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12. General equilibrium

12. General equilibrium. Contents. assumptions of the model term „efficiency“ production possibility frontier general equilibrium general equilibrium formation and its change. Assumptions of the model. there are only 2 consumers (A,B), with convex indifference curves

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12. General equilibrium

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  1. 12. General equilibrium

  2. Contents • assumptions of the model • term „efficiency“ • production possibility frontier • general equilibrium • general equilibrium formation and its change

  3. Assumptions of the model • there are only 2 consumers (A,B), with convex indifference curves • there are only 2 goods (X,Y) • there are only 2 firms – one produces X, the other produces Y, isoquants are convex • there are only 2 inputs (K,L) • all markets are perfect competition • consumers endeavour maximal TU, firms endeavour maximal economic profit • the economy is closed (without foreign trade)

  4. Efficiency Upon general equilibrium there must be fulfilled productive efficiency, exchange efficiency, and productive-exchange efficiency Productive efficiency = such allocation of inputs when eventual reallocation would not lead to the bigger total economy´s output Exchange efficiency = such allocation of the goods, when eventual reallocation would not lead to the bigger level of economy´s total utility Productive-exchange efficiency = such structure of production when its eventual change would not lead to the bigger level of economy´s total utility Pareto efficiency

  5. Production possibility frontier • PPF = set of different combinations of goods possible to produce in the specific economy • its position depends on: the volume of inputs (K,L) technological level (efficiency of use of K,L) • its slope depends on the marginal productivity of labour (upon the given volume of capital and technology)

  6. PPF upon decreasing MPL Y Spot E represents productive efficient combination of X and Y, spot A is accessible but not efficient, spot B is not accessible E B PPF is concave – for each additional unit of X, we have to sacrifice more units of Y, because in production of X the MPL is decreasing slope of PPF: MRPT (marginal rate of product transformation) – ratio of substitution one good with the other in the production – changing alongsied the PPF A PPF X QY TPL QX TPL L L

  7. PPF upon constant MPL Y PPF is linear – to an additional unit of X we sacrifice always the same volume of Y and vice versa, because MPL is constant in production of both goods MRPT is constant alongside the linear PPF PPF X QY QX TPL TPL L L

  8. PPF upon constant but different MPL Y Y MPL(X) > MPL(Y) MPL(X) < MPL(Y) PPF PPF X X

  9. PPF upon fixed proportion of production Y It is impossible to change the structure of production PPF X

  10. How does the general equilibrium form? • general equilibrium forms, when it is not possible to rearrange the structure of production to rise the total utility in the economy • for general equilibrium stands: MRSC(A)=MRSC(B)=PX/PY=MRPT=MRTS(X)=MRTS(Y) • ... if both consumers A and B find themselves in the equilibrium and also the firms producing goods X and Y

  11. General euqilibrium ...lies in spot E‘, upon the consumers´ equilibrium in spot E Y X* and Y* represent the total volume of X and Y produced upon the general equilibrium Consumer A consumes XA and YA , consumer B consumes XB and YB xB y* E' Px/Py UA+UB UB Px/Py E yA yB UA PPF xA x* X

  12. Formation of the general equilibrium price mechanism assures the equilibrium stage XB X* 0B Initial relative price ratio: pX'/pY‚... Y* CC ... but there is an overhang of demand on X market (XA+XB˃X*) and an overhang of supply on Y market (YA+YB˂Y*) YB E YA pX'/pY' pX/pY Y* 0A XA X* On the X market the price increases, on the Y market the price decreases Budget line rotates clock-wise because of the change of the relative price ratio – the new ratio of prices: pX/pY. Consumers (and the entire economy) aims to the equilibrium in spot E

  13. Exchange equilibrium X* XB 0B Y* CC ICB YB YA E ICA Px/Py Y* 0A XA X* Consumers are heading to the CC (Contract Curve), that represents the set of Pareto effective combinations of X and Y allocated between te consumers

  14. How the general equilibrium rearranges? • the impulse to change is the change of consumers´ preferences • i.e.: consumers wish to buy more Y and less X, that leads to the: • increase of the demand for Y and decrease of the demand for X • ↑D(Y) → ↑P(Y) → ↑D(LY) → ↑wY → ↑Y* • ↓D(X) → ↓P(X) → ↓D(LX) → ↓wX → ↓X* • the equilibrium shifts alongside the PPF to a different equilibrium spot

  15. Initial and the new equilibrium Y Y xB E' y* ‖ UA ‖ xB y* E E' yA yB Px/Py ‖ Px'/Py' ‖ UB Px/Py UB E yA yB UA PPF PPF xA xA x* x* X X

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