Basic Tools for General Equilibrium Analysis Demand Side: Community Indifference Curve (CIC) Shows various combinations of two goods with equivalent welfare Downward sloping And Convexity CI Good X Good Y CI 0 YY XX Diminishing marginal rate of substitution Since  Y(MU y ) = -  X(MU x )  -  Y/  X = MU x /MU y MRS = - = YY XX MU x MU y

Ordinal and Transitivity: Farther out from origin point Means higher welfare to consumer CI 1 CI 2 CI 3 Good X Good Y CI 0 Consumer demand is always satisfied with more goods

Good X Good Y CI 0 B A C Non-intersecting Community Indifference Curve CI 1 > CI 0  D > C contradiction A = B = C = D CI 1 : A = D CI 0 : B = A = C D CI 1

These are the wrong Portions of CIC. Why? Good X Good Y C0C0

Consumer equilibrium: Maximize welfare subject to the income constraint (Budget constraint) Slope of budget line:  Y/  X = (0y)/(-0x) = (I 1 /P y )/(-I 1 )P x ) = - P x /P y = MRS At point A: (P x )(0x 1 ) + (P y )(0y 1 ) = I 1  y 1 = (I 1 )/(P y ) – (P x /P y )X 1  Y = (I 1 )/(P y ) – (P x /P y )X   Y/  X = – P x /P y Good X Good Y CI 0 y1y1 x1x1 0 x y A I1I1 I2I2

Supply side: Production possibility frontier (PPF) Isoquent concept: Show various combinations of two inputs that produce same level output Capital Labor 0 Q1Q1 K1K1 L1L1 K1’K1’ L1’L1’ P P’ KK LL Marginal rate of technical substitution (  K) x (MPP K ) = - (  L) x (MPP L )  K/  L = - MPP L /MPP K  K/  L = MRTS Downward sloping and Convexity for possible substitution

Q2Q2 Q3Q3 Q4Q4 Non-intersecting Farther out from origin point Means greater quantities of outputs Capital Labor 0 Q1Q1 K1K1 L1L1 K1’K1’ L1’L1’ P P’ KK LL

Constant return to scale: a given percentage increase in all inputs will lead the same percentage increase in output Capital Labor 0 Q 1 =10 K1K1 2L 1 2K 1 P Q 2 =20 4L 1 Labor intensive output expansion path G Capital intensive output expansion path 4K 1 P’ L1L1 G’

Producer Equilibrium:At the point the isoquant is tangent to the isocost. Firm maximizes output for the given cost (i.e., most efficient production), Or firm minimizes its factor cost for the given level of output. The slope of isocost (or the factor price line)  K/  L = 0K/-0L = - (B 1 /r)/(B 1 /w) = w/r where r is labor wage, w is capital rental rate = MPP L /MPP K = MRTS At point P: B 1 = rK + wL  rK = B 1 – wL  K = (B 1 /r) – (w/r)L   K/  L = - w/r Capital Labor 0 Q1Q1 K1K1 L1L1 P K L K’ L’ B1B1 B2B2 P’ Q2Q2 H

Oc Lc Kc Increasing K Increasing L L K Oc Lc Kc Increasing K Increasing L L K C-Isoquant (K/L)c S-Isoquant (K/L)s Ks Ls S is capital-intensive (K/L)s > (K/L)c or (L/K)s < (L/K)c C is labor-intensive (L/K)s < (L/K)c or (K/L)s > (K/L)c

Resources allocation in two goods within a country Oc Lc Kc Increasing K Increasing L (K/L)c L K Oc Lc Kc Increasing K Increasing L (K/L)c L K Isoquant Os (K/L)s Ls Ks Increasing L Increasing K

The Edgeworth Box: K 0c L C1 C2 C3 C4 C5 V Not Pareto Efficiency Contract curve: production efficiency locus with increasing opportunity cost L 0s K S1 S2 S3 S4 S5

The Edgeworth Box: K 0c L C1 C2 C3 C4 C5 L 0s K S1 S2 S3 S4 S5 Not Pareto Efficiency V Contract curve: production efficiency locus with constant opportunity cost

Country II:Capital abundant country K2K2 L2L2 Steel Clothes S3S3 S2S2 S1S1 S0S0 C3C3 C2C2 C1C1 C0C0

Country I:Labor-abundant country KIKI LILI Clothes Steel S3S3 S2S2 S1S1 S0S0 C3C3 C2C2 C1C1 C0C0

Good Y Good X 0 PPF (or contract curve) with constant opportunity cost Constant increase Increasing Opportunity Cost PPF (or contract curve) Decreasing increase Constant vs. Increasing Opportunity Cost on the PPF

General equilibrium: domestic demand = domestic supply Good Y Good X PPF & budget curve CI 0 A0A0 (P x /P y ) CI 1 CI 2 Production at point A 0 is satisfied and consumed by consumers demand within a country with constant opportunity cost. (Classical case)

Marginal rate of transformation (MRT) Marginal rate Of substitution (MRS) CI 0 CI 1 CI 2 B A PXPYPXPY E (autarky price) 0 X -Cloth Y-Steel PPF

General equilibrium: domestic demand = domestic supply Good Y Good X PPF CI 0 A0A0 (P x /P y ) CI 1 CI 2 Budget curve Production at point A 0 is satisfied and consumed by consumers demand within a country with increasing opportunity cost. (Neo-classical case)

CI 0 CI 1 CI 2 Community Indifferent curves 0 X -Cloth Y-Steel PPF B A PXPYPXPY E (autarky price) Marginal rate of transformation (MRT) Marginal rate Of substitution (MRS)

LAaXLAaX 0 Good X Good Y LAayLAay PXPYPXPY Country A Given labor endowment is fixed with L yaxa LL L y x yx   Solving for x ayay axax a L Y y  the slope is - a x a y = - P x P y

Unit cost in producing X is a x or (w x a x )|w –wage in money term Total cost in producing X is a x x Then xxXX aP MCP  In perfect competition: Similarly: Thus:

Trade Triangle Concept From the export country view of point: exports 10 units imports 5 units P T =1/2 =Terms of trade becomes worse exports 10 units imports 10 units P T = 1 = terms of trade or relative price

Trade Triangle Concept exports 10 units imports 15 units P T = 3/2 = Terms of trade better off for export country