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Lecture 3

Lecture 3. Towards a spatially and socially explicit Chinese agricultural policy model: A welfare approach M.A. Keyzer. Presentation available: www.sow.vu.nl/downloadables.htm www.ccap.org.cn. Overview of the lecture. Introduction Welfare economics, AGE-modeling, CHINAGRO model

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Lecture 3

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  1. Lecture 3 Towards a spatially and socially explicit Chinese agricultural policy model:A welfare approachM.A. Keyzer Presentation available: www.sow.vu.nl/downloadables.htm www.ccap.org.cn

  2. Overview of the lecture • Introduction • Welfare economics, AGE-modeling, CHINAGRO model • New algorithm to solve very large partial equilibrium welfare program with transportation • Conclusion

  3. 1. Introduction Part I : Welfare economics, AGE-modeling, CHINAGRO model 2.1 Welfare optimization and competitive equilibrium (justifies welfare approach) 2.2 CHINAGRO general equilibrium welfare model Part II : Algorithm to solve spatially explicit partial equilibrium Prototype for next generation model (Check on transport flows and price margins in CHINAGRO)

  4. 2.1 Welfare & competitive equilibrium Consumers are indexed Commodities are indexed Consumers have concave increasing utility functions where is consumption vector with elements . Exchange economy: Consumers obtain an income from given endowments

  5. 2.1 Welfare & equilibrium: Definitions Competitive exchange equilibrium: Consumption and prices Welfare optimization: Consumption solving, given weights

  6. 2.1 Welfare & equilibrium: Theorems First Welfare Theorem: “A competitive equilibrium is Pareto efficient” (no consumer can be made better off without making some other consumer worse off) Second Welfare Theorem: “Every Pareto efficient allocation, including the welfare optimum, is a competitive equilibrium with transfers” (lumpsum transfers are efficient for income redistribution)

  7. 2.1 Welfare & equilibrium: Theorems (2) Negishi Theorem: “There exist welfare weights such that a welfare optimum is a competitive equilibrium without transfers” The Negishi-weights reflect marginal utilities of income. A competitive equilibrium without transfers is a welfare optimum where consumers with a high marginal utility of income have a low welfare weight.

  8. 2.1 Welfare & equilibrium: Theorems (end) The three basic theorems of welfare economics equally apply when production takes place and consumers obtain income from given endowments and from shares in the profit of producers indexed j: The welfare program then reads :

  9. 2.1 Welfare & equilibrium: Institutions Institutional requirements : 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 preferences (shareholder value principle).

  10. 2.2 CHINAGRO model: point of departure Point of departure: Static equilibrium welfare model from the previous lecture:

  11. 2.2 CHINAGRO full model Modifications: 1) Consider all goods simultaneously; linear trade technology. (variables become vectors; product becomes inner product) 2) Open economy, trading with the outside world at given prices. 3) Incorporate balance of payments constraint. 4) Conversion from utility to money metric utility through welfare weights. 5) Detailed component for agricultural production.

  12. 2.2 CHINAGRO full model (2) Implication for modeling: 1) Inputs agriculture subsumed under net supplies of site s ; For transport requirements : 2,3)Balance of payments with exports, imports and world market prices : where is the total of non-trade transactions. 4) Write for . 5) Write for .

  13. 2.2 CHINAGRO full model (end) Full CHINAGRO general equilibrium welfare model :

  14. 3. Partial equilibrium with transportation CHINAGRO model is suited to represent a complex economic system in a transparent way. Nonetheless, it assumes that all transportation cost within counties are truly incurred. As explained in the previous lecture, this assumption would need to be relaxed. Therefore, as a background check on transport flows and price margins in CHINAGRO, and as a prototype for next generation models, consider again the single-commodity partial equilibrium approach.

  15. 3. Spatially explicit equilibrium model Recall, from lecture 2, the model that maximized the sum of money-metric utilities minus transport costs subject to commodity balance at every site. Demand + Outflow = Production + Inflow Outflow from site s to r = Inflow into site r from s

  16. 3. Spatial model: transport cost Work focused on transport cost along main highways, railways, and waterways, and along secondary roads. Spatially explicit data were collected for rice and wheat. The resulting map of transport costs per ton-kilometer is shown on the next sheet.

  17. 3. Spatial model: transport cost

  18. 3. Spatial model: solution Objective : Find equilibrium supply, demand, flows and price on a map Tool : A new algorithm to solve a large scale, spatially explicit welfare program Advantage : Integration between disciplines

  19. 3. Spatial model: what are the costs? Costs over formal infrastructure(waterways, railways and highways) relatively low: But these are only a small fraction of the consumer price. We must also allow for storage cost, cost of changing from the informal mode of transportation to the formal and cost at both ends of the chain: collection and retail distribution

  20. 3. Spatial equilibrium models Spatial equilibrium models • Connect districts, or nodes in a network • Not spatially explicit

  21. 3. Spatially explicit model Allow for all possible flows on the Union Jack grid

  22. 3. Partial equilibrium: new algorithm • Key algorithmic principle: gravity driven flow • Gravity : water does not flow uphill • Transport : goods never flow to lower price Low price High price

  23. 3. Partial equilibrium: new algorithm (2) • Two step algorithm: Step 1 Solve gravity constrained welfare program Impose gravity rule: exclude flows from high to low prices • Per site from low to high price: (a) update availability = production + inflow (b) maximize utility of site + value of sales subject to consumption + outflow = given availability • Per site from high to low price: updatesales price on basis of customer’s value

  24. 3. Partial equilibrium: new algorithm (3) Step 2 Improvement achieved? Yes: Update gravity ordering on basis of prices of gravity-constrained program and go to Step 1 No: Otherwise, end (optimum is found)

  25. 3. Partial equilibrium: new algorithm (4) • Application to spatially explicit welfare model for China • Exogenous variables • production map cereals • population map • tariffs and world market prices cereals • freight costs per ton • Study world market price penetration • Grid of cells of 10-by-10 km = 93125 cells (markets)

  26. 3. New algorithm: zoom in on results

  27. Preliminary results for rice Price

  28. Preliminary results for rice Flow

  29. Preliminary results for rice Production

  30. Preliminary results for rice Consumption

  31. Preliminary results for rice Joint Price Flow Production Consumption

  32. Preliminary results for wheat Price

  33. Preliminary results for wheat Flow

  34. Preliminary results for wheat Production

  35. Preliminary results for wheat Consumption

  36. Preliminary results for wheat Joint Price Flow Production Consumption

  37. 4. Conclusion CHINAGRO: Multicommodity general equilibrium welfare model with spatially explicit partial equilibrium models in the background. General equilibrium model: work in progress to be discussed further tomorrow. Partial equilibrium model: preliminary results show that it is possible to generate meaningful spatially explicit equilibrium, with “very large” number of geographical units to represent transport flows and price margins in China. A next, challenging partial equilibrium application will be the pork industry considering the meat and feed markets simultaneously

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