Health Math: Grab Pencil, Paper, 1000 Knees.

With the help of for-profit clinics, you can have your new knee in August instead of May. Good deal, eh?


Assume you have 10 orthopedic surgeons, and 1000 patients needing new knee joints. That's 100 knees per surgeon.

Assume each surgeon can do four patients a week, 208 per year, and he earns $2000 for each operation. Patient number 1000 will be done when? In week 25, mid-June. And each surgeon will earn how much for doing 100 knees? $200,000, for a total cost of $2 million.

Now, assume that profit-based clinics open to do knee joint replacements.

If one tenth of the patients opt for this service, paying $12,000 to have their knees fixed, of which the doctor might receive half, the cost for 1000 surgeries becomes $1.8 million public + $1.2 million private, or $3 million.

Each surgeon still only can do 208 knees per year, but in a private clinic he gets triple the income for the same work. Or, he can get the same salary, $200,000, for only thirty-odd knees. If we assume the doctors who do the for-profit surgeries all opt for this relaxing option, that loses the equivalent of three surgeons from the public system, the worst-case scenario.

We know that the supply of surgeons is effectively inelastic. So now, with the help of the private clinics, seven surgeons are lined up to do 900 knees, a worst-case 129 knees per public surgeon. They can still only do four per week. When does patient number 900 get her knee done? In the worst case, she gets it done in week 32, early August. When would patient 900 have gotten her new knee in the original system? Sometime in May.

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By reducing the load on the public system by 100 knees, we have increased the public users' waiting time by three months, and increased the overall cost for all 1,000 knees to $3 million from the original $2 million, of which $600,000 goes to “profit”, i.e., is wasted, at least from the surgeon’s and patient’s point of view.

So who wins in the for-profit scenario? Well, for a modest cost to Canadians of an extra $1 million, Health Canada can cut $200,000 from their knee budget. Profiteers can make a profit previously not available to them. Some surgeons, perhaps the cream of the surgeons, can benefit from smaller workloads and/or larger incomes. Some patients can get immediate care without the bother of driving to the Mayo Clinic or flying to India.

Who loses? People who cannot afford the private costs get to wait even longer than they are now. In addition, we would expect to see the overall pressure on the public system to be slightly increased because although the private clinics will be happy to lick off the cupcake frosting of knee surgery profits, I doubt they will be interested in scraping out the burnt muffin pan of follow-up care.