جنگل زدایی و توسعه در یک اقتصاد باز کوچک

Our economy faces world prices and starts with a large endowment of land in forest and a small endowment of land in agriculture. Clearing of forested land yields marketable timber and a unit of land for agriculture. Early, the high price of agricultural land drives the clearing process. Later, the profit from marketing timber from the cleared land drives the process. Dates of “phase transitions” are endogenous. We also set out a submodel of perpetual cyclic clearing and reforesting, and show that it when cyclical harvesting—regrowing is optimal, the extent of clearing can be relatively large.

We investigate the argument that deforestation is a market mediated stock adjustment for a hypothetical small open economy that “opens” with “too much” land in forestry relative to agriculture. Deforestation or stock adjustment is formulated as gradual in our model, with three phases: clearing timber at a loss per tree cut, clearing timber at a surplus per tree and at a surplus per unit of agricultural land opened up, and clearing forested land at a loss per unit of agricultural land open up. The latter phase raises the question of whether, once the trees are cleared, it might not be most profitable to return the land recently converted to agriculture, back to marketable timber. We investigate the possibility of such a cycle as being the equilibrium outcome of our process of land conversion. We find support for a terminal phase of cyclical clear cutting for part of the originally forested land. We come at this topic with the history of Canada and the United States in mind. There were small open economies, starting with an underendowment of agricultural land and deforestation was a natural process, taking place within a system of markets. These are our stylized small open economies. A small, open economy generating revenue for consumption and investment from natural capital is known in the literature as a “staples economy” [8, 14], and our analysis can be viewed as an instance of the staples theory of development.2 In contrast with Faustmann [4], our cycling model has the area left for the regrowth of trees as the control variable, rather than the size or age of the trees. The cycle involves then a fixed interval of re-growth and an endogenous interval of reclearing. If an end phase of cyclical timbering is optimal, we observe examples in which the start of “replanting” occurs with more land cleared than would have been cleared in the solution with cycling ruled out, a priori. The possibility of a terminal mode of cyclical timbering “pushes” the margin of cleared land relatively far. We find that it may be optimal to push this margin beyond the level that would be the optimal steady state in the “benchmark case” (examined in Section 2) where cycling is not permitted. We refer to this result as the possibility of overshooting the steady state level of of forest land area. That is, the economy may first clear more land than the steady state of the benchmark case as the initial state of cycling is started. There are some indications that this is happening in certain areas, particularly in North America. There is, of course, an alternative explanation: one could argue that the economic and technological conditions have changed so that the steady-state amount of clerared land has changed. A complete model of development of virgin territory would have immigration a central component, and would consider the allocation of labor among three activities, sustainable agriculture, sustainable activity on forested land, and land clearing. This was done in a fuller version of this paper. To economize space, in this paper we abstract from these issues and take up a specialized version, with the labor allocation at each date left implicit. In this simpler model, there is a single control, the amount of land to clear, and a single state variable, the amount of land in forest at each date. Using this model we can address the possibility of a perpetual cycle of clearing–regrowing.

We set out a model of land clearing in a small open economy as part of “development” of the economy. The country opens with insufficient land for agriculture, given world prices for outputs, and clearing of forested land is a response to the high initial price of agricultural land. Three stages ensue: clearing with net costly removal of forests, clearing with profitable timbering while clearing, and profitable timbering while clearing but a net loss on the land being switched from forest use to agricultural use. The dates of these phases are endogenous. Clearing is in a sense an adjustment of endowments to the appropriate steady state values. Under a strategy of saving and investing for constant consumption, current rent on timber cleared is the amount to invest. Of interest is that saving will be negative in the early phase. Development involves borrowing against the value of natural resource stocks, in the early phase. In a complication of our basic model, we consider a final phase in which land is turned over in a perpetual cycle of clearing and reforesting. The model we develop is a variant of the classic Faustmann model of optimal forest management. We show that, when cycling is the dominating choice, it is optimal to overshoot the steady state of a monotone deforestation program.