## Servicios Personalizados

## Revista

## Articulo

## Indicadores

- Citado por SciELO
- Accesos

## Links relacionados

- Similares en SciELO

## Compartir

## Agricultura, sociedad y desarrollo

##
*versión impresa* ISSN 1870-5472

### agric. soc. desarro vol.1 no.2 Texcoco jul./dic. 2004

**An option value analysis of the monarch butterfly forests**

**Un análisis de valor de opción sobre los bosques de la mariposa monarca**

**Antonio Kido ^{1}**

^{1 }*Economía. Campus Montecillo. Colegio de Postgraduados. 56230. Montecillo, Estado de México. *(ankido@colpos.mx)

**Abstract**

This study compares the timber and amenity value of a particular forest, and questions whether or not harvesting a larger area of a special biosphere reserve of the monarch sanctuary is more or less efficient from an economic perspective. Results show that, when only use value is taken into account, amenity value will exceed the critical amenity value, suggesting that larger exploitation should not be allowed.

**Key words:** Amenity value, critical amenity value, timber value.

**Resumen**

En este estudio se compara el valor forestal y el valor recreativo de un bosque en particular, y se discute la conveniencia de explotar una mayor área de ese bosque, considerado como reserva especial de la biosfera de la mariposa monarca. Los resultados señalan que, sólo considerando el valor recreativo como valor de amenidad del bosque, este valor excede un valor crítico que sugiere que no debe alentarse una política de mayor explotación forestal en esta reserva.

**Palabras clave:** Valor de amenidad, valor crítico de amenidad, valor forestal.

**Introduction**

Forests have two types of values: that of the harvested timber and the value of a preserved wilderness area. The value of preservation can be divided in use value (recreation) and those that stem from protection flooding and preservation of wildlife. All of them can be, globally, referred to as amenity value (Reed, 1993). This amenity value presents greater uncertainty regarding its future benefits to society. Therefore, harvesting a forest eliminates the annual dividend of its amenity value. The biosphere of the monarch sanctuary was declared a reserve area on October 9^{th}, 1986. (Diario Oficial de la Federación, 1986). In 1999 the owners of the land asked the Mexican government to change the extension of the protected area. The specific proposal was to reduce it from 16 110 to 12 500 ha. With such a measure, the ejidatarios could use the difference for forestry. The petition to decrease the area argued the necessity of increasing the income from the forests and decreasing illegal forestry activities in the zone. The 1986 decree was revised in 2000. In November 10^{th}, 2000, a new presidential decree established a total area of 56 259 ha for the biosphere, (Diario Oficial de la Federación, 2000). The former area (16 110 ha) was increased to 56 259 ha, of which 14 000 were considered core zones where no human activity would be allowed, while the remaining area (42 000 ha) are considered buffer zones where ejidatarios are allowed to extract a certain amount of timber from the forests, using government permits during the months when the monarch is not present.

The expansion of the protected area increased landowner's protests, and also the risk of illegal extraction of wood. After the 2000 decree, year after year, media coverage continued the discussion of this issue. Two opposite positions prevail. The landowners claim for a larger forest exploitation area, while the environmentalist groups demand a greater protection of the forest. The objective of this paper was to determine and compare harvest benefits and amenity value of the biosphere reserve of the monarch butterfly.

The biosphere of the monarch butterfly has a total area of 56 259 ha and it is located in portions of the states of Michoacán and México. This reserve includes 11 municipalities: Angangueo, Aporo, Contepec, Ocampo, Senguio, Tlalpujahua and Zitácuaro in the state of Michoacán; and Donato Guerra, San Felipe, Temascalcingo, and Villa de Allende in the state of México. The biosphere has, currently, five sanctuaries open to visitors: Cerro Altamirano, Sierra Chincua, El Campanario, Cerro Chivati, and Cerro Pelón. However, since data on visitors for the 1985-2002 period exists only for the Campanario Sanctuary, the analysis of visitation will be done only for this sanctuary.

**Materials and Methods**

Assuming that all benefits and costs are considered in the conservation option of the forest management, there is an important part of the benefits which is often ignored. Consequently, there is an increasing conversion of natural areas to other uses where natural habitat and environmental functions are destroyed. The option value approach is used to determine whether or not to preserve a forest with a known timber value and uncertain future amenity value. Option value takes into account two characteristics that are common to many investment decisions: irreversibility, and the ability to delay a decision. Making an irreversible investment decision has an opportunity cost that must be considered if the desirability of the investment is to be correctly evaluated. (Forsyth, 2000).

**Logistic or geometric process**

This paper makes an application of Conrad (1997) and Forsyth (2000) examples of a wilderness area in a developing country. Therefore, the first step is to determine what process amenity value in the biosphere follows. A Dickey-Fuller test was performed on a data series of visitors of the sanctuary El Campanario located in the Michoacán State, one of the five sanctuaries included in the biosphere. The data series include 18 years, beginning with the 1984-85 season, when 7 500 visits were registered in the visitor's book of the sanctuary, (Table 1).

The regression model for testing geometric brownian motion was:

where R is the number of visitors and T refers to time. Using the data from 1985 to 2002 the null hypotheses were rejected. This means that the geometric brownian proceses was rejected. The b estimator was statistically different from zero (p **≤** 0.01), and p different from one (p **≤** 0.01).

**Models**

The stochastic process for amenity value is modeled as a logistic process in this paper, even though a geometric process can also be used. When amenity value is defined as user value only, it can be assumed that amenity value follow a logistic process, with a maximum limit in that value plus a variance, growing both linearly with time.

where A is amenity value, r the discount rate, and A_{max} the maximun expected amenity value.

The relevant equations are:

where δ is the instantaneous discount rate, and the second term on the right hand is an expected capital gain. This equation tells us that the owners of the forest must receive a return equal to A, plus the expected capital gain and this value must equal, in equilibrium, what they would receive if they sold the forest and put the proceeds in the bank at rate d. The following equation indicates the rules of thumb for harvesting or conserving a forest.

The homogeneous portion has a solution which takes the form:

Where k_{1} and k_{2} are constants, and β and α are defined as:

If δ < μ, it will never be optimal to cut the forest. For δ >μ there will exist a critical lower bound for amenity value, denoted A*. If amenity value ever drops to this level, it would be optimal to cut the forest.

Equation (8) gives the critical value, and N represents the forestry value. This critical value may be interpreted as the minimum amenity value necessary to justify continued preservation from a social point of view (Conrad, 1997).

For estimation purposes the following regression model was used to get the relevant estimators of the critical amenity value with ordinary least squares, and it responds to the idea of estimation amenity value for only one period of time.

where V is the number of visitors to the sanctuary, V_{max} the maximum number of visitors allowed in it, r is the drift rate in discrete time, and ε_{t} is normally distributed with mean zero and standard deviation σ.

**Results and Discussion**

**Carrying capacity**

It is thought that crowdedness and congestion of any place makes it less enjoyable (Cornes and Sandler, 1986). The idea is that when more visitors are in a forest, less amenity value is assigned to it. A calculation of the maximum allowable number of tourists in the sanctuary El Campanario was made, taking into account some basic elements. The length of the trail is 2500 m, 5000 m with the return trip. With a width of 3 m it was assumed that 11 people per group can easily walk on the trail, leaving a distance of 100 meters between each group. Each person, when walking, occupies 1 m^{2}, so that each group needs 11 m^{2}. According to these numbers, the optimal number of people at the same time on the trail is about 227 (2500/ 11). The sanctuary is open nine hours each day, (from 9 to 18 h) and each visit takes 1:30 h, so different groups can walk the trail six times. Multiplying the number of times a group can walk the sanctuary by the total number of visitors at each time, we can obtain the optimal number of visitors per day in the sanctuary. In this example 1363 people were estimated as the optimum number. Because the sanctuary is open from November to March each season, the carrying capacity of the sanctuary would be about 181 146 persons.

**Willingness to pay**

In a contingent valuation, 353 surveys were conducted in the sanctuary in March, 2002, asking people about their willingness to pay to protect and conserve the sanctuary El Campanario. Fifteen surveys were dropped because of inconsistencies in the income reported, remaining 338. From these 338, 97 (28.6%) represented bid responses. According to Loomis (1997) nonresponse rates of 20 to 30 % are common when the object under valuation is an amenity which people have little information about or do not know how to assign an economic value to it. From the 97 bid responses, 67 were considered protest responses, and were not included in the WTP calculation. Two of the most common protest responses were that households do not have to pay for conserving the sanctuary and the management of money was not clear and safe. The average WTP was found to be 26.2 dollars, using an exchange rate of 9.5 pesos per dollar.

**Timber value**

Pine and oyamel are the two types of trees found in the sanctuary. Of the forest surface, 90% is covered by pines and only 10% by oyamel. The trees have an average age of 60 years and it is permitted to cut some trees in buffer zones. It is assumed that 100 m^{3} of wood can be extracted from one hectare of forest. In March 2002 the cost of a cubic meter of pine was estimated at 450 pesos (47.4 dollars) and that of oyamel at 300 pesos (31 dollars). The average weighed price for a cubic meter of wood in the area was 45.76 dollars. The total value of logging the forests of the biosphere is 3 411 072 U.S. dollars. This is a rough estimate proportioned by personnel of theDirección General Forestal (SEMARNAT, 2002).

**Amenity value**

Conrad (1997) and Forsyth (2000) assumed that amenity value (A) is proportional to the number of visitors (R). This is also assumed in this paper. Since no time series data exist for amenity value, user values are used as a proxy.

where A is amenity value, γ is willingness to pay and R is number of visitors. Once it has been defined a maximum number of visitors to the sanctuary, amenity value in period t and maximum amenity value can be calculated

The maximum amenity value would be:

The relevant parameters for a logistic process were estimated through equation (9). Results are shown in Table 2.

Assuming a logistic process, values of the relevant parameters for calculating the option value are δ = 0.1, *μ* = r = 1.04, N = 3.4 million dollars, and α = -0.413. The critical value of A* is 2 312 400 dollars, meaning that annual amenity value would need to be in excess of this amount, per year, to justify preservation. The amenity value for 2002 biosphere forests was 2 560 395 dollars and maximum amenity value was 4 746 025 dollars, indicating the convenience of preserving the forests of the biosphere of the monarch butterfly.

**Conclusions**

Results show that for a relatively high discount rate of 10%, and under the assumption of 26.2 dollars as the average willingness to pay per person, the amenity value obtained from the biosphere forests is 2 560 395 dollars. The critical amenity value A* was found at 2 312 400 dollars, below the amenity value. These results suggest that best use of the biosphere is as a wilderness area, despite an appeal to the maximum amenity value and other non-user values. These results also suggest the need of finding out another causes of illegal exploitation.

**References**

Conrad, M. J. 1997. On the option value of old-growth Forest. Ecol. Econ. 22: 97-102. [ Links ]

Cornes, R., and T. Sandler. 1986. The Theory of Externalities, Public Goods, and Club Goods. Cambridge; New York: Cambridge University Press. 301 p. [ Links ]

Diario Oficial de la Federación. Octubre, 1986. Decreto que establece la reserva de la mariposa monarca. Ciudad de México. pp: 65-98. [ Links ]

Diario Oficial de la Federación. Noviembre, 2000. Decreto que amplía el área natural protegida, con el caracter de reserva de la biosfera de la mariposa monarca. pp: 137-158. [ Links ]

Forsyth, M. 2000. On estimating the option value of preserving a wilderness area. Can. Econ., 33: 413-434. [ Links ]

Loomis, J. 1997. Panel estimators to combine revealed and stated preference dichotomous choice data J. Agr. Res. Econ.: 233-245.

Reed, J. W. 1993. The decision to conserve or harvest old-growth forest. Ecol. Econ., 8: 45-69. [ Links ]

Sanctuary Record Book (Several years). Ejido El Rosario, Ocampo, Michoacán, México. 150 p. [ Links ]

SEMARNAT. 2002. Subsecretaría de Recursos Naturales. Dirección General Forestal. México, DF. (Draft). pp: 10-27. [ Links ]