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General Equilibrium General Equilibrium In this section we will combine production possibilities frontiers and community indifference curves in order to create a model of the economy as a whole. This brings together producers, who must decide which combination of goods to produce given society=s resources and technology, and consumers who choose which combination of goods provides the greatest level of utility or satisfaction. Producers, acting rationally, will be efficient by choosing that combination of goods which maximizes profits; and consumers, also acting rationally, are considered efficient by choosing the combination of goods which maximizes utility. The main question is how do these two separate choices, by producers and consumers, coincide. In our discussion of the theory of the consumer, we introduced the concept of a budget constraint. This constraint had two characteristics. The first was that it divided commodity bundles into two sets, those which were affordable given the consumer=s income, and those which were beyond the consumer=s reach. The second characteristic was the budget line=s slope. This represented the relative price of the good on the horizontal axis divided by the price of the good on the vertical axis. In this capacity the budget line served the function of what we will call a price line. A price line is an important tool because its slope reveals relative price. Recall that relative price is the price of a good in terms of another good. In the case of the consumer, the relative price of an apple is the number of bananas the consumer forgoes. The consumer of course pays the producer. Therefore, the relative price of an apple would be the number of bananas the producer receives from the sale of an apple (Papples/Pbananas). The Producers The slope of the PPF is the marginal rate of transformation (MRT), or in other words, the cost of an additional unit of the good on the horizontal axis in terms of the amount of the good on vertical axis that must be sacrificed. As a result of being on the PPF, in order to produce an additional apple, the producer must necessarily reduce production of bananas. The resources required to produce the additional apple have to be gotten by diverting resources away from their other productive activities. Profit maximization occurs when the additional revenue earned from the sale of a good is equal to the cost of producing the additional unit of the good. Referring to Graph 1, at point A the slope of the price line is equal to the slope of the PPF. This is equivalent to Papples/Pbananas = MRT. At this point, profits are maximized. General Equilibrium - page 1 M B A M M C Graph 1 Apples To be sure that the student understands this, let=s suppose that Papples/Pbananas > MRT, for example at point B. The absolute slope of the price line is greater than the tangent (not drawn in) of the PPF at point B. This would say that producers would earn more bananas from the sale of an apple than the number of bananas it would cost them to produce the apple. In this case producers, would profit from the production and sales of the additional apple. They would continue to produce more apples as long as this inequality held. But as they produce more apples, the MRT increases. This would be represented as a shift to the right along the PPF. So as apple production increases (and banana production falls), producers earn more profit. Profit is maximized when there is no longer any gain to profit from switching from banana to apple production. Take the other perspective and let Papples/Pbananas < MRT at point C in Graph 1. Here, producers= earnings from the sale of an apple, in terms of bananas are less than its cost. Producers have taken a loss from producing more apples. They would then reduce apple production (increasing banana production instead) which in turn would result in a decrease in MRT. Apple production would continue to fall until relative price equaled MRT. This would be interpreted as a shift to the left along the PPF to the point where profits are maximized. The Consumers Recall that indifference curves are a graphing of consumer preferences. Each combination of goods on an indifference curve provides the same level of satisfaction to the consumer. The consumer=s task is to allocate their income across goods with the objective of maximizing utility. This combination of goods was determined graphically by reaching the highest feasible indifference. This was shown Graph 2 at point C as the tangency of the indifference curve to a budget constraint. At this tangency, the Marginal General Equilibrium - page 2 Rate of Substitution (MRS), the slope of the indifference curve, is equal to relative price the slope of the budget constraint. In other words, Papples/Pbananas = MRS. If MRS > Papples/Pbananas at point A in Graph 2, then the value consumers place on the additional apple in terms of bananas is greater than the cost; therefore they would consume more apples and less bananas. As they consume more apples, their MRS would decrease until MRS equaled relative price. Conversely at point B in Graph 2, if MRS < Papples/Pbananas, then the opposite would be true. Rational consumers would increase consumption of bananas at the expense of apples. A U1 Uo B Graph.2 Apples We extend this consumer choice framework by making the assumption that what is true for the consumer is also true for society as a whole. This is quite a leap and requires some very restrictive qualifications. However, this leap provides us with a very important tool, the community indifference curve. Community indifference curves represent society=s preferences and are subject to the same assumptions that were made when discussing consumer indifference curves: decisiveness, consistency, more is better than less, and convexity. In fact all the characteristics of consumer indifference curves apply to community indifference curves. What is different between the consumer and society in this framework is the nature of their constraints. For the consumer, their income restricted their ability to purchase goods and services. For society as a whole, the constraint between what is feasible and what is not feasible is the PPF. Representing what society can produce, the PPF divides all combinations of goods between those which society can obtain through production and those which are beyond its means. Society maximizes its satisfaction in the same fashion as the consumer. Utility is maximized by achieving the highest feasible community indifference curve. Feasibility in this case is not determined by an income constraint but by the quantity and quality of society=s resources and the technology used to transform these resources into goods and services. General Equilibrium - page 3 Graph 3 illustrates several possible choices that society might wish to achieve. Combination A falling inside the PPF is clearly not an optimal choice since more of D l both goods could be obtained. Combination B l B falling on the PPF exhausts society=s resources C l but again is not utility maximizing since other feasible combinations of goods lie above this l A CIC3 indifference curve and are therefore preferred. CIC2 Combination C also exhausts all resources but CIC1 in this case no other feasible combination provides a higher utility level. Combination Graph 3 Apples C=s indifference curve is tangent to the PPF. Combination D lies beyond the PPF and consequently cannot be produced. Note that it is preferable to combination C but beyond the means of society to obtain domestically. Combination C is the optimal combination but the question is how does society get to it. The answer is the role of prices. If producers and consumers are both optimizers, they will respond to price changes. As noted above, if Papples/Pbananas > MRT then producers will produce more apples and less bananas, but if Papples/Pbananas< MRS then consumers will consume more apples and less bananas. Combining these two conditions, if MRS > MRT then production and consumption of CIC0 CIC1 apples will increase at the expense of bananas. This would be the case at point A in Graph 4. Here prices would adjust, moving the economy A to the right along the PPF. Conversely if MRS < C MRT, as illustrated at point B, then the cost of the additional apple (MRT) exceeds the value B of the apple (MRS) and the economy would Papples/ Pbananas reduce apple production and consumption in favor of more bananas. This would result in a shift left along the PPF. Equilibrium occurs at Apples Graph 4 point C where MRS=Papples/Pbananas=MRT. General Equilibrium - page 4 At this point you are no doubt wondering what is the importance of all this theory and what is the significance of the general equilibrium as illustrated by point C. Going over general equilibrium theory is very complicated the first few times, but as you use it more and more it will become fairly simple. The point of all this is that a closed economy can do no better than the general equilibrium at point C. What is meant by a closed economy is one that does not participate in global markets. This is given another name, autarky. So an autarkic country under the best conditions would achieve a social welfare level limited to community indifference curve CIC1. General Equilibrium - page 5.
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