# Lecture 2: Applied general equilibrium (Chapter 3) Introduction of formats Comparing the formats Model implementation –Classification –The Social Accounting.

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1 Lecture 2: Applied general equilibrium (Chapter 3) Introduction of formats Comparing the formats Model implementation –Classification –The Social Accounting Matrix (SAM) –Missing commodities and markets –Closure rules

2 Aim of lecture 2 Highlighting the characteristics of different representations of general equilibrium models (formats) Illustrating the steps from a general equilibrium to an applied general equilibrium model

3 Importance of existence proofs Non-existence of a solution implies model is inconsistent and therefore useless Existence proofs highlight crucial necessary assumptions that have to be made For applications : –Necessary assumptions indicate scope for variation of parameters –Construction of fixed point mapping to prove existence may suggest algorithm for numerical implementation

4 Excess demand format For every producer j, solves For every consumer i, solves, where All markets are in equilibrium: Define excess demand function The price, and the excess demand define an excess demand equilibrium if.

5 Excess demand format (continued) Debreu (1959) assumes convex production sets and quasiconcave utility functions. Therefore, excess demand correspondence is not single-valued. This is problematic since compatibility of allocations is not guaranteed Therefore, Debreu assumes consumer demand functions to be single-valued, and aggregates production by different producers into one single set

6 Negishi format (a) Welfare program (b) Adjustment of welfare weights such that budget constraints hold for every i, where is the profit function of producer j

7 Full format Constrained welfare optimum: for given and such that is a shadow price and for some scalar.

8 Open economy format (a)Optimization with given consumptions : (b)A feedback relation that sets by solving the consumer problem:

9 CGE format CGE format is a system of simultaneous equations: –balance equation for factors (f) and goods (g) –complemented with individual budgets: –and price relations:

10 CGE format (continued): assumptions Constant returns to scale in production –no profits in equilibrium Factors are not produced and used in production –boundedness of production Goods are not available as endowments Utility functions are continuous, strictly quasi-concave and non-satiated. For at least one consumer, utility increases in all factors

11 CGE format (continued): extensions Decreasing returns –Firm-specific inputs in CRTS technology imply DRTS in remaining inputs –Profits have to be included in budgets Markups –Compensation for inputs not included in the model –Caused by imperfect competition Closure rules

12 Comparing formats: merits Excess demand –Microfoundations Negishi and Full format –Direct link to welfare analysis –Weaker assumptions with respect to production technology –Solvable even if decentralization is problematic Open economy format –Econometric estimation of model parameters –Possibility to include non-optimizing behavioral rules CGE format –Easiest for application –Possibility to include non-optimizing behavioral rules

13 Comparing formats: mathematical requirements *These are the assumptions made in G/K needed for single-valued excess demand.

14 Mapping from theorems to “work horses”

15 Classifications Commodities –Focus on relevant characteristic that allows aggregation of different products in some common unit –Maintain link to data availability Agents –Consumers Dissimilarities between groups with respect to reactions on policy changes (employers vs employees) Similarities between agents within the same group (income sources, consumption patterns) –Producers Different production technologies for single good?

16 Organizing data: the SAM GoodsFactorsFirmsConsumers GoodsInputConsumption FactorsInputConsumption FirmsProduction(Production) Consumers(Endowments)Endowments(Profits) *Terms within parentheses are zero in the basic CGE model *This SAM represents a closed economy without government

17 The SAM (Continued) SAM structure and classification follow model architecture SAM entries are in value terms Rows and associated columns have equal value since they represent balances –Commodity balances in value terms –Budgets –Firm profits –(Government budget) –(Balance of payments) Prices follow from confronting SAM with balances in quantity terms

18 Missing commodities and markets Rough markets –Only one market for different qualities Markets for characteristics –Consumer preferences in terms of characteristics –Markets usually in terms of products –Introduce mapping from characteristics to products Commodities traded but not fully represented –Missing markets for goods implies these go unpriced Markups –Reflect reward for input not accounted for in the model

19 Closure rules Including macro-economic mechanisms in general equilibrium model –define a new variable –define balancing constraint for this variable –Example: Taxes (closure variable) and government budget (associated constraint) –Beware: Closure rule can become dominant mechanism in model!

20 Closure rules (continued) CGE model with parameters: Closure rule: Relation:

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