During the past few days, I have written extensively on the reasoning behind why society would wish to create a licensing arrangement for some professions. Today, I will review Hayne Leland’s 1979 paper which develops a mathematical model which explicitly describes the welfare implications of licensure.
Model
Leland uses a Akerlof style set-up where the seller knows the quality of their product, but the buyer does not. Thus, low-quality physicians have no incentive to lower their prices since lowering their price will signal to the buyers that they are low quality. Sellers can disguise their quality level simply by pricing at the average quality price. High quality physicians will not be able to charge a higher price since buyers cannot differentiate between high and low quality doctors. Thus, all physicians in the market must charge the same fees in equilibrium and this price will reflect the average quality of all medical services provided [see Akerlof 1970)]. The ideal remedy to this problem is to eliminate the informational asymmetry either through repeated interaction, certification, labeling, or a caveat venditor device. Leland assumes that these solutions prove too expensive in the case of physicians market and thus we are left with a classic Akerlofian framework.
Let us assume that f(q) is a function representing the potential supply of physicians at quality level q. Leland normalizes physician quality (‘q’) to a uniform distribution between 0 and 1 and thus f(q)=1. F(q) is equal to ∫q to 1 f(q’)dq which is equal to q in the uniform distribution case presented here. Finally we have R(q) which is an increasing, convex function of the opportunity costs to supply a unit of service of quality level q. The opportunity cost of quality must equal the supply price ‘ps‘.
Market supply (y) and average quality (q_bar) will thus be:
- [1] y = ∫0 to q’ f(q) dq = F(q’)=q’
- [2] q_bar = ∫0 to q’ qf(q)dq/F(q’) = q’/2
Consumers’ willingness to pay pd is a function of average quality (since it is impossible to distinguish between low and high quality doctors) as well as the market supply. So pd = p(q_bar,y). Substituting equations [1] and [2] into our demand equation we have pd=p(q’/2,q’). In equilibrium pd=ps so we have an equilibrium condition of:
- [3] R(q*)=p(q*/2,q*)
Welfare implications
Now we must determine how social welfare would change if we would change the quality level. Net benefits are measured using the Dupuit model and are calculated as follows:
- [4] W= ∫0 to y p(q_bar,y’) dy’ – ∫0 to q’ R(q)dq
Leland shows that
- [5] dW/dq|q=q*= .5*∫0 to q pq(q_bar,y’)dy’ > 0
Thus, in the case of asymmetric information, welfare would be enhanced by increasing quality.
Adding Licensing to the model
If minimum quality standards ‘L‘ were imposed, than it is easy to show that y=(q’-L) and q_bar=.5(q’+L). Our new equilibrium condition becomes:
- [3]’ p[.5(q*+L),(q*-L)]=R(q*)
What are the welfare effects? Are new social welfare equation becomes:
- [4]’ W= ∫0 to (q’-L) p(q_bar,y’) dy’ – ∫L to q’ R(q)dq
When we calculate dW/dL, the sign is uncertain. Licensure will create some benefits at first, but too much licensure will cause society to incur unnecessary costs from restricted physician supply. Leland shows that in the general case dW/dL|L=0>0. That is some licensure is always welfare improving in the case of fully asymmetric information.
Conclusion
The major qualitative points derived from this math are that licensure is most beneficial when: 1) markets are more sensitive to quality variation, 2) there is a low demand elasticity, and 3) the market has a low marginal cost of providing quality. In the case of medicine, it is likely that demand is sensitive to quality and there is a demand elasticity below 1 in magnitude, but it is unlikely that the cost of providing quality is inexpensive. Leland also extends his model to include when the level of licensure ‘L’ is chosen endogenously by the a professional group who is attempting to maximize profits of the group. When the level of licensure is chosen by a professional group, the level of ‘L’ is most often set to high or too low.
This model is elegant and shows that licensure can be beneficial. Leland acknowledges, however, that even if licensure is welfare improving, other options such as certification would likely be Pareto superior. What this paper concludes is that licensure can be beneficial, but is not necessarily optimal in light of other policy options available to society.
- Leland (1979) “Quacks, lemons and licensing: A theory of minimum quality standards” JPE, vol 87(6), pp. 1328-1346.