Pregnancy is a female state that is produced due to the implantation of the fertilized ovum in the uterine endometrium and ultimately giving rise to a foetus; and pregnancy wastage is the loss of product of conception normally or therapeutically (Jeffcoate, 1975). Pregnancy wastage can be classified as intra-uterine foetal death, abortion, and menstrual regulation (Jeffcoate, 1975; and Shaw, Soutter and Stanton 2003). In our study, we have dealt with the normal pregnancy wastage that is not therapeutic.

Every year about eight million women suffer from pregnancy related complications and over half a million die. About 99% of these are in developing countries (WHO, 2004). Most of these deaths can be averted even where resources are limited. The poor reproductive health of women, in third world countries, is an outcome of the general neglect of health and nutrition in childhood and adolescence, which affects their future well being (De Silva, 1998). In 1987 Ardebili, Kamali, Pouranssari and Komarizadeh studied the reproductive behaviour of 1525 pregnant women. The type of pregnancy termination that resulted in live birth or abortion has a significant relationship to the age of the mother. Again, the highest percentage of abortion was observed in (15-19) age group and the highest number of natural deliveries was observed in the age group (20-29).

Khandait et al (2000) examined complications of the reproductive health of married women and envisaged the age factor as a cause of stillbirth, accumulating with other factors. Yasakawa and Tayahashi (1990) observed that the age-specific maternal mortality was rising with age. They also investigated that pregnant women aged over 35 faced more pregnancy complications with high risk. Another study by Breart, Blondel, and Maillard (1987) acclaimed with the risks of late pregnancy for mothers and their births indicated that there was excess risk for mothers over age 35 but the difference is decreasing relative to the general population (mothers before 35). They also found that the risk of mothers over 34 was 3.6 times higher in 1975 and 2.6 times higher in 1983 than for the general population. Study on scheduled caste women of Punjab experienced the least number of abortion and stillbirths in the age group (25-29) and the risk of pregnancy wastage increases with age (Sidhu and Sidhu, 1988). Similar results by Banerjee and Hazra (2004) showed that the rates of pregnancy wastage in two extreme age groups (<20 and 35+) are relatively higher. This evidences indicates that there exists an age-specific relationship of pregnancy wastage and mothers' age.

Further, Kim, Byun, and Lee (1991) studied over 2874 mothers and observed 342 caesarian deliveries against 2532 vaginal deliveries. They included several factors like, education, occupation, residence (big cities, urban, and rural) and age of mother at birth to explain the delivery status. As to the mothers age at delivery they found that 10.4% of C-section (caesarian sections) were under age 24, 12.1% were in (25-29), and 14.1% were over 30. Thus, there is an increasing trend of C-section with age. But, the exact relationship of pregnancy wastage and caesarian deliveries with respect to their flows over the age of the mother, is still unknown. In this paper, an attempt has been made to investigate the age-specific flow of pregnancy wastage and caesarian delivery.

Data
The data were collected from a field survey conducted in the district of Rajshahi of Bangladesh. We collected information from 2967 mothers by preparing an open-ended questionnaire. Also, the delivery status of 6717 births were under investigation and our data evaluated only the delivery types (caesarian and vaginal).

Methods
In this paper we have used the logic of equilibrium level of satisfaction, velocity and elasticity curves. The logic of equilibrium has been extensively using in the field of economics especially in demand analyses. The concept of velocity has a greater applicability to the physical sciences and recently it has been used in human biology. On the other hand, elasticity of goods, demand and income elasticity, explain the speed of relative change and replacement (Varian, 2003; Chakravarty, 1997 and Dewett and Chand, 1999).

Equilibrium level of satisfaction
Equilibrium level of satisfaction leads to the intersection of two curves at a particular point. When one curve is downward sloping and the other is going upward from the origin, then both the curves intersect each other at a particular point. At that point values on both the curves are equal. For example, if we consider a demand and a supply curve. Then the equilibrium level of demand and supply attains at the point of their intersection (Varian, 2003, Chakravarty, 1997 and Dewett and Chand, 1999).

Velocity curve
To draw the velocity and elasticity curves we fit the polynomial regression models. The velocity curve is just the first derivative of the fitted polynomial regression line with respect to age (Gasser et al., 1984; Ali and Ohtsuki, 2001; Islam et al., 2003). The polynomial regression model of order 'p' (Gujarati, 1995 and Montegomery and Peck, 1982) is of the form:

where all the parameters ( ) and the error terms (u) follow the usual assumptions.
Now, the velocity curve is just the first derivative of the above equation and so we get

Elasticity curve
The elasticity can be computed using the formula mentioned by Dewett and Chand (1999), Chakravarty (1997) and Varian (2003) as

We can comment on the speed of relative change or replacement using the following criterion:

(a)	if then the overall process is inelastic,
(b)	if then the process is elastic and the speed of relative change is negative, that is, speed of change of y is slower than x,
(c)	if then the process is elastic and the speed of relative change is positive, that is, the values of y increases faster than x,
(d)	if then the relative change is proportionate to each other and in this case both the factors change equally likely.

Cross validity predictive power
The cross validity predictive power has been used to examine the rigidity of the fitted polynomial regression models. The cross validity predictive power due to Stevens (1996) and Khan and Ali (2003) is

where R² is the coefficient of multiple determination, n is the sample size, k is the number of regressors used in the model. Further, the stability of R²(Stevens, 1996, Khan and Ali, 2003, Islam et al., 2003) can be computed as:

First of all, we simply present the observed values, computed proportions (Table 1) and smoothed proportions (Table 2) both for urban and rural areas. The proportion of pregnancy wastage to live birth is calculated by dividing the number of pregnancy wastage by the number of live birth in a specific age group. Similarly, proportion of pregnancy wastage to mother and that of caesarian deliveries to vaginal deliveries (Table 1) have been computed. Our aim is to know the age-specific flow of pregnancy wastage and caesarian deliveries. So, we have used smoothing techniques, "4253H, twice" from Minitab window 12.0 to obtain the smoothed values (Table 2).

Plotted smoothed proportions (Fig.1) intersect each other at a certain point and at this point equilibrium status is achieved. We observe that for rural areas, pregnancy wastage to live birth and to mother, is equal at age 23. But, in urban areas this is at age 25. At these points proportion of pregnancy wastage to live birth and to mother are equal, that is, number of live birth equals number of mother. In other words, at that point every mother yields a live birth with minor risk of pregnancy wastage.

A matter of regret is that for delivery status much data for different age groups especially the last two age groups, are not available for urban and rural areas separately. Thus, we were compelled to conduct our study combining urban and rural areas together.Consequently, we have nested our focus on equilibrium level for proportion of pregnancy wastage to live birth and proportion of caesarian deliveries to vaginal deliveries. At age 25 this equilibrium level is achieved. Thus, at 25 years of mother , that is, for non-zero pregnancy wastage (Pw), Live birth (Lb), and Vaginal delivery (Vd) we have caesarian delivery that explains the minor risk of pregnancy wastage and live birth reduces the risk of caesarian deliveries. Elaborately, we can say that live birth and vaginal deliveries are fixed at certain non-zero level then increase (or minor risk) of pregnancy wastage yield increases (or minor risk) of caesarian delivery. Similarly, if pregnancy wastage and vaginal delivery is fixed at certain non-zero levels then the increase of live birth substantially reduces the risk of caesarian delivery. Moreover, we can say that if a woman gives a live birth vaginally then the risk of caesarian delivery for the next birth is very low. Here it is mentionable that these comments are valid only if such equilibrium condition is achieved. Thus, our findings elucidate that the women at age 25 in Bangladesh bears low risk for child bearing with respect to less risk of both pregnancy wastage and caesarian deliveries. To check the liability of our results we formed a control group that includes all the respondents of age 25 years. Then we performed a study over every single year. One caveat that we faced was availability of data in every single year; especially the information on birth and delivery types for respondents after 35 years of age was really shaky. However, we did it for those single year's respondents to whom data were available. To accumulate the joint effect of both factors (pregnancy wastage and caesarian delivery) we added the proportion of pregnancy wastage to live birth and proportion of caesarian delivery to vaginal delivery for every single year. We found that this was the lowest at the single age year 25 and was 0.0524. Thus, we may assure that our results related to the equilibrium level of age (25 year) are true.

Thereafter, we fitted statistical models to those smoothed proportions and found that third order polynomial regression model better explains the age-specific flow of both pregnancy wastage and caesarian deliveries. Our fitted models are highly stable (Table 3). Further, the velocity and elasticity of caesarian deliveries and pregnancy wastage (Table 4) have been computed.

Velocity curves in (Fig. 3) show that velocity of pregnancy wastage to live birth both in urban and rural areas yield negative magnitude but that of caesarian deliveries yield positive magnitude. Thus, we can say that the pregnancy wastage decreases over ages whereas caesarian delivery increases. Elasticity of pregnancy wastage to live birth is less than unity up to the age 30 and thereafter these values lie between -1 and +1, that is, up to age 30 the system is elastic and inelastic thereafter (Table 4). In other words, the risk of pregnancy wastage decreases with the increase of age and the speed is faster than the speed of age. However, the pregnancy wastage to live birth in urban areas is almost inelastic (Fig.4). But, for caesarian deliveries the elasticity is always greater than one and so the risk of caesarian deliveries increase with the increase of age (Fig.4). Furthermore, the risk of caesarian delivery (speed) increases faster than the increase of age.

Risk of pregnancy wastage and caesarian deliveries change with age. Increased age increases the risk of caesarian delivery, but decreases the risk of pregnancy wastage. However, in the extreme age groups pregnancy wastages are observed substantially larger. Equilibrium condition for risk of pregnancy wastage and caesarian delivery yields 25 year as an ideal age of child bearing for Bangladeshi women, as both the risks are in tolerable situations. Therefore, no pregnancy before 25 and only one birth at this age can avail of acceptable risks of pregnancy wastage and caesarian delivery in Bangladesh. Different country and regional differences may draw different risks and age structure for pregnancy wastage and caesarian deliveries. Early marriage (before 18 years) and teenage motherhood is a stark reality behind the plight of female health hazards in Bangladesh. A proper policy towards safe motherhood (no birth before 25 years) may be helpful to overcome the pregnancy related deficiencies as well as to control the population growth to a large extent.

A part of this research has been conducted under a project financed by the UNFPA. The authors thankfully acknowledge the Project Director, Dr. J. A. M. S. Rahman for partial support of our research work. We are also thankful to the participants of our seminar for their valuable suggestions. Last but not least, our sincere gratitude to the comments from anonymous reviewers for increasing the rigidity of our paper.

Here PwLbU and PwLbR represent pregnancy wastage to live birth for urban and rural areas; PwMU and PwMR refer to pregnancy wastage to mother both for urban and rural areas, respectively.

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Here PwLb and Caesarian represent proportion of pregnancy wastage to live birth and that of caesarian deliveries to vaginal deliveries, respectively.

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Here Caesar indicates caesarian deliveries. All other notations are same as in Fig.1.

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Here RLB, and ULB indicate elasticity of pregnancy wastage to live birth in rural and urban areas,
and C stands for elasticity of caesarian deliveries in total (urban and rural) areas.

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Here Pw, M, PwLb, PwM, V, C, and Cv indicate Pregnancy wastage, Mother, Proportion of pregnancy wastage to live birth, Proportion of pregnancy wastage to mother, Vaginal delivery, Caesarian delivery, and Proportion of caesarian delivery to vaginal delivery, respectively.

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Notations are explained in Table 1.

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Variables		Fitted Models	R2	CVPP	Stability
Urban	Pregnancy wastage to live birthPregnancy wastage to mother		0.99980.9997	0.99880.9983	0.00100.0014
Rural	Pregnancy wastage to live birthPregnancy wastage to mother		0.99970.9999	0.99830.9994	0.00140.0005
Both	Caesarian deliveries to live birth		0.9998	0.9988	0.0010

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Notations are explained in Table 1.

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