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Wrapping
Insurance
Moral Hazard
Demand
Price
• With health insurance,
the amount of
expenditures may
depend on whether you
have insurance.
• Suppose that probability
of illness is 0.5.
• Suppose demand for
care (if sick) is P1Q1.
• Actuarially fair policy
would cost 0.5*P1Q1.
P1
Exp.
Premium
Quantity
Q1
Moral Hazard
• What if demand was
somewhat elastic?
• What if insurer charges
0.5*P1Q2?
• Customer may not buy
insurance.
Price
• If insurer charges 0.5*P1Q1,
it will lose money.
• Why, because expected
payments are P1Q2.
Demand
P1
Exp.
Premium
New Premium
Quantity
Q1
Q2
Why pay $2,250 for event
w/ probability of 0.5, and
expected expenditures of
$2,500? May self insure.
Moral Hazard – Some Numbers
• Suppose that P1 = $500, Q1
= 5, and Q2 = 9.
• Without insurance, if ill,
people would spend $2,500.
Price
• If insurer charges 0.5*P1Q1 =
½ * 500 * 5, or $1,250, it will
lose money.
• Why, because expected
payments are P1Q2 = $4,500
• What if insurer charges
0.5*P1Q2 = $2,250?
Demand
P1
500
Exp.
Premium
New Premium
Quantity
Q1
5
Q2
9
Moral Hazard
• Why?
• Two dimensions to insurance
– Premium against risk. Customer wishes to
insure against this.
– Extra resource cost due to moral hazard.
The risk was P1Q1. Customer may not be
willing to pay more to insure against that
risk!
Let’s Review Coinsurance
Effective demand 40
30
Money Price
30
20
Effective Price
• Suppose a
visit costs $20.
• BUT,
insurance pays
50%.
40
20
Money price demand
10
10
Visits
What Does Moral Hazard Do?
• It makes us spend too much
on medical care.
Demand w/
insurance
Price
• At P1, we buy Q1 and
spend E1.
• With insurance, we pay
LESS than full price, so we
buy Q2, spend E2. This is
P1 (Q2 - Q1) more than we
spent before.
• Why is it too much?
Demand
P1
Exp.
Quantity
Q1
Q2
What Does Moral Hazard Do?
• Why is it too much? We
paid P1 (Q2 - Q1) more.
Demand w/
insurance
Price
• The demand curve tells us
what the care is worth to
us. So the additional (Q2 Q1) is worth:
Demand
P1
Wasted
Exp.
Value
• The “wasted” expenditures
are:
Quantity
Q1
Q2
For the Entire Economy it’s WORSE
• The demand curve tells us
what the care is worth to
us. So the additional (Q2 Q1) is worth:
Demand
Price
• Why is it too much? We
paid P1 (Q2 - Q1) more.
P2
P1
Demand w/
insurance
Producer
Surplus
Wasted
Exp.
Supply
Value
• The “wasted” expenditures
are:
Quantity
Q1
Q2
Area of Triangle = ½ * b * h
Area of Trapezoid = ½ * h * (b1 + b2)
Calculating
Demand
Price
Let:
Q1 = 10, Q2 = 12, Q3 = 14
P1 = 10
12
P2 = 12
10
E1 = 10*10 = 100
E2 = 12*12 = 144
PS = ½ * 2 * (10 + 12) = 22
Val = ½ * 2 * (10 + 5) = 15
Loss = ½ * 7 * 2 = 7
P2
P1
Demand w/
insurance
Producer
Surplus
Wasted
Exp.
Supply
Quantity
Value
Q1
Q2
Q3
10
12
14
Who pays for health
insurance?
• It is important to relate health insurance benefits to
the wage rate that workers are paid.
• The simplest way is to examine the supply and
demand for labor, in the absence of insurance, and
then institute health insurance and see what
happens.
Who pays?
Wage rate
• Consider a labor market with a
typically downward sloping
demand for labor D,
• and a typically upward sloping
supply of labor S.
• The demand for labor is related
to the marginal productivity of
workers. Employers will hire
the workers as long as the
value of their output (marginal
revenue product) is greater
than or equal to the wage that
employers must pay them.
S
W1
D
L1
Employees
Who pays?
Wage rate
• The supply of workers is
related to the wage in this
industry relative to other
industries.
• Workers will choose to
work in this industry as
long as the wage they can
earn exceeds their
opportunities in other jobs.
• The equilibrium wage is
W1 and the equilibrium
quantity of labor
demanded and supplied is
L1 .
S
W1
D
L1
Employees
Who pays?
Wage rate
• Now suppose that workers in
the market negotiate a health
insurance benefit worth
$2/hour at that margin, and
costs employers exactly
$2/hour to provide.
• What happens?
• Employers who before were
willing to pay W1 per hour for
workers, will now pay W1 less
$2. Other points on the
demand curve will shift
downward in a similar manner,
so the demand curve will shift
downward by exactly $2 to D.
S
W1
D
2
D
L1
Employees
Who pays?
Wage rate
• What will happen to the
supply curve?
• Since the workers were
willing to supply various
amounts of labor at various
wage rates according to the
supply curve before, now
that they are receiving a
benefit worth $2, they will
offer their labor for $2 less.
• Hence, the supply curve will
shift downward by exactly
$2 to S.
S
S
2
W1
D
2
D
L1
Employees
Who pays?
Wage rate
• New equilibrium is at L1, W2.
• What is the result? The net
wage remains the same, but
the money wage falls by $2.
• The equilibrium wage has
fallen to W2 or by exactly the
amount of the benefit.
• Workers have taken their
benefits in lower money
wages, and the same number
of workers L1 is employed at
the same net wage.
S
S
2
W1
Benefits
W2
Wage
Bill
L1
Employees
D
2
D
Who pays?
S
Wage rate
• By assuming that the marginal
benefit was worth exactly what it
cost to provide, the previous
example ignored the moral
hazard involved in health
insurance.
• Recall that for many types of
health care, fractional
coinsurance leads consumers to
consume health care past the
point at which marginal benefits
equal marginal costs.
• This provides benefits that, on
average, may be worth less to
the workers than what they cost
to provide.
S
2
W1
W2
D
2
D
L1
Employees
Who pays?
S
Wage rate
• Suppose, for example, that
workers negotiate subsidized
coverage for prescription drugs.
This benefit might induce workers
to purchase drugs beyond the
point at which marginal benefits
equal marginal costs.
• If the average benefit is worth
$b/hour, or less to the workers
than the $2/hour that it costs to
provide, then the new supply of
labor curve S will have fallen by
less than the demand for labor
(still D, reflecting what it costs to
provide the benefit).
S
b
2
W1
W3
W2
D
2
D
L2 L 1
Employees
Who pays?
Wage rate
• Our new equilibrium
yields wage W3, which is
higher than W2.
• The net wage (W3 + 2) is
higher than the original
equilibrium wage W1
(without insurance).
• Not surprisingly,
employers react to the
higher net wage by
reducing employment in
the industry from L1 to
L2 .
S
S
b
2
W3+z
W1
W3
W2
D
2
D
L2 L 1
Employees
In MI, minimum wage is
$8.15/hr.
What happens with
“mandated benefits?”
Workers can’t take pay
cut even if they wish
to.
It is likely that this will
lead to unemployment
L 1 – L 2.
Wage rate
Minimum Wage
S
$8.15
D
D
L2
L1
Employees
So … who pays?
• Fundamentally, the employees pay for
insurance, in the form of lower money
wages.
• Some may pay in the form of
unemployment.