14
CHINAGRO[1]
TRAINING COURSE (II)
Policy Decision Support for
Sustainable Adaptation of China’s Agriculture to Globalization
September 23-24, 2003, Beijing
NOT FOR QUOTATION
Lecture 3
Towards a spatially and socially explicit Chinese agricultural policy model:
a welfare approach.
M.A. Keyzer
Centre for World Food Studies
SOW-VU, Amsterdam
1. Introduction
The present lecture consists of two parts. In part I we expand on the relationship between the general equilibrium welfare optimization and competitive equilibrium. This provides the major justification of our methodology. This part essentially discusses the established micro-economic principles as described in chapter 1 of my textbook on applied general equilibrium written jointly with Victor Ginsburgh, to which I may refer for further reading.
Besides the fundamental justification, one practical reason, discussed in the previous lecture, for moving from partial to general equilibrium is that one seeks to achieve a proper multi-commodity multi-agent representation, for example to reflect the diversity of the resource basis and cropping patterns of farms and the non-tradability of some of the inputs between them. At the same time, we want to account for the substitutability on the demand side, and perhaps most importantly, for the technological interactions between the livestock and the crop sector, through feed requirements, draft power, and availability of manure.
Yet, as was also mentioned in the previous lecture, we also want to keep track of the implications generated by the aggregation over markets. Therefore, in the second part of the lecture, we return to the single commodity partial equilibrium model, briefly sketching the algorithm designed especially for it, and showing you some recent findings.
2. Introduction to welfare, AGE-modeling and the Chinagro-welfare model
2.1 Welfare and competitive equilibrium: basic results
Before describing the Chinagro general equilibrium model, I provide some background on general equilibrium theory, in particular on the relation between welfare optimization and competitive equilibrium, as spelled out in the first and second welfare theorems.
In a nutshell, a competitive equilibrium is an allocation of commodities, in which consumers maximize their utility subject to a budget constraint, producers maximize profits subject to a technology constraint, all take prices as given, and total demand does not exceed total supply.
The competitive equilibrium, rather than being an abstraction in mathematical economics, has the important normative virtue of being Pareto efficient, as proved in the First Welfare Theorem.
The Second Welfare Theorem states that any Pareto efficient allocation can be achieved as a competitive equilibrium with transfer. Hence, distributional considerations can be met through transfers, and there is no need to use the price mechanism for this. Consequently, there is room to let the price mechanism operately freely.
An important theorem that forms the bridge between both says that any Pareto efficient allocation, can if utility functions are well behaved, be expressed as a welfare optimum with given welfare weights on individual utilities.
Finally, the Negishi Theorem says, that there exist weights, such that the solution of the welfare program corresponds to a competitive equilibrium without transfers.
As Pareto efficiency has become such a high-prized property, the conditions of competitive equilibrium have gradually been transformed from a theoretical construct to a policy recipe, witness the so-called Washington consensus.
Note that these conditions are non-trivial in terms of the institutional requirements they impose. In particular, the fact that consumers should take budgets as given, and that producers maximize profits at given prices is important, since it implies, among others:
(1) all goods in the economy are priced (no free use)
(2) no one can manipulate prices (no monopoly)
(3) all consumers pay the price of what they use, and receive the price for what they sell (no crime).
(4) producers maximize profits independently of the preferences of the shareholders who own it (shareholder’s value as principle).
2.2 The Chinagro welfare model
We are now ready to present the Chinagro general equilibrium welfare model, in its static version for a single year. For this we expand on the partial equilibrium model with aggregation over markets considered in the previous lecture. Recall the partial equilibrium welfare program with aggregated markets from the previous lecture.
The generalization that is introduced to formulate a general equilibrium version consists of the following steps:
(1) We consider all goods simultaneously. Hence, the variables of this program are now vectors with commodities as elements. Furthermore, products terms such as denote inner products.
Specifically, denotes the vector of net supplies of site s, with positive entries for outputs and negative entries for inputs. Hence, we no longer distinguish the inputs into agriculture , since these are now subsumed under net supply, that obeys a linear technology, as the vector of inter-regional transport requirements (and in fact only requires non-agriculture as input) and , the vectors of intra-regional requirements:
(3.2)
(2) The economy is an open economy that trades with the outside world at given prices. By contrast, in the partial equilibrium model, the outside world is represented through separate offshore sites, just across the border. Hence, the partial equilibrium model is a simplified world model with endogenous prices, and is in this respect more complete than the general equilibrium form.
(3) The general equilibrium model imposes a balance of payments constraint: at given import prices , and export prices , such that , the imports from the outside world should not exceed exports incremented by a given, possibly negative balance of trade deficit:
(3.3)
(4) The general equilibrium model does not require utility to be in money metric. It has a general utility function that is symmetric across goods. This, among others, makes it possible to represent meat demand in a more satisfactory way. The welfare function now performs the conversion from site-specific utility to money metric through a given, positive welfare weight , and thus made comparable across consumers:
. (3.4)
(5) The general equilibrium model has a detailed component for agricultural production. Tomorrow’s lectures will provide you with further details on this. For now we merely represent this by replacing the production function through a strictly quasiconvex transformation function .
Consequently, the Chinagro general equilibrium welfare model reads:
This is the full model we are concerned with in its static version. Indeed, this illustrates the major practical advantage of the welfare approach that it can accommodate a complex economic system in a transparent way.
One qualification is in order. For simplicity we have assumed here that all transportation costs within site are truly incurred. For the reasons explained in the previous lecture, this is an unwarranted assumption.
3. New, homotopy-based algorithm for to solve very large partial equilibrium welfare program with transportation
In the last part of my three lectures I discuss the spatially explicit, but partial equilibrium model with transportation, that operates as was mentioned earlier, in the background of the Chinagro-general equilibrium model, to check its transport flows and price margins, and as the prototype for the next generation of this model. Hence, we return to the partial equilibrium welfare model of the previous lecture, and for simplicity treat production as given:
So far, the work for the partial equilibrium model have focused on the evaluation of transport costs, along the formal infrastructure of highways, railways and waterways, one the one hand and along the less formal infrastructure of secondary roads and pathways on the other, which provide the link between the farmer’s field and the main transport infrastructure. The calculations to evaluate the unit cost per ton-kilometer by grid cell are necessarily somewhat tentative.
For the formal infrastructure we merely evaluate the mean unit costs, by applying statistically recorded expenditures on transport in each category per ton kilometer to the available infrastructure. For the less formal infrastructure, which essentially covers the whole space the per tonkilometer transport costs are modulated to rise with altitude and variability in slope, and to fall with population density a proxy for the availability of vehicles. The resulting map is shown here.
It is important to note that transport costs are prohibitive in many parts of the map, indicating that for example in the high mountains, transport is only possible along highways and railroads. Hence, the unit costs do not and should not coincide with observed average transport cost per unit, which also makes their measurement less easy.
We also remark that the term transportation cost itself is problematic. The cost of physical transportation along formal infrastructure of highways, railroads or waterways, is often relatively low, also in China, and especially for waterways. Indeed, if we were to account for the pure per ton-kilometer cost of moving the commodities, only a small fraction of the consumer price is on transportation. HHoHoHowever, we must also allow for the storage cost, and the cost of changing from one, informal mode of transportation to the other. In fact, the time needed for a farmer to reach the collection points, and for the retailer to reach the end-consumer, are major elements of the transportation cost, and are not suppressed in our approach since most of these will generally extend over distances larger than 10 kilometers.
Spatial data for the partial equilibrium model were collected for production and consumption of rice and wheat, determining the optimal demand, routing and equilibrium pricing for given production levels. We report on this shortly.
Algorithm
The algorithm designed to solve this partial equilibrium model is monotonically converging for any given price ordering, and improves from one price ordering to the next. Consequently, it ends after a finite number of orderings.
If we start from a spatial grid of points, describing, say the map of a country, in two dimensions, we may note that every cell has 8 neighbors.
To solve this problem, we have formulated a new algorithm that has monotonic convergence. Its basic idea is that of imposing a gravity ordering inspired by hydrological modeling. At given prices, optimal transport flows never run from a destination with a high price to one with a lower price, just like gravity ensures that water never flows to a higher location. This makes it possible develop an algorithm that recursively runs from one site to the next, and proceeding in the following four steps.
The first step imposes such a gravity order ruling out any flow from low to high price
In the second step, for given price ordering, we solve for all sites starting from the lowest ranking price a site specific welfare program, that maximizes money metric utility plus sales, at given sales price and inflow volume
The third step proceeds in reverse order from high to low price, that is from delivery to source, adjusting the sales price to marginal value of inflow. After this step we return to step 2, until convergence
Finally, if any aggregate welfare improvement was achieved after convergence since the last ordering, we return to step 1. Otherwise, the global optimum has been found.
To illustrate the operation of the algorithm, we present an application that determines the optimal spatial spatial distribution of consumption, price and inflow will be depicted by shadings on a map. This application is for China and is based on a population map and a production and consumption map, on a 10-by-10 kilometer grid, that is for over 94000 markets, over 2300 counties, coupled through flow possibilities in eight, so called union jack directions.
The application is for rice and for wheat.[2] You will see maps entitled price, flow, production and consumption, of which only production is given exogenously. Consumption is endogenous but to a large extent reflects the given distribution of population. The price map highlights the major imbalances in supply demand given the assumed transportation costs and availability and capacity of border crossings.
The combined the maps of consumption, production, flow and price are rather informative. They highlight a few well known points.
For rice consumption, which obviously is largest in regions with high population density, it appears that production is generally not located far from production. The production and the consumption map do not differ too much. Prices are lower in supply zones, especially in distant ones. And flows are largely domestic. International trade only plays a limited role, and the country is so large, that local production is reasonably well protected against foreign imports, which enter at seaports. Clearly, this has significant implications for the effect of possible trade liberalization under the WTO-process, and bilateral agreements with Europe and America.
Wheat production overlaps in some areas with rice production and exhibits similar patterns but it is somewhat more distant from production, witness the longer stretches and more dispersed flows.
Furthermore, for optimal flow shares, it is possible to trace how deep the flows from a given import site reach inland in the import and export maps. However, this only refers to the physical linkage. The price linkage extends much deeper, because at the boundary of an import or export delivery zone there may be a site that obtains product both from imports and from its neighbors. At such a site the price of domestic deliveries is the same as for foreign deliveries and consequently, all upstream suppliers and consumers in the basin are affected by it. To depict this, we also show the regions with local autarky that are truly isolated from the world market. The dark shaded parts in the map of local autarky represent the areas that do not have any inflow of the product from outside. The lighter dots and lines are the points that were “shaved off” by the algorithm, that is the points that do not receive the product but form isolated dots or open lines segments. We note that there are few zones with both local autarky and internal trade. Such zones are light areas enclosed by a dark line. In fact, in the optimum shown, most autarkic areas are essentially unpopulated mountains, deserts or steppes and do not trade at all.
The model describes optimal consumption and transportation of rice in China and on a 10-by-10 kilometer grid, that is for 93125 markets. The flows can leave and enter the country at a limited number of seaports, and inland border crossings. The introduction of these Rest of the World Units makes it possible to deal with a model of the whole world, in which only China is represented in full detail, and the other regions in a more stylized way.