iii. Scarcity - a theoretical approach

Scarcity has two sides: the infinite nature of human wants and the finite or limited nature of resources available to produce goods and services. We can explore this idea theoretically by using what economists call a Production Possibility Frontier (PPF).

PPFs in health care

Let us start by looking at the production of health care within a single hospital and in particular at the ability of a specific hospital unit to carry out surgical procedures such as heart bypass operations. Suppose the heart bypass unit has 10 surgeons working in it, and assume that the only factor which affects the quantity of operations provided is the number of surgeons assigned to them.

(Figure A)(Figure B)

If all the surgeons are assigned to heart bypass operations then the unit can carry out 50 heart operations per week (see Figure A). If, on the other hand, all the surgeons are assigned to other operations, then the unit can carry out 50 of these other operations per week (see Figure B). Graphs A-F show the production possibility frontier for this unit. The graph charts all the possible maximum combinations of operations that the unit can achieve given the quantity and productivity of resources available.

The shape of the graph

(Figure C) (Figure D)

What determines the shape of the graph? Look at Figure C. It is a straight line, with a gradient of -1. This reflects the fact that if we transfer one surgeon to heart bypass from other operations, we get five more heart bypasses but we lose five of the other operations, i.e. the trade-off between the two possibilities is one to one (see Figure D). This is what is called the marginal rate of transformation, MRT.

In fact it is highly unlikely that the marginal rate of transformation would be constant. The surgeons carrying out heart bypass operations would be working with a fixed quantity of operating theatres, heart monitors, and other inputs. So the more surgeons carrying out bypass operations, the less equipment each one would have. Therefore, the output per surgeon would fall.

So, the number of additional bypass operations carried out by an extra surgeon is different depending on how many surgeons are already doing bypasses. If there are already a lot of surgeons doing bypass operations, the extra one creates only a small increase (see Figure E) in the number of bypass operations. This bends the line downwards, making it concave. This increase is smaller than if there were only a few surgeons (see Figure F) already doing bypass operations.

(Figure E)(Figure F)

This phenomenon is called the Law of Diminishing Returns and makes (see Figure G) the PPF concave to the origin (like Figure H).

(Figure G)  (Figure H)

Efficiency

Now look at point A in Figure I. It corresponds to 14 bypass operations combined with 10 other operations. This lies within the PPF in this case (the curve passing through points B and C). Clearly this is a possible combination in the sense that the hospital has enough resources to achieve it, but is it an efficient combination? What do we mean by efficient?

(Figure I)(Figure J)
 
The definition of efficiency used by economists is named after the Italian economist, Vilfredo Pareto, who formulated it. He said that an allocation of resources is efficient if it is impossible to change that allocation to make one person better off without making someone else worse off. Look at combination A again (Figure I). Obviously it would be possible to re-organise the hospital's resources to increase the number of other operations without having to reduce the number of heart operations. This is shown by point B on Figure J. Moving from combination A to combination B is clearly in society's interests: we are getting an extra four other operations, i.e. more medical care from our scarce resources.

Opportunity cost

(Figure K)

In fact at point B (Figure J) we are getting a maximum combination possible, given the resources we have. It is a Pareto efficient allocation. If we choose to move from combination B to combination C (Figure K), then although we are getting five more bypass operations this has been at the expense of nine other operations. Thus moving from combination B to C involves a cost, which economists call an opportunity cost. Formally, this is defined as the benefit given up by not choosing the next best alternative. In this case the opportunity cost of moving from point B to C is nine other operations (Figure L). All combinations which lie on a PPF are, by definition, pareto efficient.

(Figure L)