El espacio metafórico

Due to the fact that Taiwan’s health care system is public and open to all people, the government is assumed to be the social planner. The government sets the premium R, the copayment rate c, and the payroll tax rate t of the national health insurance. In addition, I also assume homogeneity among individuals.

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The objective of the government is to choose the copayment rate c, the payroll tax rate t and premium R in order to maximize the individuals’ well-being (expected utility).8

RS GKxYzyzYzCD OH βU_J8 1 * βU 8 βI PβQβ (c,R.t)

Stewart (1994) assumed that an insurance company maximizes patient’s expected utility with respect to the copayment parameter. Here in my model, the insurer is Taiwanese government, and it considers this objective function subject to four difference constraints:

1. The patient’s individual budget constraint as in equation (1):

8 31 8 6 ∗ 7∗ 8 F 8 +, β 1 2. The government’s budget constraint in equation (5):

F 8 31 β1 * 67O∗βPβQβ

3. The constraint given by individual’s medical service optimization (F.O.C of equation (7))

678 +.

4. The constraint due to individual’s optimal unhealthy behavior in equation (9):

_{β β. * J. 8 βb+ J. a 8 1 * β?+ @.} * β J. Where _J 1 * 31 * 67* F * +, β 8 β, 1 * 31 * F * +β Therefore, the objective function of the government (insurer) to maximize individuals’ well-

being is:

8

61 RS GKxYKyzYzCD OHβH1 * 31 * 67 * F * +, β 8 β, I 8 6, 3, F 1 * β1 * 31 * F * +β 8 βIPβQβ (11) Subject to 8 31 8 6 ∗ | ∗ 8 F 8 +, β 1 F 8 31 β1 * 67O∗βPβQβ , 678 +. , and _{β β. * J. 8 βb+ J. a 8 1 * β?+ @.} * β J.

4.4.2 The effect of policy parameters on individual’s well-being

After substituting the government’s budget constraint, the new well-being expected utility function can be written as:

RS GKxYKyzYzCD OHβH1 * β1 * 67 * 67 * +, β 8 β, I 6, 3, F 81 * β1 * β1 * 67 * +β 8 βIPβQβ Where _J 1 * 31 * 67* F * +, β 8 β, 1 * 31 * F * +β With L 0, S}Q

L 0 , the F.O.C with respect to changes in copayment rate c can be derived as9

9

62 TU

L

OH*β7J8 β7βJ8 1 * β * β1 * 67=βJ8 1 *

β * β1 * 6 β=7βJ8 1 * βI PβQβ (12)

In equation (12) above, the first term is the marginal effect of decreasing medical spending for patients, the second term is marginal indirect effect of medical spending on individuals, the third term is the indirect effect from individual’s the premium and payroll tax reduction from government, and the last term is the indirect effect of the marginal probability of unhealthy behavior from the premium and the payroll tax reduction.

If government increases individual’s copayment rate, it would affect the well-being function in two aspects: If the decreasing in medical spending for patients is at a rate greater than the combined negative effects from decreasing the premium (R), payroll tax rate (t) reduction and medical spending through decreasing unhealthy behavior, individual’s welfare will decrease, i.e., V_L 0 . On the other hand, if the first term is smaller than the last three terms, an increase in the copayment rate will increase the individual’s welfare, ~. . ,V

L 0

The F.O.C of changes in the payroll tax rate (t)and the premium (R) can be analyzed in the same manner.

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€3 {H* β1 * 67rβJ8 1 * β * β βr1 * 67βJ

8 1 * βI PβQβ 0

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With _E 0 and β_E 0, the payroll tax rate has a positive effect on the individual’s welfare (V

E 0. The first term is the direct effect from decreasing medical spending and indirect effect from government payroll tax reduction on medical services due to a decrease in the individual’s medical service utilization. The second term is the direct effect from decreasing medical spending and indirect effect of from a premium due to the individual’s decrease in unhealthy behavior. The health care bill has two positive effects on an individual who pays the bill. The first positive effect is from decreasing individual’s medical spending because higher payroll tax rate causes less medical service consumption as well as less unhealthy behavior. The second positive effect is from the indirect effect of government payroll tax and premium reduction, because a higher payroll rate causes medical service consumption as well as unhealthy behavior to decrease. This implies that when the government imposes a payroll tax, an individual will expect to pay more for healthcare cost. However, an individual also could gain more social welfare not only from the positive direct effect of decreasing medical spending, but also from the positive indirect effect from government payroll tax reduction due to the decrease in unhealthy behavior.

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€F {H* β1 * 67‚βJ8 1 * β * β β‚1 * 67βJ

8 1 * βI PβQβ 0

(14) With _‚ 0 and β_‚ 0, premium also has a positive effect on the individual’s welfare (V

‚ 0. The first term is the direct effect from decreasing medical spending and indirect effect from government premium reduction on medical services due to a decrease in the individual’s medical service utilization. The second term is the direct effect from decreasing medical

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spending and indirect effect of from a premium reduction due to a decrease in the individual’s unhealthy behavior. When an individual pays the health care bill, there are two positive effects from the premium increase. The first positive effect come from the decrease in individual’s medical spending because higher premium causes a decrease in both medical service consumption and unhealthy behavior. The second positive effect is from the indirect effect of government payroll tax and premium reduction because higher premium can cause a decrease in both medical service consumption and unhealthy behavior. This implies that when the government imposes a higher premium, an individual will expect to pay more for healthcare cost. However, an individual also could gain more social welfare not only from the positive direct effect of decreasing medical spending, but also from the positive indirect effect from government premium reduction due to a decrease in unhealthy behavior.