Effects of a grazing permit market on pastoralist behavior and overgrazing in Kenya

The success of market-based mechanisms in reducing conflicts and internalizing externalities depends on their ability to clarify property rights amongst heterogenous resource users. We investigate the effectiveness of novel markets in achieving their goals using the case study of grazing markets in Laikipia County, Kenya. In this system, sheep- and goat (shoat)- and cattle-rearing pastoralists negotiate land access for cattle with neighboring cattle ranchers. Using data on pastoralists’ livestock and contracting preferences and a model of pastoral herd management, we show that contracting for cattle grazing access on private property alters relative input shadow prices for grazing resources in communal pastoral lands, ultimately resulting in relieved cattle grazing pressure. However, the permitting process is less attractive to pastoralists who prefer rearing shoats instead of cattle. These shoat-rearing pastoralists instead fill some of the vacated space with shoats instead of purchasing permits themselves. This leakage offsets some of the conservation benefits arising from the contracting program and results in a greater share of shoats in the communal herd mix. Approximately 0.59 cows’ worth of free space persists on the commons per permit sold, indicating reduced grazing pressure, but this represents a small proportion (3.8%) of the total livestock in the system. The narrow introduction of the cattle-focused permit market and lack of strong management institutions on the commons dampen the permitting program’s conservation benefits, necessitating further interventions. Alleviating these factors and dramatically scaling up the program has the potential to turn the permitting system into a successful conservation tool.

significantly undermine the benefits of voluntary pollution control policy, even if the result is still netpositive for society (Montero 1999, Millard-Ball 2013, Bento et al 2015. PLA concerns are less well-studied for other environmental markets. We use the case study of novel grazing markets in Laikipia County, central Kenya, to investigate how PLA concerns may complicate environmental markets. Laikipia is a semi-arid rural county characterized by high livestock densities alongside high biodiversity. Laikipia boasts the second highest abundance of wildlife in East Africa, after the Mara-Serengeti ecosystem (Sundaresan and Riginos 2010). Laikipia also supports the largest population of endangered megafauna in Kenya and has the largest diversity of large mammals of any region its size in the world (Butynski andJong 2014, Witt et al 2020). The county exists as a mosaic of land parcels, with about 30 private ranchers controlling half the land area and most of the rest existing as a combination of smallholder farmland, communally-managed pastoralist group ranches, and unmanaged land owned by absentee landlords. Droughts are common in Laikipia and often lead to land use conflict as different actors compete for scarce resources (Fox 2018).
We consider two major land users: pastoralists and ranchers. Both are livestock herders. After a complicated history of colonization, treaties, and land tenure reforms, pastoralists are largely confined to communally-managed 'group ranches' , which are de facto 'commons' and perennially overgrazed by livestock (Fratkin 2001, Desta and Coppock 2004, Boles et al 2019. This overgrazing results in reduced vegetation cover (among other issues) and has driven declines in wildlife populations on group ranches, as observed across Kenya (Ogutu et al 2016). Ranchers manage properties similar in area to the communal lands, but private property rights enable excludability. Private ranches often double as wildlife conservancies, stocking livestock at densities 3.5 times lower than pastoralists do (Odadi et al 2011). This results in higher quality and more abundant grass on private ranches than on the commons, driving conflicts over grazing access that flare up when droughts or other disturbances make grazing resources more scarce (Bond 2014). In these tense periods, some pastoralists illegally move livestock onto private ranches, which can escalate into violence (Burke 2017, Leithead 2017, Fox 2018, Boles et al 2019. The conflicts are sometimes driven by pastoralists from outside Laikipia, who bring their herds through the county when droughts render neighboring counties unsuitable for livestock, affecting both types of local land users. This drove a particularly violent set of conflicts in 2017 (Burke 2017, Leithead 2017. Therefore, ranchers incur large costs to enforce their property rights, for example by hiring and arming guards. In response to these conflicts, pastoralists and ranchers created a system of cattle grazing permits allowing pastoralists to graze their cattle legally on private ranches in exchange for a monthly per-head fee. Pastoralists are not required to purchase permits unless they wish to graze their cattle on private ranches, and grazing activity on communal pastoral lands remains unrestricted. In most cases, the total number of permits is set by the rancher and sold in aggregate to the neighboring pastoral community, who decide how to allocate the permits amongst themselves. In other cases, ranchers have established relationships with a select number of (generally wealthy and influential) pastoralists and sell permits specifically to them. The terms of the grazing leases vary widely, with some ranchers offering herding labor, metal 'predator free' enclosures, and tick repellant. The grazing permits only apply to cattle, so other important forms of livestock, such as sheep and goats ('shoats'), must remain on the communal pastures.
Shoats are increasingly important in Laikipia because of their high fecundity, their ability to subsist on degraded landscapes, and the relative ease with which herders can sell them. Still, cattle remain culturally important for East African pastoralists, who use cattle as bride price and measures of wealth (McCabe 1997, Österle 2008, Huho, Ngaira and Ogindo 2011. Although five shoats are considered equivalent to one head of cattle using the common tropical livestock unit (TLU) measure 5 , this shift to shoats brings large changes to the landscape. Goats share cattle's preference for high-quality forage, can graze for longer periods without water than cattle, and are able to eat woody stems and shrubbery that cattle do not eat (Steinfeld et al 2006, Hart 2008. Sheep graze similar plant species to cattle but leave less vegetation cover behind, due to their small mouths and resulting ability to clip grass closer to the soil than cattle. At the high stocking densities present on pastoral lands, shoats have large impacts on the ecosystem and their heavy grazing can reduce available forage for wildlife such as the endangered Grevy's zebra (Equus grevyi) (Peacock andSherman 2010, Rosa García et al 2012). This is part of the reason private ranches exclude shoats from the permitting system.
Aside from the goal of reducing conflict, the permitting system intends to ease grazing pressure 6 on the commons by offering pastoralists alternative grazing patches. This conservation goal is complicated by the non-excludability of pastoral lands. Pastoralists who are committed to increasing their cattle herds 5 1 TLU equals one head of cattle or five shoats. One shoat is therefore equal to 0.2 TLU. 6 In this article we use the term 'grazing pressure' to reflect the intensity of livestock grazing, correlating with stocking densities. High grazing pressure stresses grass resources, while low grazing pressure relaxes grass resources and makes them available for wildlife.
have strong incentives to purchase grazing permits and move cattle to private ranches. Conversely, pastoralists who prefer to rear shoats have little reason to spend money on cattle grazing permits instead of expanding their shoat herds for free on the commons as it becomes less heavily grazed by cattle. This sets up a potential leakage, posing a threat to the success of grazing permits in promoting conservation on the commons.
Laikipia is an ideal setting to study the ecological effects of these market-based mechanisms because few other places in Africa have such a widespread program of leased grazing. Furthermore, Laikipia's permitting system has been proposed as a model for other regions (Regional Pastoral Livelihoods Resilience Project 2020). Here, we study the effects of the permitting system on pastoralists' livestock rearing decisions and investigate whether permits relieve grazing pressure on communal lands. Our model is rooted in pastoral culture and the results are contextualized with Laikipia's history of resource conflict. Using economic theory and data from 301 household surveys, we develop empirical methods to explain how heterogeneity in the use of the commons may complicate conservation policies and lead to PLA concerns.

Theory
An "indifference curve" traces out the combinations of shoats and cattle that make pastoralists equally well off. Pastoralists' shoat-cattle indifference curves enable evaluation of the effect of permit price on their chosen livestock bundle (see appendix A for derivation). We model grazing permits as a decrease in the implicit (shadow) input price of cattle for pastoralists who purchase the permits ('ranch-users'). The permit system is expected to reduce the input shadow price of cattle because permits increase aggregate grazing area, reduce biological constraints on cattle production, and make cattle easier to rear. After ranch-using pastoralists move animals to ranches, any leftover space on the commons is accessible to the remaining pastoralists. This implicitly increases the non-ranch-using pastoralists' income as well (by reducing scarcity in the commons and decreasing the shadow price of communal grass), allowing them to also rebalance their shoat-cattle bundles.

Ranch users
Ranchers set the quantity of permits sold to allow them to maintain space on their ranch for wildlife and their own cattle. At this quantity, the observed permit price must be no lower than ranchers' marginal opportunity cost and no higher than pastoralists' marginal demand. The efficient market-clearing equilibrium exists where both hold as equalities-the intersection of supply and demand. Because quantity remains fixed by ranchers, any deviation from the market-clearing price generates a transfer of economic surplus from one agent to the other 7 .
Since grazing permits are currently widespread in Laikipia, we use pastoralists' observed herds as a baseline to compare to a counterfactual where no permits are offered. We obtain each pastoralist's observed surplus by calculating their share of the total consumer surplus in the market. We express this cash value in terms of grazing permits by dividing by the current market price and subtract it from the cattleintercept of the current budget constraint (the dotted lines in figure 1) to rotate the constraint inwards. This simulates an increase to the choke price, where quantity demanded is zero (the y-intercept), effectively modeling a scenario without the permit market (the solid lines in figure 1). The slope of this new, steeper budget constraint is used to identify a tangency with a lower indifference curve, yielding the optimal bundle of shoats and cattle under the nopermits scenario.
We also compute the marginal impact of grazing permits. To do this, we use the simulated nopermits scenario as a new baseline and add the consumer surplus associated with one grazing permit to each ranch-user's cattle-intercept following the same process as above.
See appendix A for the derivations associated with this rotation of the budget constraints. Our analytical process, visualized in figure 1, assumes it is costless to obtain new animals and that grass availability is the only constraint on cattle production that is affected by grazing permits. These assumptions are reasonable in Laikipia, where new animals are generally bred instead of purchased and herding labor is largely fixed.

Non-ranch-users
After ranch-users move cattle to private ranches, they leave free space behind on the communal lands. This gives other pastoralists who do not purchase permits ('non-ranch-users') an opportunity to expand their herds to fill the space. The freed space thus provides an implicit income bump for non-ranch-users. In the same way that permits make cattle easier to rear for ranch-users-by reducing biological constraints on production-the extra grass on the commons makes both forms of livestock easier to rear for non-ranchusers.
For every TLU of freed commons space, nonranch-users' shoat-intercept increases by five and their cattle-intercept increases by one 8 . Graphically, this is a shift in the budget constraint as opposed to a rotation (figure 2). Because there are many more non-ranch-users than ranch-users, each non-ranchuser's income increase only reflects a fraction of the total freed space. We scale the freed space by the ratio of ranch-users to non-ranch-users when computing the change in implicit income.
To calculate new optimal livestock bundles, we follow the same analytical process used for ranchusers, summarized in appendix A. We do the same to evaluate the marginal impact of the permits. All the curves are calibrated using empirical data (see the Supplementary Material for the script used in data analysis available online at stacks.iop.org/ERL/17/ 035002/mmedia).

Data collection
We surveyed pastoralists living in Laikipia County 9 (figure 3) to collect information about their livestock production preferences and responses to grazing permits. Many sections of the survey ask about past and current decisions, while others rely on stated preference or behavior. We follow the recommendations of Johnston et al (2017) as much as local circumstances permitted, including qualitative pre-testing, tailoring questions to reduce cognitive burden, thoughtfully deciding between willingness-to-pay and willingness-to-accept, and allowing respondents time to think through their responses.
To inform survey design, we conducted semistructured interviews with pastoralists and ranchers to learn contextual information that also aids interpretation of the results. To refine the survey and add clarifying information, the survey was piloted with pastoralists living in the same villages as the ones we ultimately sampled. An English-language version of the questionnaire is shown in appendix B 10 .
The survey was administered in July and August of 2019, during a wet period in central Kenya 11 . 301 total responses were collected. Study villages were chosen to represent a large geographic spread across Laikipia (figure 3). Because our goal was to study the effects of grazing permits on pastoral behavior, all villages surveyed had some formal permit marketplace with a nearby ranch, with some of the most heavily surveyed villages having the most universal access to permits. These heavily surveyed villages were also the most accessible by road. Within each village, manyattas (family housing clusters) and village centers were sampled randomly. At each site, every adult present was interviewed.
To incentivize participation in the survey, each interview included an Eckel-Grossman risk game Grossman 2002, Dave et al 2010), where respondents bet on the outcome of a dice roll and received up to 135 ksh 12 depending on the result 13 . In general, we found respondents to be very risk averse. Approximately 58% of our sample is composed of women, partially because we surveyed most pastoralists at their homes, where women spend most of the day. The median age of our sample was 30. Most respondents had not completed primary school.
A local Maasai enumerator presented the questionnaire on a tablet in Kiswahili and read it verbally in Maa, the native language of most of the Laikipia pastoral community. Respondents who did not speak Maa had their interviews conducted in Kiswahili. Because our aim was to understand pastoral behavior, 10 Many questions present in the survey were not used for the analyses in this paper. 11 The high rainfall could reduce demand for grazing permits overall and lower respondents' willingness-to-pay, but this is true of the entire sample and does not impact our calculation of livestock preference parameters, which are the fundamental inputs to our model. 12 Kenyan shillings, approximately 100 ksh per $1 USD. 13 The results of the Eckel-Grossman game are used in a different study. we did not formally survey ranchers, though they participated in qualitative interviews.

First-order effects: ranch-users
Pastoralists pay well below market price for permits (figure 4) 14 . There are 54 ranch-users in the sample who collectively purchased 979 permits at an average market rate of 450 ksh/head/month ($4.50). By calculating the aggregate demand curve in our sample and intersecting it with the fixed supply of permits, we estimate that the market-clearing price for grazing permits is 762 ksh/head/month ($7.62). This disparity transfers an economic surplus from ranchers to pastoralists equal to 5662 ksh/head/month ($56.62) 15 . This is paid by all ranchers collectively to each ranch-user. Given current contract prices, this transfer is borne by pastoralists as an average of 12.58 'free' contracted cattle per ranch-using pastoralist.
Our modeling suggests that pastoralists use this transfer to expand their cattle herds and increase their ratio of cattle to shoats, as seen in table 1. When permits are not offered, current ranch-users are expected to maintain a cattle/shoat ratio of 0.08. This changes to 0.23 with the permit market in place.
To analyze the ecological impacts of pastoralists' decisions, we express the livestock changes in TLUs, where five shoats are equivalent to one head of cattle. When permits are not offered, current ranchusers are expected to keep a median herd size of 26.62 TLU. This increases to 32 TLU when permits are introduced.
These TLU increases are offset when animals are moved to private ranches, dividing grazing pressure between ranches and the commons. The median herd size kept on the commons by current ranch-users is expected to be 26.62 TLU with no permits in place and is 20.00 TLU with permits. This implies the commons see less grazing pressure from ranch-users after permits are purchased.

Indirect effects: non-ranch-users
Non-ranch-users are expected to keep a median of 35.12 TLU of livestock without a permit market and 30.00 TLU with a permit market. Much of this drop in TLU associated with the permit market comes from a switch that non-ranch-users make towards rearing shoats. When there are no permits, the median cattle/shoat ratio for non-ranch-users is modeled to be 0.31. This drops to a median of 0.23 when ranchusers receive the permits.
Herd expansion by non-ranch-users encroaches on much of the freed space that ranch-users leave behind. Each ranch-user is expected to leave a median of 4.01 TLU of free space when permits are offered. Non-ranch-users collectively fill over half of this free space. This equates to a net reduction 1.79 TLU of commons grazing pressure per ranch-user-just under two cows.  Note: All reported numbers are the median for the sub-sample. It is a coincidence that ranch-users and non-ranch-users have equal median cattle/shoat ratios with permits in place.

Marginal impact of grazing permits
To contextualize the results from this analysis, we multiplied the marginal effect of permits by the total number of permits sold in our sample. This gives us a rough practical sense of the effects of the permitting program on conservation, assuming the marginal effects scale linearly. For every permit sold, ranchers leave behind approximately 1.33 TLU of free space. The extra 0.33 TLU of freed space could arise from many factors not explained by our model. Non-ranch-users collectively fill around half of this freed space, such that for every permit sold, there is a 0.59 TLU net reduction in grazing pressure on the commons. This equates to 576 TLU of reduced grazing pressure on the commons when scaled to the level of the sample. All pastoralists in the sample collectively own 15 037.2 TLU of livestock, meaning the reduction in grazing pressure accounts for approximately 3.8% of the total pastoral livestock population.

Caveats
These numbers underestimate the degree that leakages dampen the conservation benefits. At the population level, there is greater competition for space left behind by ranch-users. Most of this dataset comes from villages with high ranch access, whereas most other communities in Laikipia have less universal access. Our modeling also does not account for leakages arising from pastoralists outside the system moving into Laikipia to graze their animals after ranch-users leave behind free space. This adds to the second-order effects described in this section and puts further pressure on already stressed resources (Burke 2017, Leithead 2017, Fox 2018. The only (non-ecological) limit to this leakage is the ability of the resident pastoral community to enforce their property rights, often through force since formal legal institutions are nonexistent. Our interviews suggest that these leakages are driven in part by a perception that communal rangelands in Laikipia are awash with free grazing area after ranchusers move their cattle away. Qualitative data in our survey support this, with 82% of respondents (Laikipia residents) stating that they expect others to expand onto the freed grass left behind after cattle move onto private ranches. However, we did not survey pastoralists from outside Laikipia, so our study cannot estimate the magnitude of the additional leakage.
The ecological underpinnings of this analysis also underestimate the effect of non-ranch-users and pastoralists from outside Laikipia, since our use of TLU does not account for the differences in grazing/forage behavior that make the ecological consequences of mixed shoat herds much different than cattle (Steinfeld et al 2006, Hart 2008. The analysis ignores changes in the number of camels, donkeys, or other livestock pastoralists may rear. Our estimate of 1.79 TLU of freed space per ranch-user, and 0.59 TLU of freed space per permit, should thus be considered an upper-bound.

Conservation outcomes
The overall effect of the permitting system on commons conservation is small, but positive. After ranchusing pastoralists move cattle off the commons, pastoralists who do not purchase permits expand their own shoat herds to fill some of the empty space. This alters the aggregate herd mix on the commons in favor of shoats. While we find some benefits from the permitting system in curbing overgrazing, they should be appreciated in the context of these herd mix changes and the sheer number of livestock currently owned by pastoralists in Laikipia.
A 3.8% reduction in grazing pressure does little to promote wildlife habitat. Consider that the 576 TLU total reduction in grazing pressure we estimate equates to approximately 720 zebras distributed across Laikipia 16 . With a total Laikipia zebra population around 30 000 (Georgiadis et al 2011), 720 animals is a positive but low proportion of the total population. Also, in reality zebras must also compete for space with other wildlife and cattle moving in from outside Laikipia, factors not included in our model. Finally, recall that private ranchers in Laikipia generally stock livestock at less than 1/3 the density that pastoralists do. This implies that, assuming constant abiotic conditions, pastoralists would need to reduce their herds by over 2/3 (67%) to produce a landscape that looks similar to private ranches. While such an extreme reduction in herds may be more than is necessary to achieve conservation goals 17 , it demonstrates that the 3.8% reduction due to permits is very small compared to the standard set by ranches in the area. 16 Assuming one zebra = 0.8 TLU. This is a reasonable estimate given that donkeys (0.7 TLU) are often used as surrogate zebras in the planned grazing literature (as in Odadi et al 2011). 17 Emulating private ranches is not necessarily a policy goal and the comparison is made here merely as a heuristic. Thus, it may not be necessary to reduce herds by the full 67% that would roughly equate pastoralists with ranchers. However, ranches provide a useful point of comparison due to their ability to host large resident wildlife populations.
The TLU reductions also do not account for differences in the ecology of the commons due to the new herd mix. The 'new' commons after permits are established contains a higher proportion of shoats, reducing the availability of browse compared to when those TLU were composed of cattle. This is troublesome for browsing wildlife species.
These ecological changes arise from exclusion of shoats from the permitting system, which creates incentives for many pastoralists to opt out of the permit market and flood the commons with shoats. This leakage demonstrates a complication seldom discussed in canonical models-the marginal entrant may have a different impact on the resource than the average user. If institutions reduce the average user's activity, marginal users can expand and impact the landscape in unforeseen ways. This has implications on the permitting system's ability to allay PLA concerns. While our results do not comment on additionality, they present a clear leakage via the indirect effects, and this leakage threatens the permanence of conservation benefits that arise from the ranchusers' reduced grazing pressure. However, the leakage is small enough that it still allows for some conservation benefits.

Conflict outcomes
Grazing permits are generally not offered to pastoralists who live outside Laikipia. This is a consequential omission, considering one major impetus for the permitting system is the conflict that results from these pastoralists moving into Laikipia from outside the system. However, our interviews indicate that lingering distrust between Laikipia Maasai and pastoralists from other tribes outside of the county make it risky for ranchers to develop strong relationships with these 'outsiders' . Ranchers risk alienating their Maasai neighbors if they provide permits to herders from outside the county, so they instead leverage strong partnerships with these neighbors to help defend against trespassing by the outsiders.
This dynamic motivates a secondary finding of this study: ranch-using pastoralists are able to use the permit market to extract economic rents from ranchers by leveraging the threats of violence and illegal grazing. Ranchers rely on ranch-users to help police their communities for illegal grazing and serve as the first line of defense if others move in from outside the system. This conciliatory dynamic is dependent on the goodwill extended by ranchers in the form of cheap permits, creating a mechanism for ranchusers to continue demanding below-market prices 18 . The arrangement represents a unique ability for pastoralists to exercise greater market power in a system 18 This arrangement is still economically efficient as long as the profit losses to the ranchers are less than or equal to the cost of hiring extra guards to enforce their borders or being subject to violence. with no regulatory oversight and violent unrest in its recent history.
Another unintended consequence of the permitting system is persistent inequality. Qualitatively, wealthy pastoralists generally have better access to grazing patches on private ranches and are more likely to be ranch-users (Hauck and Rubenstein 2017). While the permitting system benefits non-ranchusers through relieved cattle pressure, the benefits of the program appear to accrue disproportionately to ranch-users since they additionally receive economic surplus from ranchers (increasing their welfare). The larger per-TLU economic value of cattle compared to shoats also means pastoralists dependent on shoats receive smaller economic returns from increasing their herds 19 . Thus, while the permit system appears to increase welfare for all, it does so unequally, which carries its own potential for intracommunity conflict.

Takeaways
All of the dynamics described in this article play out over a long-term equilibrium, where pastoralists have time to grow their herds and encroach on freed space. However, in practice, semi-arid ecosystems in East Africa rarely reach equilibrium due to regular drought shocks (Ellis and Swift 1988). These droughts dampen the second-order effects described in this article by periodically devastating livestock herds or inducing pastoralists to sell off their small stock, ironically making droughts positive for wildlife due to reduced competition with livestock. However, the status quo of intensive land use by pastoralists keeps wildlife away from the commons for much of the year. Thus, the grazing permits alone are not a reliable tool to promote conservation and rehabilitate wildlife habitat, and should be paired with practices such as planned grazing that have been demonstrated to improve conservation outcomes on pastoral lands (Odadi et al 2017, Crawford et al 2019. If the program were able to significantly expand in size and scope, the small marginal improvements could translate into large conservation gains. Exactly how much the program needs to expand depends on the goals of decision-makers and stakeholders, but any expansion should include shoats and be accompanied by improved management institutions that enable excludability on the commons or implement planned grazing 20 . These changes would help close 19 One head of cattle raised on a private ranch generally sells at a market rate of approximately 30 000 ksh ($300). Compare this to shoats, which fetch 3000 ksh ($30) per head. Thus, 1 TLU of cattle will yield twice the economic return as 1 TLU of shoats, should pastoralists ever need to sell their stock. 20 Encouragingly, such management institutions are currently being developed on some pastoral lands in Laikipia, which could help promote conservation and reduce future conflict (Ostrom, 1990). the leakages driving PLA concerns and improve the conservation outcomes of the program.
However, selling more permits would cut into ranchers' grass bank and ranchers are not currently interested in offering permits for shoats, making it unlikely that ranchers would support the large expansions of the permitting program necessary to recover wildlife populations. Resolving this tension is an important intervention for local planners interested in making the permitting system successful. Still, this novel market has given ranchers and their pastoral neighbors a reason to work together and resolve their differences while modestly improving the quality of the pastoral rangeland.

Data availability statement
The data generated and/or analyzed during the current study are not publicly available for legal/ ethical reasons but are available from the corresponding author on reasonable request. Research Centre in Kenya, which hosted the researchers during field work. We also thank the ranchers of Laikipia County, who took time to participate in meetings and interviews. Special thanks to the pastoral community of Laikipia County, who welcomed the researchers into their homes and shared information about their lives. Finally, a very special thanks to our enumerator Emmanuel, our pastoralist partner Grace, and our ranching partner David, all of whom were indispensable to the research process from design to implementation.

Ethical statement
This study was granted a waiver of approval by the Yale University Institutional Review Board under Protocol ID 2000026182. No identifying information was collected from respondents and the exemption was granted under 45CFR46.104 (2)(ii). Consent was obtained by all study participants.

Construction of the indifference curves
To estimate indifference curves, we assume a constant elasticity of substitution (CES) household production function, taking the following specification where income from household production, U, subsumes the technology parameter: (1) C represents number of owned cattle, G represents number of owned shoats, α is the CES share parameter, and ρ is the CES substitution parameter. Along a household production level set, we derive a first order condition: (2) Survey data on C and G enable estimation of α, ρ, and the livestock price ratio w C /w G , the latter of which is equal to the marginal rate of technical substitution (MRTS). Assuming pastoralists balance shoat and cattle herds to maximize U, the implicit function theorem for a fixed factor budget constraint, A, yields an equivalent expression of MRTS: To recover the right-hand side of equation (4), we calculate the change in the herd sizes of cattle and shoats as a function of permit price up to a secondorder Taylor approximation: where p is the monthly price for grazing permits, C is total cattle herd size, and G is total shoat herd size. These curves can be used to compute the right-hand side of equation (4): Equation (7) expresses the MRTS for the subset of pastoralists who have a defined slope for cattle and shoats as a function of grazing permit price, which is about a quarter of the sample 21 .

Rotating the budget constraints
To simulate the budget constraint rotation (a shift to a counterfactual of no permit market), we begin by rearranging equation (2) for C: Equation (8) expresses the optimal number of owned cattle as a function of the number of owned shoats and individual preferences. The current budget line-with permits in place-takes the following form: where G 1 is the shoat-intercept of the budget constraint and MRTS equals the magnitude of the slope. In figure 1, equation (9) is the straight dashed line. This line is rotated in by subtracting the consumer surplus (put in terms of grazing permits) from the original cattle-intercept. After the budget constraint is rotated inwards, the new slope is denoted as b: the slope of the straight solid line in figure 1. To find the shoat-cattle bundle chosen without permits, we substitute C from equation (8) into equation (9), and change the slope term, MRTS, to the new slope b.
Solving jointly for the new optimal number of shoats, G * , and cattle, C * , yields:

Empirically estimating the indifference curves
To estimate the CES preference parameters, we rearrange the first-order condition to a form that can be estimated by linear regression, noting that the price ratio w C /w G is equal to MRTS at each price level. Taking the natural log of the first-order condition in equation (2) and simplifying yields: where i indexes the five given permit prices and j indexes individuals. The index j accounts for all nonprice varying attributes of individuals in the survey. Equation (12) is suitable for estimating mean values of α and ρ for the sample. In order to get parameters for each individual, we add in fixed effects γ j and κ j : Equation (13) allows computation of a CES indifference curve for each respondent with a computable MRTS. The estimated slope identifies the substitution parameter: B is the calculated global parameter on log ( C G ) in equation (13). To solve for the individual share parameterα j , whereᾱ is the α inside the first log term on the right-hand side of equation (13): We use theseα j 's andρ j 's to compute individual CES indifference curves for every respondent. We assign the medianρ j and medianα j to the three-quarters of respondents whose MRTS cannot be computed from the data.

Appendix B
First, I want to get to know you Next, I want to gauge your preferences through a couple short activities (Note: the order of the options in Q20 was randomized.) 20.If someone approached you and wanted to take a 450 kg heifer from you, how much of the following items would they have to give you in return?
Remember that if another community offers a lower price, then the trader will likely trade with them and not you. It also okay to say you would not trade a heifer for any amount of the good being offered. _____ steers _____ I would never give up a heifer for any amount of steers _____ sheep/goats _____ I would never give up a heifer for any amount of sheep/goats _____ months of the right to graze one cattle on a nearby ranch _____ I would never give up a heifer for any amount of grazing rights _____ ksh of SIM card airtime _____ I would never give up a heifer for any amount of SIM card airtime _____ smartphones _____ I would never give up a heifer for any amount of smartphones _____ terms of school fees for son _____ I would never give up a heifer for any amount of school fees for a son _____ terms of school fees for daughter _____ I would never give up a heifer for any amount of school fees for a daughter _____ kg of maize _____ I would never give up a heifer for any amount of maize _____ months of electricity for your house _____ I would never give up a heifer for any amount of electricity _____ ksh cash _____ I would never give up a heifer for any amount of cash 21.Imagine a nearby ranch will sell rights to graze on its land to only a few households. Everyone will make an offer, put it in an envelope, and seal it. Nobody will know each other's offers, but the rancher will see them all and choose the households who offered the most money. How much money would you offer the ranch per head of cattle, per month, to graze on their land under the following deals? The rancher provides herders and metal bomas, sprays for ticks twice a month _____ ksh/head/month The rancher provides only metal bomas and dictates where you are allowed to take your cattle _____ ksh/head/month The rancher provides nothing, but you may manage your cattle how you wish on the land _____ ksh/head/month 22.Please tell us what would most likely happen on the group ranch if you won the right to graze two animals on a nearby ranch during the dry season.
(a)I would get more cattle to graze on the group ranch.