fraction of the informal, nonagricultural sector in the countries where data were available; and in just under half, women make up the largest share (particularly in Africa).

On the demand side, women tend to be more credit-constrained than men and, therefore, more likely to select themselves into microcredit contracts with all kinds of strings attached—namely, small loans, training sessions, weekly meetings, and joint responsibility. From the microlender's viewpoint, serving women has at least three potential advantages.

The first advantage is purely financial: Women are often more conservative in their investment strategies, and are often more easily swayed by peer pressure and the interventions of loan officers—making women more reliable bets for banks worried about repayment. As we described in chapter 5, evidence from Grameen Bank—and replications elsewhere in Asia—shows that women are better about repaying loans. For example, Khandker, Khalily, and Khan (1995) find that 15.3 percent of male borrowers were struggling in 1991 (i.e., missing some payments before the final due date), while only 1.3 percent of women were having difficulties. That finding is echoed in studies elsewhere in Asia. The field experience of Grameen replications in southern Mexico indicates a similar pattern, and evidence from credit scoring regressions using data from Latin American microlenders confirms this tendency too. (These are studies of repayment rates, in which gender is an explanatory variable.) While the advantage of women in the credit scoring studies falls after considering factors such as age, income, region, and other covari-ates, it is the simple correlation that is most important in determining the attractiveness of women as customers.3 In this line, Kevane and Wydick (2001), for example, find that at a group lending institution in Guatemala, female borrowing groups misused funds least often, and, as a result, outperformed male borrowing groups.

The next two advantages pertain to institutions pursuing social objectives—namely, aiming resources to women may deliver stronger development impacts. One reason is that women tend to be more concerned about children's health and education than men (e.g., Blumberg 1989). The second reason is that women are overrepresented among the poorest of the poor, and are too often oppressed by their husbands and by prevailing social norms. In its 1990 World Development Report, the World Bank reports that women are lagging behind in many key indicators of economic development. Literacy rates, for example, were found to be 61 percent of that of men in

Africa, 52 percent in South Asia, 57 percent in the Middle East, 82 percent in South East Asia, and 94 percent in Latin America. Moreover, the report finds that, relative to men, women in low-income countries face far greater social, legal, and economic obstacles.4 In addition to everything else, microfinance is thus seen as a road to "gender empowerment."

Region-specific studies on gender bias abound. One stark example is provided by population sex ratios that are so skewed that Sen (1992) has written of a crisis of "missing women."5 While in developed countries there are approximately 105 females for every 100 males, the ratios are lower in South Asia, the Middle East, and North Africa, due to exceedingly high female mortality rates. The very large female-to-male death ratio in these regions is attributed to parents' neglect for their female infants and, in some cases, to selective abortion of female fetuses. Sen (1992) estimates that the number of missing women (those who died prematurely or who were selectively aborted) in the early 1990s was over 100 million people. Among the reasons that young girls are discriminated against is that they are not viewed as an important source of income and, in some instances, are seen as a burden due to dowry obligations. Less extreme forms of discrimination are manifested in day-to-day living. Poor women, for example, tend to work longer hours for less pay. The World Bank (1990) reports: "Women typically work for longer hours, and when they are paid at all, will be so at lower wages." Studies in numerous developing countries emphazise that when unpaid home-production activities are included, women seem to work even longer hours than men.6

Ethical considerations aside, the gender bias has clear implications for policy. Unequal access to health, nutrition, and educational status of women in low-income households has been linked to high fertility rates, low labor force participation, low hygiene standards, and the increased incidence of infectious diseases. And all these variables are clearly related to productivity and household income.

Against this are arguments that male entrepreneurs may more aggressively expand enterprises when given access to credit. There may thus be a trade-off between lending to women in the name of poverty reduction and lending to men in the name of economic growth. Kevane and Wydick (2001), though, find that gender differences in economic responses to credit access are small in the Guatemalan group lending program they investigate. While they find that young male entrepreneurs tend to be more aggressive in generating employment than older male entrepreneurs, older women tend to be more aggressive in generating employment than younger women or older men. Holding all else constant, Kevane and Wydick thus find no statistically significant overall difference in the way that credit affects the ability of female and male entrepreneurs to generate increases in gross sales within an enterprise.

7.3 Neoclassical Approaches to Household Decision Making

The traditional neoclassical economic approach to household decision making leaves no room for analyzing conflict between men and women. Households are seen as acting as a single unit, making choices as if household members were in full consensus. Even here, though, a case for targeting on the basis of gender can be made.

The so-called unitary approach goes back to seminal work started by Gary Becker in the 1960s. In particular, in his Treatise on the Family, Becker (1981) assumes that male and female preferences can be aggregated into a common household objective function to analyze decisions about expenditures and "noneconomic" investments such as the number, education, and health of children. Households maximize their joint objective utility function subject to constraints on time use, technology, and joint resources. While the time allocation of each household member between the production of market and household output matters (since it may affect total household output), the distribution of income among family members is totally irrelevant. A dollar is a dollar, no matter who in the family earns it. The approach, so focused as it is on efficiency, is sometimes called the "pure investment" model; and it leaves no scope for intrahousehold conflict.

One of Becker's objectives was to understand how households allocate individuals to activities, with household members seeking to gain from their comparative advantages. According to this approach, if the wage in the market sector is higher for males than for females, it would be efficient for men to work more in the market sector and for women to stay in the household (or to work in the informal sector). Becker argues that this is the best way to increase the household's total output, and he claims that this is a good representation of patterns seen in the United States in the 1960s.

In principle, Becker's predictions also apply to developing countries. In most agricultural economies, there are a number of high-wage activities that require certain skills, such as physical strength, for which gender matters. Becker's framework in this case suggests that it is optimal for men to benefit from their comparative advantage by specializing in strength-intensive marketable agricultural activities outside the house. Women, on the other hand, should devote more time to unpaid household work and those marketable activities that require considerably less physical strength, even if the monetary rewards are often low due to market discrimination. It remains unclear whether such unequal specialization within the household truly reflects women's preferences.

Rosenzweig and Schultz (1982) provide early evidence on the pure investment model, finding that survival probabilities for female infants in rural India are higher in areas where opportunities for female employment are greater. Their argument is that asymmetric mortality patterns result because parents are forced to invest in children with the greatest earning potential. It is argued that such strategic decision-making results from the need to sometimes make tragic, brutal choices in the struggle for basic survival.7

But microfinance advocates repudiate the helplessness that is implied. First, by helping to raise incomes, advocates argue that microfinance can lift the constraints that force households to make such life-and-death choices. As important, advocates argue that microfinance can also change the nature of basic trade-offs. Rather than taking the structure of wages and employment as given, microfinance advocates aim to improve opportunities and the economic returns to women's work, and thus to change the economic value of females within the home. Raising those returns can, in principle, reduce discrimination of the sort documented by Rosenzweig and Schultz (1982).

The pure investment model is a useful starting point, but microfinance advocates go further. They argue that by raising women's status within families, the nature of decision making can change too. Rather than assuming that households work by consensus, as argued by Becker, economists have recently started deconstructing household choices, finding them to be driven often by inequalities, bargaining, and conflict.8 Browning and Chiappori (1998), for example, derive implications of a model in which bargaining power is driven by the ability of women to credibly threaten to leave the household. The credibility of those threats will depend on factors like earning power and other factors that affect women's relative power within the household, such as divorce or employment legislation. Access to microfinance can potentially be part of this equation.

To venture further, we first need to turn to a framework in which parents care intrinsically about the education and health of their children (rather than as in the pure investment model, where concern is purely instrumental, restricted to how improving health and education raises earning power). A simple approach is given by Behrman, Pollak, and Taubman (1982), and we follow Strauss's and Beegle's (1996) exposition. We assume that there are two children in a household, a girl and a boy. If the mother is exceedingly averse to inequality in the well-being of her children, she will care most about the child that is worst off. Dia-gramatically, at the extreme her preferences are L-shaped, or, in the public finance jargon, the mother's preferences are "Rawlsian."9 This is shown as an "L-shaped indifference curve" in figure 7.2, where the mother has preferences over the health of her son and daughter. In the case depicted, if the daughter's health improves, we will see a horizontal move from A to B in the diagram. This change will not improve the mother's condition, though, because she dislikes inequality. In contrast, take the opposite extreme in which the mother does not care about inequalities between the two children. In this case, the indifference curve will be completely linear, as shown in the downward-sloping line I-I. Here, the mother will invest more in household

Figure 7.2

The role of preferences in intrahousehold allocation.

Figure 7.2

The role of preferences in intrahousehold allocation.

members whose returns are the greatest (which is the case emphasized by Becker). Preferences between these two extremes are captured by the more plausible indifference curve C, where preferences for equality are traded off against the need to ensure earning capacity.

Such trade-offs shift with income. In particular, at very low income levels, the household may favor males for survival reasons, and mothers may support that decision. Take the example of food, which is often controlled by women. At very low incomes, women's preferences may be biased against females because survival is all that matters, and sons may represent higher earning opportunities for the household. Women may therefore allocate more food to males who can potentially bring a higher level of income to the household. Distributions become more equal, though, as the general level of income increases.

Berhman (1988), for example, shows that household nutrient intakes and health outcomes in his sample from India are positively correlated with earning profiles. He also shows that the pro-male bias is more severe during the "lean" seasons, when resources are tight. In particular, households tend to allocate food to members who receive the greatest returns in the labor market, resulting in greater intrahousehold inequality in the lean seasons, but they are more egalitarian in surplus seasons.

Another layer of complexity is added by allowing that men and women may have different preferences, and that conflicts are resolved through negotiation. In the context of figure 7.2, women's preferences, say, may tend to be more L-shaped while men's preferences tend toward linearity. The more power a woman has in the household, the more the household's decisions reflect her preferences. Increasing income can thus lead to households changing the pattern of allocations for reasons that get mediated through the bargaining process. Browning and Chiappori (1998), for example, show that in bargaining contexts, preferences tend to shift with income.10 Microfinance may thus affect household choices through a variety of channels: by changing bargaining power, by raising overall resources, by affecting the returns to investments in human capital, and by influencing attitudes and norms.

7.4 Are Women Better Customers?

There are at least three reasons that lending to women may have advantages for the bank—and may enhance efficiency in a broader economic sense. The first has to do with poverty, the second with labor mobility, and the third with risk. We address the poverty-related argument first. Women are poorer than men. According to the UNDP Human Development Report (1996), 70 percent of the world's poor, about 900 million people, were women. Under the standard neoclassical assumptions about the production function, if women have less access to capital than men, returns to capital for women should therefore be higher than for men. Endowing women with more capital can thus be growth-enhancing in principle.11

This assumes, though, that capital is not completely fungible within households—that is, the money of all members is not fully pooled and treated as a common resource. Given that the once common assumption of full within-household resource pooling has come under steady attack, the case for a gender focus in microfinance is strengthened. While there is concern that credit directed to women might end up being re-directed to male household heads (who are the ones that actually carrying out investment projects of their own, with the resources borrowed by women), evidence from Bangladesh delivers a reassuring response. Goetz and Sen Gupta (1996), for example, report that 40 percent of women in their survey have little or no control over their own investment activities, but optimistic observers respond that this means that 60 percent have full or partial control. Thus, investments do seem to be undertaken by women, despite norms that place restrictions on women. To the extent that—as reported by Goetz and Sen Gupta—women already enjoy a comparative advantage in small-scale microenterprise activities, the efficiency-augmenting argument by neoclassical theorists is further enhanced.

The second argument hinges on labor mobility. Women tend to be less mobile than men and are more likely to work in or near the home. Bank managers can therefore monitor women at a lower cost. Moreover, less mobility facilitates delegated monitoring under group lending methodologies. Typically, peer borrowers who undertake investment activities at home—and stay at home most of the time—can more easily monitor each other. Similarly, lower mobility reduces the incidence of strategic default under the fear of social sanctions.12

This brings us to the third argument in favor of a pro-female bias. Because women are less mobile and more fearful about social sanctions, they tend to be more risk-averse than men and more conservative in their choice of investment projects. This makes it easier to secure debt repayments and create a reputation for reliability.13

7.5 Why May Impacts Be Greater When Lending to Women?

Khandker's (2003) evidence suggests that lending to women yields greater social and economic impacts than lending to men. Policymakers have long been aware of the potential impact of delivering aid for disadvantaged households to women. Food stamps in the United Kingdom and Sri Lanka, for example, and staple food and cash deliveries under the PROGRESA (now called Oportunidades) program in Mexico were directed to women rather than their husbands. The fear is that if such aid was given to men, they might sell the food stamps and misspend the resources—possibly wasting money on gambling, tobacco, and alcohol. Skoufias (2001) reports that Oportunidades in rural Mexico indeed led to sharp social improvements: Poverty decreased by ten percent, school enrollment increased by four percent, food expenditures increased by eleven percent, and adults' health (as measured by the number of unproductive days due to illness) improved considerably as well.14

Similarly, Thomas (1990) reports that child health in Brazil (as measured by survival probabilities, height-for-age, and weight-for-height) along with household nutrient intakes, tend to rise more if additional nonlabor income is in the hands of women rather than men. With respect to survival probabilities, income in the hands of a mother has, on average, twenty times the impact of the same income in the hands of a father. In a subsequent study, also on Brazil, Thomas (1994) reports that increasing the bargaining power of women is associated with increases in the share of the household budget spent on health, education and housing as well as improvements in child health. Engle (1993) similarly studies the relationship between a mother's and father's income on child nutritional status (height-for-age, weight-for-age and weight-for-height) for hundreds of households in Guatemala, and reports that children's welfare improves as women's earning power increases relative to their husbands'. Schultz (1990) finds that in Thailand nonlabor income in the hands of women tends to reduce fertility more than nonlabor income possessed by men. He also finds that the impact of nonlabor income has different effects on labor supply, depending on which household member actually controls that income.15

Anderson and Baland's (2002) article on ROSCAs, already discussed in section 3.2, reports on a survey of hundreds of women in Kenya. An overwhelming majority of the women responded that the principal objective for joining a ROSCA was to save, and nearly all of the respondents were married. Anderson and Baland conclude that an important motive for women joining ROSCAs is to keep money away from their husbands. Other studies, not necessarily confined to ROSCAs, suggest that savings considerations (and protection of assets) apply as well to women's involvement in microfinance institutions.

Udry (1996) provides related evidence. Using panel data from Burkina Faso, he finds that, controlling for soil quality and other variables, agricultural productivity is higher in plots that are cultivated by men. He also finds that relative to plots cultivated by women, the higher yields of male-cultivated plots are due to a greater intensity of productive inputs (including fertilizer and child labor). He thus concludes that productivity differentials are attributed to the intensity of production between plots cultivated by men and women, and not to inherent skill differentials. This outcome is not efficient since there are sharply diminishing returns for fertilizer. Not only are resources not fully shared, they are allocated in ways that diminish total household income. Udry suggests that input reallocation toward plots cultivated by women can thus enhance efficiency. Another solution (i.e., the microfinance solution) is to provide women with credit sufficient to purchase additional inputs. A second way that microfinance can potentially address problems like this is by tackling the social norms that prevent women from having adequate access to inputs and marketing facilities in the first place. This could be done through demonstration effects or from pressure created by the microlender to ensure high returns to borrowers' investments.

7.6 Gender Empowerment

Advocates argue that microfinance can increase women's bargaining power within the household. Women will become "empowered" and enjoy greater control over household decisions and resources. To the extent that group lending in microfinance entails peer monitoring by other borrowers in the same group, microfinance is likely to provide protection to women within their households. In particular, violent acts and abuses by men against women can now be subject to third party scrutiny as peer borrowers will want to find out why a woman in their group has stopped attending repayment meetings. This, in turn, should act as a deterrent against domestic violence, and, more generally, as an instrument for women to promote their rights and improve their bargaining power vis-à-vis their husbands or other male family members. Rising household incomes in general can also diminish conflicts between husbands and wives by loosening constraints.

Evidence on the effect of microfinance on women's rights delivers an unclear picture, however. Hashemi, Schuler, and Riley (1996) and Kabeer (2001), on the one hand, report that microfinance in Bangladesh has indeed reduced violence against women. Kabeer argues that the rationales for targeting women, over and above the desire to empower, include the observations that (1) men are less likely to share their loans with women than women are likely to share loans with men; (2) loans to women are more likely to benefit the whole family than loans to men; and (3) loans to men have little impact on intrahousehold gender inequalities—in fact, they can reinforce them by providing men with a base to prevent wives from engaging in income-generating self-employment. But the opposite conclusion is reached by Rahman (1999), albeit with evidence from just one village. As many as 70 percent of Grameen borrowers in his survey declared that violence in the household had increased as a result of their involvement with microfinance. Rahman's explanation for the upsurge in violence is that microfinance exacerbates tensions because men feel increasingly threatened in their role as primary income earners in traditional societies.

Another way in which microfinance can affect women's empowerment is with regard to the use of contraceptives. Especially in Bangladesh, microfinance has been promoted as a way to limit the number of children, and positive impacts have been found on contraceptive use (e.g., Rahman and Da Vanzo 1998; Schuler, Hashemi, and Riley 1997). This can be explained by the fact that microfinance increases the opportunity cost of women's time. This effect may be reinforced by peer pressure as women are urged to reduce family size in order to increase education and health expenditure, and to better manage the ability to repay. On the other hand, Pitt et al. (1999) argue that microfinance could be positively associated with higher fertility as access to microfinance raises income (holding all else constant this should increase the demand for children), but may only raise opportunity costs slightly (since, unlike factory work, women can engage in self-employment activities from home while simultaneously caring for children). They show confirming evidence from a cross-sectional survey in Bangladesh.16

While microfinance can potentially empower women within the household, there is less evidence that it has been effective in trans forming social norms and traditions. Mayoux (1999), for example, reports on a survey of fifteen different programs in Africa, finding that the degree of women's empowerment is household- and region-specific, and thus, she argues, depends on inflexible social norms and traditions. The findings have to be weighed against the fact that impacts on empowerment will, of course, also depend on how well the particular programs were designed.

7.7 Criticisms

We have argued earlier that microloans have played an important role in the promotion of self-employment in traditional activities where, relative to men, women already enjoy a comparative advantage. By enhancing women's specialization in those activities, microfinance may thus improve efficiency.

The focus on gender empowerment as a broader goal has come under fire from a variety of angles. The ever-provocative Adams (Adams and Mayoux 2001, 4), coming from the right, argues that the widespread use of the term "empowerment" by the microcredit crowd makes me uneasy. To the unwashed it conveys the impression that smearing a dab of additional debt on a poor woman will transform her into Super Woman. Those who insist on using this bloated term grossly overstate the contribution that indebting crusades play in easing poverty. More debt does not cure malaria or HIV/AIDS. It does not provide clean drinking water or prevent flooding. It does not improve law-and-order or eliminate weeds in a borrower's crops. It does not make crops grow in barren soil or provide secure title to land that squatters occupy. It does not provide schools or teachers for the poor .. .

A loan provided by the microdebt industry, for say $100, is no more an empowerment tool than is a similar loan from an evil moneylender or a relative, unless the intent of the lender somehow transforms the usefulness of the money borrowed—which it doesn't.

The critique mirrors Adams's broader critique of microfinance as a poverty alleviation tool, discussed earlier in chapter 2. The argument hinges on the (much-disputed) assertion that poor women have adequate access to credit through informal means, so that microfinance might change the terms on which credit is obtained, but it does not open access.17 The argument also dismisses the role of training or social capital that may be generated through participation in microfinance programs. Mayoux takes Adams to task, but agrees that credit alone is not enough to bring meaningful change to women; empowerment

"also depends on how far [programs] are able to build on group organization to enable people to organize on other issues" (Adams and Mayoux 2001, 5).

Mayoux's critique of minimalist, banking-only approaches is taken further by observers from the left. Rankin (2002), for example, argues that microfinance may entrench—rather than challenge—traditional gender roles. First, she cites the Goetz and Sen Gupta (1996) evidence that it is often men, not the women borrowers, who actually control the microenterprise investments and income. Second, even when women maintain control, Rankin argues that "they are often encouraged to take up enterprises such as sweater knitting that do not disrupt practices of isolation and seclusion within their households (Rankin 2002, 17)." This raises a more complicated question: Is increased specialization within the household a good thing from an equity standpoint? Many critics, notably, Gibbons (1995), Goetz and Sen Gupta (1996), and Dawkins-Scully (1997), forcefully argued that it isn't. Within-household specialization, the argument goes, reinforces women's reliance on male family members due to women's limited access to inputs, supplies, and marketing facilities.

One answer to these criticisms is that unskilled women have very few working opportunities outside the household (in the formal sector, at least). So microfinance helps women to make the most out of the traditional activities that they are restricted from in the short run. Meanwhile, the hope is that they acquire new skills and accumulate resources that improve their family's living conditions.18 Thus, microfinance advocates who stress gender empowerment tend to look to programs that add training and consciousness-raising—such as the training program organized by BRAC, the largest microlender in Bangladesh, or the credit with education strategy of Pro Mujer in Latin America. BRAC not only provides lessons on new productive activities, but they also hold sessions on legal and social rights and basic health practices. Such training is costly, though, and BRAC defrays expenses through funds from the government and international donors.

7.8 Summary and Conclusions

In this chapter we first argued that enhancing opportunities for women can be good for both efficiency and intrahousehold equity. Advocates argue that microfinance can also improve long-term development, as women are the main brokers of children's health and education. In par ticular, we highlighted the potential for microfinance to play a role in increasing the scale and scope of self-employment opportunities and skill acquisition, protecting women's rights through monitoring by third parties, for facilitating savings, and for enhancing social capital. These are not achievements that will necessarily arrive as a matter of course. Rather, to be achieved, programs need to be designed with these outcomes in mind. When and whether the goals can be met without sacrificing other goals—such as financial performance— remains an open question. Microfinance practitioners who are most interested in building strong financial systems have viewed discussions of gender empowerment with a wary eye—quite understandably, given the lack of systematic data—but we find a great deal of evidence from other quarters to support the potential of microfinance to make a difference here.

In many ways, the discussion in this chapter just scratches the surface, and more research is needed on at least three important dimensions. First, the empirical evidence is scattered and incomplete. In particular we would like to learn more about the relationship of gender and social capital in microfinance; about the impact of microfinance on skill acquisition, education, and women's access to the formal sector; and about the effect of microfinance on intrahousehold income distribution. The broader interrelationship of gender and class also deserves consideration within the microfinance context.

Second, how does the emphasis on gender affect the design of microfinance institutions? Should financial services be bundled with the provision of complementary inputs and training by NGOs, governments, and/or donor agencies? How should the lending contract or savings devices be modified to increase women's opportunities within the household and the broader community? A third question involves the extent to which microfinance can contribute to changes in social norms, rather than being a vehicle for reinforcing existing norms. These are all "frontier" issues, and will no doubt be revisited regularly.

7.9 Exercises

1. Discrimination against women occurs for many reasons. Why do you think it has been so persistent over time? And why might microfinance have the power to bring changes?

2. Provide at least three reasons why microfinance can potentially benefit women.

3. Provide at least three reasons why, relative to men, women may be better clients, from the standpoint of a microlender simply interested in maximizing profits. What does this say about empowerment? Is there a contradiction?

4. Consider a household where there are two children, a girl and a boy. Parents in this household derive utility from their children's educational attainment. Suppose that in order to have their children educated, parents have to spend an amount x per month if it's a girl, and y if it's a boy. Let the household's utility be as follows:

If income w < W, then U = x + 2y. But if income w > W, then U = 2 x min(x, y). (Households' preferences are Rawlsian in this case). Let W = 1,500 taka and x + y < w.

a. If the woman in this household does not work additional hours in her investment project, which can be potentially financed by a microfinance enterprise, then the households' income is w = 1,100 taka. Compute the household's optimal decision in this case.

b. Suppose that she is successful at obtainting a loan from a microfinance institution, in which case she carries out her investment project and brings an additional 700 taka to the household. What would be the household's optimal strategy?

5. Suppose the same problem as in the previous exercise, except that the household in this case involves five children, three girls and two boys. Consider the household's utility to be as follows. If income w < W, then U = x1 + x2 + x3 + 3y1 + 3y2, where xi (i = 1,2,3) is the amount invested in the girl i's education, and yj (j = 1,2) is the amount invested in boy j. Assume that, relative to the girl, the boy is capable of generating a higher level of income for the household, and that this is the reason why the household puts more weight on him. But if income w > W, then U = 4 x minfe + x2 + x3; y1 + y2). In this case, the household has to spend an amount c on basic consumption goods before actually investing in their children's education. Let W = 1,800 taka; c = 1,100 taka.

a. If the woman in this household does not work additional hours in her investment project, which can be potentially financed by a microfinance enterprise, then the household's income is w = 1,500 taka. Compute the household's optimal decision in this case.

b. Suppose that she is successful at obtaining a loan from a microfinance institution, in which case she carries out her investment project and brings an additional 1,000 taka to the household. What is the household's optimal strategy in this case?

6. Consider a household similar to that of exercise 5, except this household's utility takes the following form:

Um + Uw = wm (3y + x) + [min(3x; 3 y)], www w where wm, ww are, respectively, the man's income and the woman's income; w = wm + ww, and y and x are, respectively, the amount of resources invested in the boy and in the girl. Let (wm/w); (ww/w) denote the within-household bargaining power, with respect to the household's income.

a. Suppose the man is the only source of labor income in this household, and assume that he earns wm = 1,000 taka per month. Compute this household's optimal decision.

b. Assume that the woman can work in a project financed by a microfinance institution, and that as a result she generates an additional amount ww = 1,000 taka per month. What would be the optimal strategy for the household in this case?

7. Consider exercise 6, and compute the threshold rate ww/wm, below which the woman's preferences have no bearing on the decision that the household will ultimately take.

8. Consider a man and a woman who request a loan of size I from a bank. If the loan is obtained by either individual, it can be invested in either of the following two projects. If invested in project 1, which involves an investment I, the yield is y1 = $520. If invested in project 2, which also requires an investment I, the yield is y2 = $1,020 with 50 percent probability and zero otherwise. Suppose that the man is risk-neutral and only seeks to maximize expected profits, while the woman is risk-averse. Her utility function is uw = (x05/0.5), and both the man and the woman are assumed to both start with zero wealth. Suppose that the gross interest rate set by the bank is R = $120, and that this rate is fixed. Borrowers are protected by limited liability. Will the bank decide to lend to the man or to the woman?

9. Consider exercise 8, except that in this case, the utility function of the man is now um = (x08/0.8) and that project 2 yields a gross return of $1,120 with 50 percent probability and zero otherwise. To whom will the bank decide to extend the loan in this case?

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