A government can be cost-efficient but have poor allocative efficiency. Cost efficiency achieves the maximum health benefit at a given cost while allocative efficiency maximizes the health of society by achieving the right mixture of health goods and services according to preferences.

Say for example the government wants to produce more midwives under a national scholarship program to address the lack of health care professionals in community health care settings, particularly in BEMONC facilities. The choice of producing more midwives gained traction because it was perceived as relatively cheaper than producing medical doctors. If the cost of producing one midwife is 150,000, the cost of producing one doctor is 200,000 and the budget is 100,000,000, the government will have to look for a combination of inputs that results in the maximum output at minimal costs in order to be cost-efficient.

Figure 1. Number of midwives and doctors produced

Figure 2. Allocative efficiency of producing midwives

The red points in the first graph (Figure 1) shows different combinations at which the production of midwives and doctors are technically efficient. The green point shows the maximum number of midwives and doctors that can be produced at the given budget of 100,000,000. In this example, the government is cost-efficient if it produces 400 midwives and 200 doctors.

While producing these numbers of midwives and doctors are said to be cost-efficient, it would not immediately mean that the action depicts allocative efficiency. This type of efficiency occurs when goods (midwives/doctors) are distributed or allocated according to consumer preferences. Usually, allocative efficiency is seen as an output level where price (P) is equal to the marginal cost (MC) of production because the willingness to pay is equivalent to the marginal utility derived from the good consumed. Thus, the optimal distribution is achieved when marginal utility (MU) equals marginal cost.

At an output of 100, the marginal cost of the good is roughly 100 (Figure 2). But at is this output, society is willing to pay a price of 600. Therefore, society is said to be under-producing midwives. At an output of 500, the marginal cost is 600, but society is willing to pay only 100. Thus, society is said to be over-producing midwives. In this example, allocative efficiency will occur at a price of 350 with an output of 300. This is the point where the marginal cost is equal to marginal utility.