San José State University
Department of Economics
Thayer Watkins
Silicon Valley
& Tornado Alley

The Effects of Group Payment versus
Individual Payment on Demand and Prices in
Competitive and Monopolistic Markets

For John San Filippo

The purpose of this material is to explain how binding the spending of a group of people together results in an artificially elevated demand compared to what it is when the same people make their choices and payments individually. Consider a group of people going to a restaurant and instead of requiring individual checks they agree to divide the total bill equally among the members of the group. For people who are family or close friends this arrangement probably would not be abused, but among strangers there may well be some who would not have ordered steak or lobster or steak-and-lobster who choose to do so when the bill is split evenly. In fact they may all order more than they would have with individual payments. The arrangement results in an increase in demand.

This example is easy to understand but the real target of the analysis is the so-called insurance programs for healthcare. The term Insurance should be applied only to insuring against unavoidable and unpredictable risks. Typically health insurance covers this but also includes coverage for routine and predictable services. It is this latter part that is the source of problems. The nature of the problem is the same as the restaurant example.

Let n be the number of consumers in a group expenditure program. Let their identical individual demand functions be

q = a − bp + cy

where q is the quantity demanded, p is the price to the consumer, y is consumer disposable income and {a, b, c} are constants characterisitic of the consumer. The market demand QD is just nq.

On the supply side let us suppose for now there is a supply function of the form

QS = −d + ep
for p>d/e and zero otherwise

Under conditions of competition the market determines an equilibrium market price peq as shown below for arbitrary units. The number of consumers is 10.

The equilibrium price is 8 in the example.

The algebraic solution is given by:

n(a − bp + cy) = −d + epeq
which reduces to
n(a+cy) + d = (nb+e)peq
and thus
peq = [n(a+cy) + d]/(nb+e)
and the equilibrium quantity being
Q = d + e[n(a+cy) + d]/(nb+e)

If a poll or income tax t is imposed then the equilibrium is altered and the equilibrium price is reduced to

peq = [n(a+c(y-t)) + d]/(nb+e)

Now consider what happens when the total expenditure is divided equally. An individual consumer experiences only a price of p/n and thus the quantity demanded is based upon p/n rather than p. The cost of the other (n-1) consumers' purchases is like a tax being deducted from disposable income. Thus the quantity demanded by one individual is

q = a − p/n + c(y−(n-1)q)

The solution for the equilibrium price is matter of solving the two equations

Q = n[a −bp/n + c(y-(n-1)Q/n]
Q = −d + eQ

This is facilitated by solving the first equation for Q. This works out to be

Q(1+c(n-1)/n) = n(a + cy) − bp
and hence
Q = n(a+cy)/(1+c(n-1)/n) − [b/(1+c(n-1)/n)]p

Thus the solution is

peq' = [n(a+cy)/(1+c(n-1)/n) + d]/[b/(1+c(n-1)/n) +e]
or, upon multiplying numerator and denominator by (1+c(n-1)/n)
peq' = [n(a+cy) + d]/[b +e(1+c(n-1)/n)]

The solutions can be put into a more comparable form by multiplying the numerator and denominator of the last equation by n. The equilibrium prices take the form

peq = [n(a+c(y-t)) + d]/(nb+e)
peq' = n[n(a+cy) + d]/[nb +e+ec(n-1))]

The numerator for the group demand is increased by a factor of n and the denominator is increased by the quantity ec(n-1).

The graph below shows the case of the group demand in comparison to the case for individual payment. The scale had to be increased significantly.

The equilibrium price went from 8 to slightly under 20. The quantity demanded at a price of zero should be the same in both cases. The effects of a unit increase in price are for individual payment are ten times greater than for the case of group payment. The consumers in the group payment case are increasing their consumption up to the point where their marginal benefit is equal to p/n; this is generally less than the marginal social costs of production. There therefore must be a net social loss involved in this arrangement of group payment.

As bad as this result is in terms of social efficiency the actual situation is even worse. The medical establishment has been running a cartel for about a century by artificially restricting the production of physicians. A cartel functions like a monopoly; i.e., the quantity supplied is adjusted to maximize the profits of the cartel participants.

Monopoly Pricing

For the case of a straight line demand function and a constant marginal cost the price that maximizes profit is the average of the marginal cost and the price that reduces the quantity demanded to zero, call this price pmax. In the case of the example max is 10. In the example it was assumed that none of the good or service would be provided unless the price was above 4, so let 4 is the marginal cost.

Thus the monopoly price when there is individual payment would be ½(10+4)=7. (This is lower than the equilibrium price found in the example because an arbitrary short run supply curve was assumed.)

For individual payment demand the quantity does not go to zero until the price equals 10. For the group payment case an individual consumer does not experience a price of 10 until the price is 100 so 100/10=0. Thus the pmax for the group payment case is 100. The cartel would then maximize profits at a price of ½(100+4)=52. Thus for the example the group payment arrangement increased the price by a factor of over 7 to 1.

The practice of putting the payment for routine and predictable medical services into a group payment arrangement and charging a minimal co-payment artificially stimulated demand for those services and the medical cartels raised prices exorbitantly making it seem that one has to have this so-called "insurance" to be able to afford medical care. The creation of this "insurance" came when the Federal Government allowed employers to count for tax purposes the payments made for emplyee medical plans but did not require the employees to pay taxes on these benefits.

The solution to the problem is to break the hold of medical cartel on the number of medical personnel trained. The U.S. should be exporting doctors instead of importing them.

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