When we consider the welfare effects of the policy, the consumer surplus has increased from GEP0 to GBC (so buyers are better off), and the producer surplus has increased from P0EH to FDH (so sellers are better off), but the area of the subsidy (FDBC) is being provided into this market by taxpayers (which makes them worse off). Total welfare has decreased as a result of the subsidy (from GEH to GEH-EDB). That is, there is a deadweight loss of EDB.
So, the policy results in a transfer from taxpayers to new home buyers and new home sellers. But even worse than that, because the supply curve is much less elastic in the short run than the demand curve, the sellers gain most of the benefit from the subsidy. You can see this from the relative change in prices - the price for sellers increases by relatively more than the price for buyers decreases. You can also see this in the change in welfare - the consumer surplus increases by just P0EBC, whereas the producer surplus increases by FDEP0 (of course, I have exaggerated the difference in elasticity between demand and supply, but the difference is still likely to be large). This policy makes home construction firms much better off. Little wonder then that builders are hugely in favour of it.
So, what about Labour's policy alternative? Building more houses directly increases the supply of new housing. This should lower the price of new housing, and increase the number of new houses. Housing affordability is solved and everyone's a winner, right? Not so fast - if it was that easy, both parties would be advocating this solution, and it would already have been done.
What this policy is describing isn't an increase in supply of new housing though - it is an increase in quantity of new housing supplied. This might seem like a semantic difference, but the difference is critical. There is no increase in capacity for constructing new houses and no new construction firms entering the market, so the supply curve remains unchanged. The effect is shown in Figure 2 below. The quantity of new houses being sold increases from Q0 to QD (which is Q0 plus 100,000 additional new homes). In order to induce buyers to buy the additional homes, the price must fall from P0 to P1. (Note: as above, the price only needs to fall a small amount in order to increase quantity demanded by a lot, as potential buyers are prepared to move into the market). At this lower price though, construction firms want to produce fewer homes, so the quantity of new homes supplied falls to QS. The difference between QD and QS is excess supply, but this excess supply is met by the government. Notice that the government would need to build much more than 100,000 new homes in order to increase quantity supplied by 100,000 - because they would need to also make up for the fewer homes that the construction firms want to produce at the lower price.
What about the welfare effects? The consumer surplus increases from GEP0 to GBP1, but the producer surplus decreases from P0EH to P1JH, which is why builders are much less in favour of this policy. The government is intervening in the market, and all houses between QS and QD are actually being sold at a price below the marginal cost of production. The taxpayer loses the area JDB. Total welfare decreases from GEH to GEH-EDB. That is, there is a deadweight loss of EDB.
Now, I've had to make an additional assumption here, and that is that the houses cannot be sold 'at cost'. At least, not as economists interpret 'at cost', which includes all of the implicit (opportunity) costs of production (in addition to all the direct monetary costs). Otherwise, the marginal cost of the last house is much higher than the current market price - besides which, the market operating at equilibrium already delivers the marginal house 'at cost'.
Comparing the policies
Now, if you compare Figure 1 and Figure 2, you will notice that the areas of deadweight loss are very similar. In fact, if the HomeStart subsidy increased the number of new houses constructed by exactly 100,000 then the size of the deadweight loss would likely be identical for both policies.
And the second-order effects of the policies would be the same if the number of additional homes constructed was the same. That is, increased construction increases the demand for construction materials, and raises their prices. Lower prices for buyers of new housing decreases the demand for existing housing and lowers the price there. And so on.
So, how to choose between the policies?
If both policies induce the same deadweight loss for the same increase in housing (which seems plausible given the simple comparative statics above), and both have the same second-order effects (again plausible if they increase housing by the same amount), then any difference must come down to the costs of administering the policies. If Labour actually intends to build houses themselves (through some subcontracting arrangement), it seems clear to me that the administrative costs of increasing the HomeStart subsidy would be lower. After all, not much in the way of additional bureaucracy would be required since the market is providing the services. Whereas with Labour's approach, new bureaucratic processes would be required (in order to pay subcontractors, sell the newly constructed homes, etc.).
So, if there is a 'crisis' to be solved here, and these are the two options on the table, I would be more in favour of the subsidy approach. Of course, simply lowering the costs of supplying new housing through freeing up land and easing development restrictions, would probably be even more effective.