Basic Tools for General Equilibrium Analysis Demand Side: Community Indifference Curve (CIC) Shows various combinations of two goods with equivalent welfare Good Y Downward sloping And Convexity CI Since Y(MU y ) = - X(MU x ) -Y/X = MU x /MU y Diminishing marginal rate of substitution Y X Y MRS = - = X MU x MU y CI 0 Good X
Consumer demand is always satisfied with more goods Good Y Ordinal and Transitivity: Farther out from origin point Means higher welfare to consumer CI 0 CI 1 CI 2 CI 3 Good X
Non-intersecting Community Indifference Curve Good Y CI 0 : B = A = C CI 1 : A = D A = B = C = D B CI 1 > CI 0 D > C contradiction A D C CI 0 CI 1 Good X
Good Y These are the wrong ortions of CIC. Why? C 0 Good X
Consumer equilibrium: Maximize welfare subject to the income constraint (Budget constraint) Good Y y I 2 I 1 Slope of budget line: Y/X = (0y)/(-0x) = (I 1 / y )/(-I 1 ) x ) = - x / y = MRS y 1 A CI 0 At point A: ( x )(0x 1 ) + ( y )(0y 1 ) = I 1 y 1 = (I 1 )/( y ) ( x / y )X 1 Y = (I 1 )/( y ) ( x / y )X Y/X = x / y 0 x 1 x Good X
Supply side: roduction possibility frontier (F) Isoquent concept: Show various combinations of two inputs that produce same level output Capital Downward sloping and Convexity for possible substitution Marginal rate of technical substitution K 1 K 1 K L (K)x(M K ) = - (L)x(M L ) K/L = - M L /M K K/L = MRTS Q 1 0 L 1 L 1 Labor
Capital Non-intersecting Farther out from origin point Means greater quantities of outputs K 1 K 1 K L Q 1 Q 2 Q 3 Q 4 0 L 1 L 1 Labor
Constant return to scale: a given percentage increase in all inputs will lead the same percentage increase in output Capital Capital intensive output expansion path 4K 1 G Labor intensive output expansion path 2K 1 G K 1 Q 2 =20 0 L 1 2L 1 4L 1 Q 1 =10 Labor
roducer 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. Capital K K K 1 B 2 B 1 H 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 = M L /M K = MRTS Q Q 2 1 At point : B 1 = rk + wl rk = B 1 wl K = (B 1 /r) (w/r)l K/L = - w/r 0 L 1 L L Labor
Increasing K Ks K S-Isoquant (K/L)s 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 Kc (K/L)c C-Isoquant Oc Ls Lc L
Resources allocation in two goods within a country Increasing K K Ls Os Kc (K/L)c Ks Oc (K/L)s Lc L Isoquant
K L The Edgeworth Box: Not areto Efficiency C4 C5 0s C2 C3 V C1 0c S5 S4 S3 S2 Contract curve: production efficiency locus with increasing opportunity cost S1 L K
K L The Edgeworth Box: C5 0s C4 C2 C3 C1 V Not areto Efficiency 0c S5 S4 S3 S2 S1 Contract curve: production efficiency locus with constant opportunity cost L K
Country II: Capital abundant country Steel S 0 S 1 K 2 C 3 S 2 C 2 S 3 C 1 C 0 Clothes L 2
Country I: Labor-abundant country S 0 Steel S 1 C 3 K I C 2 S 3 S 2 C 1 C 0 Clothes L I
Constant vs. Increasing Opportunity Cost on the F Good Y F (or contract curve) with constant opportunity cost Increasing Opportunity Cost F (or contract curve) Decreasing increase 0 Constant increase Good X
General equilibrium: domestic demand = domestic supply Good Y ( x / y ) roduction at point A 0 is satisfied and consumed by consumers demand within a country with constant opportunity cost. (Classical case) A 0 CI 1 CI 2 CI 0 F & budget curve Good X
Y-Steel A E CI 2 CI 1 B CI 0 X (autarky price) Y F 0 Marginal rate of transformation (MRT) MRT XY MC MC X Y X Y MU MU X Y MRS XY X -Cloth Marginal rate Of substitution (MRS)
General equilibrium: domestic demand = domestic supply Good Y ( x / y ) roduction at point A 0 is satisfied and consumed by consumers demand within a country with increasing opportunity cost. (Neo-classical case) A 0 CI 1 CI 2 CI 0 F Budget curve Good X
Y-Steel A E Community Indifferent curves CI 2 CI 1 B CI 0 X 0 Marginal rate of transformation (MRT) MRT XY MC MC F X Y X Y Y (autarky price) MU MU X -Cloth X Y MRS XY Marginal rate Of substitution (MRS)
Good Y Country A Given labor endowment is fixed with L L L a x x + L x + a y y y L A a y X Solving for Y Y a L - y a x a y x 0 Good X L A a X the slope is - a x a y = - x y
Unit cost in producing X is a x or (w x a x ) Total cost in producing X is a x x w wage in money term Then MC X X (a x x) a x In perfect competition: X MC X > x a x Similarly: y MC y y a y Thus: x y a a x y labor units required to produce1unit of labor units required to produce1unit of X Y
Trade Triangle Concept From the export country view of point: T = 1 = terms of trade or relative price imports 10 units exports 10 units imports 5 units T =1/2 =Terms of trade becomes worse exports 10 units
Trade Triangle Concept imports 15 units T = 3/2 = Terms of trade better off for export country exports 10 units