Theoretical Evidence That the Hicksian Model Attempts to Enhance the Consumer Theory - Essay Example

Theoretical Evidence That the Hicksian Model Attempts to Enhance the Consumer Theory Thesis: The Hicksian compensated demand function attempts to enhance neo-classical consumer theory. Introduction Consumer theory is one of the centerpieces of the neoclassical branch of microeconomics. Neoclassical consumer theory is the foundation on which modern economics has its basis. In the early 20th century, neoclassical consumer theory had a breakthrough due to the indifference curve analysis. The indifference curve analysis acted as a bridge between application of reversed methods of differential calculus to economics and the fact of ordinal utility. Due to the success with which differential calculus had been an aid to physicists in the same period, economists adopted its utility and it became an integral part of modern day economics. The principles and models that arise from neo-classical consumer theory are the basis for modern day economic analysis. Although consumer theory is not under unanimous acceptance, modern economists that try to criticize the theory lack enough evidence. The critiques against neoclassical consumer theory lack in evidence and fact, and most of those critiques misrepresent the neoclassical approach to economics. Several assumptions are necessary for the neoclassical consumer theory to work efficiently. The assumptions made in neoclassical consumer theory double as its differences with the Austrian approach to economics. The first assumption in neo classical consumer theory is that every individual is only a consumer. This means that every individual is a purchaser of consumption goods and services. The consumer theory ignores the fact the individuals under analysis could be producers in the market, but it does not deny it. In this study, the various models applied in neo classical consumer theory will be under analysis, in order to gain a better understanding on the best models to use in different analytical situations (Hicks & Allen, 1934). Marshall's model (consumer theory) Marshall’s model on consumer behavior assumes that the consumer has a perfect knowledge of the market. The model also assumes the consumer is a rational buyer who knows his or her desires and knows the best way of satisfying them. According to this model, buyers are bound to spend on the goods that satisfy their desires. The satisfaction of these desires is dependent on the relative price and the taste of the buyers. In his model, Alfred Marshall also states that the price and output of any given good is dependent on demand and supply (Marshall, 1961). The demand and supply curves cut each other like scissors and their point of intersection is the equilibrium. Marshall was the first economist to develop the standard supply and demand curves and he proved the relationship between price and quantity in relation to supply and demand and the law of marginal utility. A mathematical presentation of Marshall’s model in form of X as the object on demand is dependent on all prices, income and preferences. Its presentation is as follows: x* = x(px,py,I) Assuming that the price of y (py) is held constant, a graph of the individuals demand for x is convenient (Marshall, 1961). General background of Hicks’ function and theory, define and explain Hicks' model for compensated demand function. A compensated approach is the alternative to holds utility. It is applicable in a case where a price changes but the individual remains indifferently on the same price curve. The indifference arises from the compensation of the individual’s price by the income. In a compensated case, the utility is constant and reaction to change in prices is solely inclusive of substitution effects (Hicks & Allen, 1934). Hicks came up with a function in the compensated sense that shows the relationship between the price and quantity. As opposed to Marshall’s model, Hicks used the assumption that other prices, and the utility is constant. He came up with a Hicksian function that showed the relationship between demand, quantity and price. Presentation of the Hicksian function is as follows: x* = xc(px,py,U) The curve representing this function is: Contrasting approaches between Hicks and Marshall Both the Hicksian and Marshallian demand attempt to tackle the same problem from different perspectives. They both try to satisfy the consumer utility with the budget the consumer earns. Consumption duality attempts to clarify the Marshallian and Hicksian demand in means of maximizing utility and minimizing cost. The consumer’s primal demand attempts to maximize the utility despite keeping the budget fixed. As a consumer, I would want to get the maximum services from a small budget. The second aspect associated with consumption duality states that the consumer sets a target utility, and minimizes the cost associated with acquiring the target utility. Both Marshall and Hicks’ model prove viable in microeconomic analysis, one could be eliminated and the other adopted as the major economic model. Instead, both models are still viable today as the demand functions in consumer theory. The models have a slight difference that makes them both viable for use in an ideal market situation. The Marshallian model and function shows a relationship between price and budget, while the Hicksian model and function is the representation of how price relates to utility. In his model, Marshall assumes that money income is constant and he uses this as a basis for studying the shift in demand. Marshall’s measurement is also different from that of hicks since he also measures the effect of the demand change on the price (Marshall, 1961). Hicks’ measures the shift in demand with utility held constant. In this case, utility is the real income, and the representation is on an indifference curve. Plotting on an indifference curve ascertains that Hicks values give the substitution effect while Marshall’s curve shows the total effect of change. From the latter summary, it is true to state that the major difference between Marshallian and Hicksian functions is the type of income that each economist holds constant (income effect). The relationship between the price of a good and the quantity that is in demand for that good is the basis for the Marshallian model. In Hicksian demand, the price and demend relationship is still active, but the prices of other goods are constant and so is the consumer’s utility. The point of equilibrium for the Marshallian and Hicksian model is visible at the point where the quantity demanded for the goods is equal on both sides. The Marshallian demand curve has an assumption that only nominal wealth fails to change, hence the Hicksian demand curve has more wealth past the equilibrium point. The latter arises because the Hicksian model holds all income as constant. According to Marshallian demand curve, the consumer is better off if the price levels drop while the nominal wealth remains the same for the consumer. In the Hicksian model, if the price levels drop, the consumer has real wealth and he is worse off. Marshallian demand curves are more stable since they consider both substitution and rent effect. The Hicksian model is also applicable, but it uses the substitution method alone hence, it is less stable. Where X is the price, the Marshallian function is X*=dX1(PX1, PX2, m), while the Hicksian function is X*=hX1(PX1,PX2,U). Derive Marshall and Hicks' models using indifference curves, budget constraints, finding equilibrium points and projecting the different demand curves themselves The initial equilibrium point is applicable in finding the first point of the demand curve. After mapping the demand, a consideration in price increase gives a corresponding change to the demand and price. In order to find the new price of the commodity, it is important to find the new equilibrium point of demand. In the latter explanation, it is clear that demand and price affect each other and this causes motion along the curve. After finding the new equilibrium point for the commodity, it should help us to derive the Marshallian demand curve. The Marshallian function is derived by finding the distance between the new price and the old price. The latter gives a reflection on how the demand curve shifts. After deriving the Marshallian model, we use the same representation to see what happens in compensated situations. If a consumer is compensated with enough money to replace the spent income, several factors are bound to change. The consumer will consume more in the market hence increasing the demand for commodities. An increase in demand helps in price reduction, which leads to more consumption and more demand. Increasing the compensation helps by raising the budget constraints until there is contact with the difference curve. In compensation, an assumption is made, which ensures that the consumer is back to the original utility level. Compensation occurs through raising the consumer’s income to the level where there is equality between the new and the original utility level. The demand for X in this case is in accordance to the substitution after commodity price increase due to more money in the market. Compensation brings about a concept introduced by Hicks; hence, this is the process of deriving the Hicksian demand curve. The graphical representation below shows the various market shifts and the changing equilibriums in the market. It also represents the budget constraints arising from the compensation. It contains the Hicksian curve and the Marshallian curve. Define Slutsky model and show relation to the other two models. Show implications of the model.  The Slutsky model consists of an equation that shows that the change in demand for a good, due to a change in the price of the good is dependent on two effects. The two effects arise from a change in the relative price of two goods, which is the substitution effect, and a change in the consumer purchasing power due to a change in the price of the good, known as income effect. The Slutsky model shows a relation between the Hicksian model of compensated income and the Marshallian model of uncompensated income. The Slutsky equation is as follows: (Slutsky, 1936). The left side represents the total effect that is a derivative of the quantity x in respect to price (p). The equation reflects the consumption quantity changes when the price of an item changes. The substitution effect is obtained by substituting the Hicksian demand in relation to price. The implication of this model is that it gives a more comprehensive demand curve that aids in economic analysis (Slutsky, 1936). An example of the three combined curves in one representation is present below: Similarities and differences of Hicks and Slutsky models The main difference between the two models is that the Hicksian model keeps the real income constant (utility) while Slutsky’s keeps the purchasing ability of the consumer at a constant level. Another difference arises because the Slutsky’s model gives a consumer enough money to get back to the former consumption level while Hicksian model gives the consumer adequate money to get back to the former indifference curve (Hicks & Allen, 1934). The graphical representations below show the difference in the substitution effect of the two models Hicksian Substitution effect: Slutsky’s substitution effect Apart from the substitution effect, all other aspects of the Hicksian and Slutsky model are almost identical. Both models use compensation of income in projecting the demand curve as opposed to the Marshallian model of uncompensated income. Distinguish between compensating variations (CV) and equivalent variations (EV) CV also known as compensating variation is the income change that originates from returning the consumer to the original utility. The latter condition comes about only after an economic change that causes a shift in the income. The maximum a consumer could pay for an economic change to happen comes about after a positive CV, which entails the drop in a price. After a negative change such as price increase, the minimum is what a consumer should pay to afford the economic change (Hicks & Allen, 1934). EV on the other hand stands for equivalent variation. This is a form of income adjustment that changes the consumer’s utility to a level of equality. This equality would only occur IF the event had happened. In case of a positive change in the economy, the EV would be the income increase that would give the same additional utility to the consumer if the price did not fall. In negative economic change, EV would be the income taken from the consumer to lower the consumer’s utility to the level equal to that of the change occurring (Hicks & Allen, 1934). The presentation below shows the graphical presentation of CV and EV In a case where y is the composite commodity and x is the interest on the good, the price of commodity y is Py and that of x is Px. After normalization of the price of y, Py =1, the budget for the consumer is B. the latter statement enable us derive the equation that: B=PyY+PxX=y+PxX Rewriting the budget constraint in terms of a standard slope intercept format of y=mx+c, the equation becomes y=B-PxX ((Hicks & Allen, 1934). Impact of CV and EV on consumer demand curve When the price of a good falls, the consumer is usually on the original budget line E0 and the utility of the consumer at that point is I0. The budget line rotates out with a subsequent fall in the price of commodity x. After rotating out of the budget line, the new equilibrium point for the demand curve is E1, while the new utility line is I1. The compensation variable acts in the manner of an old indifference curve with a new price ration. Due to the latter, a shift of new budget line to a tangent point of the old indifference curve with a vertical intercept line on point C. The intercept C arises from the dotted budget line under translation. The compensating variation of a price fall is the distance BC between the parallel shifts of the new budget line (Angus, 1980). Equivalent variation on the other hand is the opposite of CV. The EV mains the old price ration but introduces a new indifference curve. To derive the EV, the new budget line translation has to be tangent to the new indifference curve. The derived tangent has an intercept M similar to that of the CV (Angus, 1980). The distance BM gives the equivalent variation as shown below: Hicks’ model of compensation shows a shift in demand, and its effect on price changes. The model holds utility as a constant in relation to price. Since neo classical consumer theory attempts to understand the behavior of a rational consumer in a market with normal market forces, Hicks model satisfies the neo classical consumer theory. Hicks’ model is a method o explaining the market structure from a different viewpoint to compliment the Marshallian model and the Slutsky model. The Hicksian model applies differential equations in its functions to calculate consumer behavior, which is also a characteristic of the neoclassical approach to consumer theory (Angus, 1980). Subsequent theoretical debates using Lancaster theory According to Kevin Lancaster, classical economists were wrong in characterizing commodities as objects with single output utilities. In his theory, Lancaster claims that commodities have several characteristics that appeal to buyers. Consumers go for certain utilities due to the several characteristics that appeal to their sense of satisfaction. A commodity with more characteristics that satisfy a consumer is likely to be on higher demand as opposed to a commodity with one characteristic.” The chief technical novelty lies in breaking away from the traditional approach that goods are the direct objects of utility and, instead, supposing that it is the properties or characteristics of the goods from which utility is derived “(Lancaster, 1966). In his paper, Lancaster gives an example of consumerism behavior towards food, he claims that food appeals to the buyer not only for the nutritional value but also due to the pleasure one derives from eating the food. There is a likely scenario where more people opt for better tasting food despite its low nutritional content. The latter means that consumers consider the characters that are the most satisfactory to their sense consumerism (Lancaster, 1966).” In an economy with a complex consumption theory, relative price change may lead to a cluster of goods attaining poor characteristics hence replacement by another bundle. Alternatively, relative price change may alter the consumer’s characteristic preference due to the budget shift” (Lancaster, 1966). Conclusion All through the research, the neoclassical consumer theory has been under discussion. In the research, it is evident that economists understand the significance of differential equations in predicting consumer behavior under different circumstances. Marshallian and Hicksian functions have been important in understanding the basis of neo classical consumer theory. The curves from the Marshallian and Hicksian models have been under thorough analysis in this research. The research into other models such as the Marshallian theory and the Slutsky theory has been supporting the fact that Hicks theory enhances neo classical consumer theory. Neoclassical consumer theory is an important are in modern day economics since all proven theories revolve around it as the thesis. Other models such as the Austrian models attempt to refute the neo classical theory but their arguments and critiques are not compact and in some cases, they become irrelevant. Integration of differential equations in calculus to economics has been an important stepping-stone in understanding consumer theory. Deriving the functions from the day-to-day market setting ensures that the functions derived for differentiation are accurate and relatable. Evolution of economics from the classical period where assumptions were that the consumer’s behavior is static, to the neo classical period that introduces dynamic market settings has been successful and important. Dynamic market and consumer behavior help modern day economists relate to the marketplace changes. Relating to marketplace shifts in demand and price change enable modern day entrepreneurs to practice predictive market analysis. Bibliography Arrow, Kenneth J., and Gerald Debreu, (1954):. “Existence of an Equilibrium for a Competitive Economy,” Econometrica 22 pg.265-290. Aubin, Jean-Pierre, (1998). Optima and Equilibria: An Introduction to Nonlinear Analysis, trans. Stephen Wilson.New York, Springer-Verlag. Andreu Mas-Colell, Michael D. Whinston and Jerry R. Green, (1995), Microeconomic Theory.Oxford University Press. 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