Competitive Equilibrium in Exchange Economy - Essay Example

? Competitive equilibrium in an exchange economy and its representation using an Edgeworth Box In an exchange economy, it is every consumer’s goal to be at a competitive advantage than all other consumers. In the endevor to attain pareto optimality in consumption, several assumptions have been fronted in the analysis of attaining the desired efficiency. These include; Consumers are assumed to be price takers, only two goods and individuals exist in the given economy and that there is a fixed and definite endowments of the goods that they are allowed to trade. More over , it is assumed that consumers will usually maximize their consumption within the indifference curves with the fact that their individual utilities will not be interdependent.In an exchange economy, pareto optimality will exist in an instance where one has to be made worse off if another is to be made better(Mackintosh & Andrew pg. 126) The figure above indicates the consumption possibilities, the indifference curves and the budget constraints for the two consumers; Aisha and Robin. Let F represent food and C represent clothing; A=Aisha and R= Robin Therefore FA + FR= F and CA+CR= C The utility of Aisha, UA= FA + CA = B on the indifference curve The utility of Robin, UR= FR + CR = A on the indifference curve 1 A) Based on the figure above, points A and B indicates the pareto optimality points. These are the points at which the consumers will attain an efficient utility of the goods in the economy. At point A, Robin will be consuming the maximum he could for both the food and clothing. This is the point indicating how much he is ready and willing to lose for an equal amount from Aisha. In addition, at point A, Aisha is at optimal utility consuming a paltry UA= FA + CA while Robin has UR= FR + CR; this point indicates that Aisha though utilizing more of food than Robin she is satisfied as Robin utilize more clothes at this point than her. At point B, both consumers are efficiently utilizing the available goods. Robin is at, UR= FR + CR while Aisha is at UA= FA + CA. This point indicates that Robin is consuming more food than Aisha. To obtain an optimum exchange, Aisha utilizes more clothes than Robin. More over, points A and B lie on the indifference curves that measure the marginal rate of substitution of a given good for another by the consumers; UA and UR. Points A and B indicate the rates at which both Robin and Aisha are willing to substitute either good and still remain on the same indifference curve (Mackintosh & Andrew Pg. 126). B) Neither point A nor point B is on the contract curve. This is because, points A and B indicates the pareto optimality of both consumers. They indicate the levels at which Aisha and Robin are efficiently utilizing food and clothes. Under point A and B, all the consumers are well off and none is better than the other. In the exchange box, a contract curve indicates all the emerging points that are not under pareto optimality. The points on the contract curve shows that the utility of one consumer can be increased only by decreasing the utility of the other consumer. Remarkably, contract curve shows all the pareto efficient points. Further more the indifference curves of both the consumers at tangential to each other. This is as indicated at point T where curve UA is tangential to curve UR. At this point, the marginal rate of substitution for both food and clothes is the same for Robin and Aisha (Mackintosh & Andrew pg.126) That is MRSAF, C = MRSRF, C C) Food has more demand than clothes. This is indicated in the above figure with both consumers have high initial amounts of food This is as shown at point P for Robin and point X for Aisha. From the indifference maps, it is indicative that, both Aisha and Robin have tried to maintain large amounts of food than clothing. Notably, the consumers’ marginal rate of substitution of food for clothes is low. More over, the indicated reductions in the amounts of food for both consumers are minimal showing their unwillingness to lose the good. Further more; the marginal propensity to consume for food is higher than that of the clothes for both Aisha and Robin. This is more evident, with all the consumers utilizing food at higher indifference curves. From the contract curve and indifference curves of both Aisha and Robin, both consumers are utilizing equal amounts of food indicating how both demand it equally (Mackintosh & Andrew pg. 128). In the Aisha side at endowment she has CAP of clothing and FAP of food. High demand of food by Aisha may want to utilize more food than clothes; to move to point Q from the initial point P. With this, she may need to trade some clothes (CAP - CAA) units for food (FAA - FAP) units to move to point Q along the budget constraint .high demand of food will make him to trade (CRP – CRB) units of clothes (FRB – FRP) units for food (Mackintosh & Andrew pg. 131). 2. Price Adjustment In pareto optimality, for an exchange economy, consumers are price taking with none of them influencing the market price. On high demand of certain goods prices tend to be high than when the demand is low. From the Edgeworth’s box, the demand for food is relatively higher than that of the clothes. To attain equilibrium in the market excess demand for any given good must be zero (Mackintosh & Andrew pg. 131) On the B1, at point E, the indifference curves of the consumers are tangent the budget line and to each other. Both Aisha and Robin would like to move from point P to H with compatible trade proposals. At this point, Aisha and Robin will trade equal amounts of food and clothes. The slope of budget constrain B1 is PF/PC and it represents the equilibrium price at point E. The fact that, point E is on the contact line makes it a pareto efficient. As noted on the contact line both consumers have equal MRSF, C nd it is given by the slope of the indifference curves. There fore the MRSF, C equals the equilibrium price (Mackintosh & Andrew pg. 136) MRSF, C = PF/PC. 3) From the above figure, it clear that, Aisha is concerned about very low consumption of food and clothing by Robin, but Robin was only concerned about his own consumption. The contract box is only constrained within the utility box of Robin (Mackintosh & Andrew. pg.139) References Mackintosh M., Andrew, M. (Chapter 8) General Equilibrium: efficiency, welfare and redistribution Read More