To recap, the government made this change effective from 1 January 2013. There was a fair amount of media coverage at the time (see here and here), and a 2014 editorial in the Journal of Primary Health Care (PDF).
What effects can we expect from this change? Well, first we need to consider the market for prescription medications. There are two aspects to this market: (1) the government (through Pharmac) negotiates prices directly with drug suppliers, then supplies the drugs to pharmacies at set wholesale prices (the wholesale market); and (2) the government maintains the retail price of prescription medicines by using a subsidy that is paid to the pharmacists (by District Health Boards), for the difference between the wholesale price and the retail price (which increased from $3 to $5) (the retail market). We know there must be a subsidy in the retail market because it is unlikely that the equilibrium retail price of prescription medicines would be as low as $3, and it is also unlikely that the low price is achieved through a price control otherwise we would observe excess demand.
So, considering the retail market only, an increase in the prescription price from $3 to $5 is essentially achieved through a decrease in the subsidy paid to the pharmacists. As shown in the diagram below, the supply curve without a subsidy is S, and the initial subsidy is shown by the curve S+subs. If there was no subsidy, the equilibrium price would be P0 (and the quantity of medicines sold and consumed would be Q0), but with the subsidy the consumer pays the price P1 ($3), and the pharmacist receives the effective price P2 (which is the $3 the consumer pays, plus the subsidy paid by the government), and the quantity of medicines sold and consumed increases to Q1.
Now consider the economic welfare effects. The consumer surplus is the difference between the price the consumers are willing to pay, and the price they actually pay. With no subsidy, consumer surplus is ABP0, but with the subsidy this increases to ACP1 (which makes sense - consumers consume more prescription medicines with the subsidy than without it, and pay a lower price for those medicines). The producer surplus is the difference between the effective price the pharmacists receive, and their costs (which are shown by the supply curve). With no subsidy, producer surplus is DBP0, but with the subsidy this increases to DEP2 (which again makes sense - producers sell more prescription medicines with the subsidy than without it, and receive a higher effective price for those medicines).
The value of the subsidy paid by the government per unit of medication is the difference between the effective price the pharmacists receive (P2) and the price the consumers pay (P1, or $3). The total cost to the government of the subsidy is this amount multiplied by the quantity of subsidised medicines sold (Q1), or the area P2ECP1.
Total economic welfare is made up of the consumer and producer surplus, minus the area of the subsidy. This is actually ABD-BEC. The area BEC is the deadweight loss of the subsidy, which arises because total economic welfare is actually maximised at the quantity where marginal social cost (MSC) is equal to marginal social benefit (MSB), which is at the quantity Q0, and the market is therefore trading too many medicines relative to this quantity. [*]
Now think about the effect of the decrease in subsidy, shown on the diagram below by the new curve S+subs2. Compared with the previous subsidy, the consumers pay a higher price (P3, or $5), the pharmacists receive a lower effective price P4, and the quantity of medicines traded decreases to Q2.
Now consider economic welfare. The consumer surplus with the new subsidy has decreased to AFP3, and the producer surplus has decreased to DGP4. The cost to the government has decreased to P4GFP3. Total economic welfare, on the other hand, has increased to ABD-BGF, with the smaller deadweight loss BGF.
So, considering this change we might expect to hear complaints from consumers, who were made worse off by the change. And indeed:
"A lot of people are saying it had to go up at some point, [but] $5 was too, too much for several people, especially with rent skyrocketing. For some people $3 is the limit - $5 is actually becoming quite considerable."We might expect to hear complaints from pharmacists too, who were also made worse off. And indeed, read the editorial from JPHC (the lead author is based at the School of Pharmacy at the University of Otago).
The cost to taxpayers decreases, and the government at the time argued that the savings would be reinvested into the health sector. Presumably the government felt that there were better value health care alternatives that the subsidy savings could be applied to. Without a careful analysis though, there is no way to evaluate this claim.
[*] From a strict utilitarian perspective the deadweight loss means that this subsidy is not a good idea. However, those who benefit most from the subsidy are likely to be people on low incomes (especially the chronically sick, the elderly, children, etc.), so the deadweight loss might alternatively be considered a reasonable cost of a transfer of wellbeing from taxpayers as a whole to these vulnerable groups.