Consumer Equilibrium

4 Key excerpts on "Consumer Equilibrium"

• 

  eBook - ePub

  Economics for Investment Decision Makers

  Micro, Macro, and International Economics

  • Christopher D. Piros, Jerald E. Pinto(Authors)
  • 2013(Publication Date)
  • Wiley

    (Publisher)

  Exhibit 2-10 . The investor’s choice of a portfolio on the frontier will depend on her level of risk aversion.

  EXHIBIT 2-10 The Investment Opportunity Frontier

  Note: The investment opportunity frontier shows that as the investor chooses to invest a greater proportion of assets in the market portfolio, she can expect a higher return but also higher risk.

  5. Consumer Equilibrium: MAXIMIZING UTILITY SUBJECT TO THE BUDGET CONSTRAINT

  It would be wonderful if we could all consume as much of everything as we wanted, but unfortunately, most of us are constrained by income and prices. We now superimpose the budget constraint onto the preference map to model the actual choice of our consumer. This is a constrained (by the resources available to pay for consumption) optimization problem that every consumer must solve: choose the bundle of goods and services that gets us as high on our ranking as possible, while not exceeding our budget.

  5.1. Determining the Consumer’s Equilibrium Bundle of Goods

  In general, the consumer’s constrained optimization problem consists of maximizing utility, subject to the budget constraint. If, for simplicity, we assume there are only two goods, wine and bread, then the problem appears graphically as in Exhibit 2-11 .

  EXHIBIT 2-11 Consumer Equilibrium

  Note: Consumer Equilibrium is achieved at point a , where the highest indifference curve is attained while not violating the budget constraint.

  The consumer desires to reach the indifference curve that is farthest from the origin while not violating the budget constraint. In this case, that pursuit ends at point a , where the consumer is purchasing

  Wa

  ounces of wine along with

  Ba

  slices of bread per month. It is important to note that this equilibrium point represents the tangency between the highest indifference curve and the budget constraint. At a tangency point, the two curves have the same slope, meaning that the MRSBW must be equal to the price ratio,

  PB

  /

  PW

  . Recall that the marginal rate of substitution is the rate at which the consumer is just willing to sacrifice wine for bread. Additionally, the price ratio is the rate at which the consumer must

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  Economics for Investment Decision Makers

  Micro, Macro, and International Economics

  • Christopher D. Piros, Jerald E. Pinto(Authors)
  • 2013(Publication Date)
  • Wiley

    (Publisher)

   A consumer’s relative strength of preferences can be inferred from his marginal rate of substitution of good X for good Y (MRS XY ), which is the rate at which the consumer is willing to sacrifice good Y to obtain an additional small increment of good X. If two consumers have different marginal rates of substitution, they can both benefit from the voluntary exchange of one good for the other.  A consumer’s attainable consumption options are determined by her income and the prices of the goods she must purchase to consume. The set of options available is bounded by the budget constraint, a negatively sloped linear relationship that shows the highest quantity of one good that can be purchased for any given amount of the other good being bought.  Analogous to the consumer’s consumption opportunity set are, respectively, the production opportunity set and the investment opportunity set. A company’s production opportunity set represents the greatest quantity of one product that a company can produce for any given amount of the other good it produces. The investment opportunity set represents the highest return an investor can expect for any given amount of risk undertaken.  Consumer Equilibrium is obtained when utility is maximized, subject to the budget con- straint, generally depicted as a tangency between the highest attainable indifference curve and the fixed budget constraint. At that tangency, the MRS XY is just equal to the two goods’ price ratio, P X /P Y —or that bundle such that the rate at which the consumer is just willing to sacrifice good Y for good X is equal to the rate at which, based on prices, she must sacrifice good Y for good X.  If the consumer’s income and the price of all other goods are held constant and the price of good X is varied, the set of consumer equilibria that results will yield that consumer’s demand curve for good X.

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  Lectures on the Mathematical Method in Analytical Economics

  • Jacob T. Schwartz(Author)
  • 2018(Publication Date)
  • Dover Publications

    (Publisher)

  The main advances to date in the study of equilibrium models are associated with the names of Walras, Wald, McKenzie and Arrow and Debreu. To Walras we owe the first sophisticated formulation of the equilibrium phenomenon. Wald later carried out a comprehensive mathematical analysis of Walras’s equations and established the existence and uniqueness of solutions to these equations under a wide variety of conditions. Finally, McKenzie, and Arrow and Debreu independently formulated general models of equilibrium and proved the existence of a competitive equilibrium. None of the three models (Walras-Wald, McKenzie, Arrow-Debreu) subsumes any of the others as a special case; rather, all three should be viewed as variant descriptions of equilibrium in a competitive economy. Alternative analyses of the same models or other versions of equilibrium have been proposed independently by Gale, McKenzie and Uzawa.

  It will soon be seen that we regard this theory somewhat critically.

  Our model will be like that of Arrow and Debreu, but with linear Leontief-like features as introduced in the first four lectures, differing only in an expanded treatment of consumer preference. Thus the equilibrium price theory will be strictly comparable to the price theory developed in the first four lectures: we will be able to see explicitly how much or how little is added to the conclusions we are able to draw, by the introduction of consumer preferences.

  The elements of the model are to be as follows. In the first place, we will have a number of competing firms, each of which seeks to maximize its own profits; secondly, we will have a number of consumption units (families) each of which places a subjective “utility” upon each “bill of goods” that their labor and their dividends from ownership of industry will purchase. Each consumption unit then seeks to maximize this subjective utility, measured by an individual “utility function.” A careful formulation of the law of supply and demand will then allow us to find the conditions under which there exist prices at which all of these maxima are simultaneously realized; continuing, we shall investigate the further properties of such a “competitive equilibrium.”

  1. The Model Explicitly Defined

  Our model of the whole economy will consist first of a number m of “firms” or “investment syndicates” each of which is capable of producing (i.e., has the ability and the freedom to produce) any, several, or all of the n commodities

  C1

  , · · ·, C n of the economy. Labor will first be considered (inessentially) as being homogeneous and regarded as commodity

  C0

  ; consequently we will generalize the model to include various distinct labor sectors. The k th firm in the first instance is described by a set of numbers π

  ij (k)

  which represent the amount of Cj required by firm k for the production of one unit of Ci. We shall take these numbers as being the same for all firms, however, and write πij for each of them. Thus we assume that no firm can have a clear technological advantage over another firm. We measure the wealth of each firm by assuming that firm k has an initial ownership inventory of

  qi(k)

  units of commodity

  Ci , (i =

  1, · · ·, n) and that this inventory is economically liquid, i.e., could be freely sold or traded for equal value (under prices yet to be determined). In this model, then, the only distinction between different firms is their total capitalization as reflected in their ownership inventories. In the same way we assume a fixed capital matrix with elements ϕ

  ij ,

  taking ϕoi =

  ϕio

  = 0 for all i.

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  Health Economics For Nurses

  Intro Guide

  • Stephen Morris(Author)
  • 2014(Publication Date)
  • Routledge

    (Publisher)

  7. By supply we mean the quantity of a good that producers will wish to offer for sale at a particular price per time period. 8. The quantity supplied of a good is also influenced by a number of variables, such as the price of the good, the prices of other goods and the costs of production. 9. There is, in general, a positive relationship between the price of a good and the quantity supplied of that good. 10. The supply curve may be derived using the Law of Increasing Costs and the assumption that producers wish to maximise their profits. 11. The equilibrium price is the price at which the wishes of consumers and producers coincide.

  12. If the market price is different from the equilibrium price, then either an upward or downward pressure on price, exerted by market forces and caused by excess demand or excess supply, will cause the market price to tend towards the equilibrium price.

  13. Changes in the demand and supply curves, caused by changes in the determinants of demand and supply, will cause the equilibrium price to change. 14. There are four basic changes which can occur to the equilibrium price: a rise in demand; a fall in demand; a rise in supply; and a fall in supply. 15. The intuitive reason for using the market framework to address the issue of scarcity is that markets provide a means of allocating resources which is efficient.

  16. Aiming to maximise their utility, consumers will spend the amount of money which will maximise their well-being, resulting in allocative efficiency. At the same time, producers, seeking to maximise their utility through maximising their profits, will compete for custom by producing goods most highly valued by consumers at least cost, thus behaving in a technically efficient manner.

  17. Consumers in the market have the knowledge and ability to determine the level of price at which demand equals supply. The dominance of consumer preferences is known as consumer sovereignty, and is a necessary condition for the market to allocate resources efficiently.

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