Topic 9 General Equilibrium and Market Efficiency

Topic 9 Econ 203 Page 1

Topic 9 General Equilibrium and Market Efficiency

Chapter Reference 16 In this topic we will investigate the properties of an interconnected system of markets. This is referred to as general equilibrium analysis and its focus is to make explicit linkages between individual markets.


A Simple Exchange Economy This is the simplest possible general equilibrium model: a pure exchange economy with only two consumers and two goods. Result: for any given initial allocation of the two goods between the two consumers, a competitive exchange process will always exhaust all possible mutually beneficial gains from trade. Analysis: Suppose we have a simple economy in which there are only two consumers and two goods. The goods are not produced in this economy and they arrive in fixed quantities in each time period.


Text Example Goods: Food and Clothing Suppose there is a total of 100 units of food each time period and total of 200 units of clothing for allocation between the two consumers.

One possible assignment of allocation is individual 1 receives 70 units of clothing and 75 units of food. The remaining 130 units of clothing and 25 units of good go to individual 2.


Ann Burt

70 units clothing C1=70 130 units clothing C2=130 75 units food F1=75 25 units food F2=25

In general if individual 1 receives F1 units of food and C1 units of clothing, then individual 2 will get [100 – F1 ] units of food and [200 – C1] units of clothing. These amounts of the two goods with which the individuals begin each time period are referred to as their initial endowments.


For now, we will assume these initial endowments are externally determined. The question: What will the individuals do with their initial endowments? They could consume the initial endowments, but this is highly unlikely since the initial endowments rarely are the best option available. The allocation can be represented as a point in a single rectangular diagram referred to as an Edgeworth Exchange box.


The height corresponds to the total amount of food available per time period: 100 units. Its width is equal to the total amount of clothing: 200 units. OA is the origin for individual 1. The left and bottom sides are the axes that measure her quantities of food and clothing.

OB is the origin for individual 2. Movements to the left from OB correspond to increase in his amount of clothing. Downward movements from OB correspond to increases in his food. Because of the way the rectangle is constructed, every point that lies within it corresponds to an allocation that exactly exhausts the total quantities of food and clothing available.



What will these two individual do? They could either consume what they already have or engage in exchange with one another. Exchange is purely voluntary. Trade will only occur if they it makes both parties better off. We assume that exchange is costless. In order to makes someone better off from an exchange, it must place them on a higher indifference curve.


Individual 1’s indifference map has the conventional orientation, while individual 2’s is rotated 180°.


The I curves are indifference curves. Individual 1’s satisfaction increases as we move to the northeast in the box, individual 2’s as we move to the southwest. At the initial endowment allocation, individual 1’s MRS between food and clothing (at R) is much larger that individual 2’s. Any point within the lens-shaped shaded region in the figure 16-2 is one for which each party lies on a higher indifference curve than at R. Point T is one such point.


The movement from R to T does not exhaust all possible gains from exchange. There is a smaller lens-shaped region enclosed by the indifference curves that pass through T by both parties.


Through the process of repeated exchanges or a single exchange at the correct exchange ratio, the individuals can finally reach a point at which further mutual gains from trade are no longer possible. The two parties’ indifference curves that pass through from any such point will be tangent to one another, as at point M.


At M the marginal rates of substitution of the individuals are exactly the same. It was a difference in these rates that provided the original basis for exchange, and once they are the same, all voluntary trading will stop.

One allocation is said to be Pareto superior to another if at least one party prefers it and the other party likes it at least as well. Allocations like the one at M, are called Pareto optimal. Here there are no other feasible reallocations that are preferred by one party and liked at least equally well by the other party.


In any Edgeworth exchange box, there will be an infinite number of mutual tangencies. The locus of these tangencies is called the contract curve. The contract curve identifies all of the efficient ways of dividing the two goods between the two consumers.

Where individuals end up on the contract curve depends on the initial endowments with which they start.


In this simple two-person economy exchange took place through a process of personal bargaining. In most market economies, exchanges take place more impersonally. Relative prices are adjusted until the quantities demanded of each good match the quantities supplied.


Suppose we start with the allocation at E. Each has 50 units of food and 100 units of clothing. Also assume that the ratio of food to clothing prices announced is PC/PF = 1. (Each good has the same price.)


We know that E has to be on the budget line of each consumer. If individual 1 wants to sell some food and use the proceeds to buy more clothing, she can do this by moving downward from E along the line HH’. If she wants to sell clothing to buy more food, she can move upward along HH’.

Bill can do the same from his point of view. Given their budget constraints and preferences the consumers face a simple choice problem. The optimal bundle for each consumer is found where the highest attainable indifference curve is tangent to the budget line.


The optimal bundles are not attainable in this market with the total endowments available. At the present price ratio, there is excess demand for clothing and excess supply of food. At this price ratio, the markets are not in general equilibrium. Solution: a new price ratio in which the price of clothing relative to food is higher than before. If there is an excess of demand for clothing, the price ratio has to be higher until the excess demand in each market is exactly zero.


Starting with the allocation at E, the price ratio that produces general equilibrium is shown above. On the budget line through E with the new slope, the highest attainable indifference curves for each consumer are tangent.


New price ratio is 6/5. The condition for consumption efficiency in our exchange economy: at the equilibrium point: MRS1 = Pc/PF = MRS2 It must also be the case that the price ratio satisfies: Pc∆C1 +PF∆F1 = 0 This condition ensures that the equilibrium bundle is affordable for both consumers.

From the information given, we are able to determine only the ratio of clothing to food prices, no the actual value of individual prices.


Adam Smith’s The Invisible Hand Theorem

An equilibrium produced by perfectly competitive markets will exhaust all possible gains from exchange.

This is also known as the first theorem of welfare economics. Another way to state this is that equilibrium is competitive markets is Pareto optimal. The invisible hand theorem tells us that every competitive equilibrium allocation is efficient.


The second theorem of welfare economics says that under relatively unrestrictive conditions, any allocation on the contact curve can be sustained as a competitive equilibrium.

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Topic 9 General Equilibrium and Market Efficiency