This section begins to address the case of exchange of more than two commodities. For stability of an equilibrium in this context, it must be the case, as before, that a drop in the price of X will tend to make the demand for X greater than the supply. Regarding stability, Hicks asks whether such an effect must be assumed to happen when the prices of all other commodities are given, or when these other prices are allowed to adjust so as to preserve equilibrium in the other markets. Hicks argues that the answer is "that it is what happens when all other prices are adjusted that is really most important." He notes that if a small rise in the price of X makes supply greater than demand, not by the working of the X-market alone, but rather through repercussions in the other markets, "the establishment of an equilibrium price system is going to be a more awkward business; but once equilibrium is reached it will still be a stable equilibrium, properly speaking. A movement away from equilibrium will set up forces tending to restore equilibrium."
Hicks proposes to call a system in which all conditions of stability are satisfied perfectly stable. He uses the term imperfectly stable to describe a system in which some conditions of stability are not satisfied, "but in which supply does become greater than demand when price rises if all repercussions are allowed for."
Hicks gives a brief preview of the fact that there are some problems where imperfect stability plays an important role. As he notes, "Some of the most remarkable of them arise in connexion with the famous 'instability of credit.'" He does not go into detail in the present section, but notes that "a pure system of multiple exchange, if it is stable at all, is likely to be perfectly stable." He concludes the section by dismissing wholly unstable systems as "hardly interesting" and calling the derivation of their laws of change "a nonsense problem."
Sunday, January 31, 2016
Saturday, January 23, 2016
Value & Capital, CHAPTER V, Section 2
Hicks begins his examination of the stability of equilibrium with the case of simple exchange of two goods, X and Y. In this case, the equilibrium condition is that supply equals demand for one of the goods (as this implies that supply equals demand for the other good as well). The stability condition for equilibrium is that "a fall in the price of X in terms of Y will make the demand for X greater than the supply of X." Hicks defines the excess demand as the difference between demand and supply at each price. Given this definition, the equilibrium condition is that excess demand must equal zero, and the stability condition is that a fall in price should increase the excess demand (since it must become positive, after having been zero). Hicks plots supply, demand, and excess demand curves together on Figure 14.
Hicks states that it is "obvious" from this diagram that "when the demand curve slopes downward to the right, and the supply curve upwards to the right, the excess demand curve must be downward sloping." Just in case this doesn't seem obvious, note that on this diagram the demand curve is a line with negative slope, and the supply curve is a line with positive slope, therefore demand minus supply must be a line with negative slope. (Note also that this figure, like most in economics, plots price on the vertical axis, so we read the quantity for a given price horizontally -- hence the price level at which the excess demand curve crosses the price axis is exactly the price level at which supply equals demand.)
Hicks then asks what can be said in general about the effect of a fall in price on excess demand.
As seen in Chapter II, both supply and demand effects can be analyzed in terms of income and substitution effects; thus, Hicks argues, excess demand can be analyzed this way as well. The substitution effect of a fall in price will work to increase demand and reduce supply; thus the fall in price will tend to increase excess demand. The income effect works by making buyers better off and sellers worse off. If the good in question is not an inferior good, this will tend to increase both demand and supply. Then, as Hicks concludes, "the direction of the income effect on excess demand depends on which of these two tendencies is the stronger." These income effects could cancel each other out entirely, in which case the excess demand curve will slope downward, and the equilibrium will be stable. In general, however, there will be some net increase or decrease in excess demand due to the redistribution of income between the buyers and sellers. Because there will likely be some cancellation in effects, however, Hicks recommends that, "when dealing with problems of the stability of exchange, it is a reasonable method of approach to begin by assuming that income effects do cancel out, and then to inquire what difference it makes if there is a net income effect in one direction or the other."
Hicks points out that the equilibrium will still be stable if the net income effect goes in the same direction as the substitution effect. He notes that the only possibility for instability comes "when there is a strong income effect in the opposite direction -- that is to say, the sellers of X will have to be much more anxious to consume more X when they become better off than the buyers of X are." He illustrates such a case using Figure 15, in which point Q is unstable. Even here, however, he notes that this excess demand curve "would still be able to turn round and produce stable positions (such as P or P')."
Hicks points out that the difficulty in a situation such as the one illustrated here is that there may be more than one stable equilibrium. A change in the tastes of consumers may move the excess demand curve to the right, which in the case of starting from the equilibrium of P', could result in a sharp and discontinuous jump to the new equilibrium position of P.
Hicks then asks what can be said in general about the effect of a fall in price on excess demand.
As seen in Chapter II, both supply and demand effects can be analyzed in terms of income and substitution effects; thus, Hicks argues, excess demand can be analyzed this way as well. The substitution effect of a fall in price will work to increase demand and reduce supply; thus the fall in price will tend to increase excess demand. The income effect works by making buyers better off and sellers worse off. If the good in question is not an inferior good, this will tend to increase both demand and supply. Then, as Hicks concludes, "the direction of the income effect on excess demand depends on which of these two tendencies is the stronger." These income effects could cancel each other out entirely, in which case the excess demand curve will slope downward, and the equilibrium will be stable. In general, however, there will be some net increase or decrease in excess demand due to the redistribution of income between the buyers and sellers. Because there will likely be some cancellation in effects, however, Hicks recommends that, "when dealing with problems of the stability of exchange, it is a reasonable method of approach to begin by assuming that income effects do cancel out, and then to inquire what difference it makes if there is a net income effect in one direction or the other."
Hicks points out that the equilibrium will still be stable if the net income effect goes in the same direction as the substitution effect. He notes that the only possibility for instability comes "when there is a strong income effect in the opposite direction -- that is to say, the sellers of X will have to be much more anxious to consume more X when they become better off than the buyers of X are." He illustrates such a case using Figure 15, in which point Q is unstable. Even here, however, he notes that this excess demand curve "would still be able to turn round and produce stable positions (such as P or P')."
Thursday, January 7, 2016
Value & Capital, CHAPTER V -- THE WORKING OF THE GENERAL EQUILIBRIUM SYSTEM, Section 1
In this section, Hicks briefly outlines how the laws of change of the price system will be derived from stability conditions. In the context of an exchange system, stability means that slight movements away from an equilibrium position will tend to cause reactions that push the system back toward equilibrium. Under perfect competition, a rise in price tends to cause supply to exceed demand, which will tend to cause the price to fall. Similarly, a fall in price tends to cause demand to exceed supply, which will cause the price to rise. These relationships between supply and demand constitute the stability conditions for an equilibrium in an exchange system.
Since the theory of exchange is based on the theory of demand, Hicks proposes to check his investigations of the stability of exchange for consistency with the theory of demand as worked out in Chapters II and III. From the stability conditions, Hicks will deduce laws of change, i.e. "rules about the way in which the price-system will react to changes in tastes and resources." This investigation (still of a pure exchange economy) will occupy the eight sections of Chapter V. In Chapter VI he will begin to examine markets with production.
Since the theory of exchange is based on the theory of demand, Hicks proposes to check his investigations of the stability of exchange for consistency with the theory of demand as worked out in Chapters II and III. From the stability conditions, Hicks will deduce laws of change, i.e. "rules about the way in which the price-system will react to changes in tastes and resources." This investigation (still of a pure exchange economy) will occupy the eight sections of Chapter V. In Chapter VI he will begin to examine markets with production.
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