Partial and general equilibrium, law of demand and demand analysis

Apart from considerations of presentation and clarity the major advance which indifference curve analysis offered was its ability to distinguish between the income and substitution effects of a price change. Moreover, Hicks and Allen pointed out that the sign of this income effect could not be predicted from the simple assumption that the consumer seeks to maximise utility. However they demonstrated that in the absence of income effects the substitution effects were remarkably regular. For example, they were able to show that not only is the direct substitution effect of a change in the price of X on the quantity demanded of X always negative, but that a number of secondary substitution theorems could also be deduced – the most important being the proposition that the substitution effect of a change in the price of X on the quantity demanded of Y must be exactly equal to the effect of a change in the price of Y on the quantity demanded of X.

The latter substitution theorem refers to the cross elasticity of demand and its importance derives from the fact that it success­fully cleared up the elasticity problem that had initially prompted the Hicks-Allen article. Specifically, Henry Schultz had estimated some cross elasticities of demand (the demand for X against the price of Y and vice versa) and found them to be non-symmetric whereas Marshallian demand theory suggested they should be symmetric. Hicks and Allen were then able to point out that ‘Schultz had left out the income effects which for direct elasticities may indeed be negligible, as Marshall (in effect) supposed them to be; but for cross elasticities there is no reason why they should be negligible’ (Hicks, 1974b).

This quotation is important in another respect. Basically, Marshall had ignored the income effect by assuming a constant marginal utility of money. The quotation suggests that from the point of view of ordinary demand analysis Hicks accepted Marshall’s neglect of the income effect. Indeed, such a neglect is justifiable as long as the good in question represents a small part of the consumer’s budget and Marshall was always careful to make this assumption. Thus in Hicks’s view the ordinal approach ‘was not so clear an advance (on the older marginal utility approach) as is usually supposed’ (1976, p. 137). By the same token Hicks has never accepted the extension of his analysis via Samuelson’s revealed preference approach as either necessary or desirable. ‘Marshall’s consumer who decides on his purchase by comparing the marginal utility of what is to be bought with the marginal utility of the money he will have to pay for it is more like an actual consumer’ (Hicks, 1976, p. 138). In fact in his Revision of Demand Theory (1956a) Hicks rejects the revealed preference approach even for econometric purposes, stating that for the data to which econometrics is usually applied on ordinal scale of preferences seems the most sensible hypothesis with which to begin the analysis.

However, despite his own reservations, Hicks’s ordinal ap­proach in the end met with very little criticism and quickly became a standard part of the economist’s tool kit. Moreover, many observers would claim that Hicks has underestimated the step forward that his use of indifference curves entailed, e.g. Blaug explains that European marginal utility doctrine around the First World War proliferated ‘in subtle distinctions and metaphysical classifications. [Thus], one is made to realize how much has been swept away by the Hicksian Revolution – all to the good we would say’ (Blaug, 1976, p. 388).

3.8 Price formation and discovery

This factor focuses on the process by which the price for an asset is determined. For example, in some markets prices are formed through an auction process (e.g. eBay), in other markets prices are negotiated (e.g., new cars) or simply posted (e.g. local supermarket) and buyers can choose to buy or not.

Assume a representative firm in an imperfectly competitive market, producing a

single good for which imperfect substitutes are produced abroad. The planned

price of the good is determined as a mark-up over marginal costs
pr = μ + mc, (2.2)
where μ is the mark-up and mc are marginal costs. The mark-up is not necessarily constant and may be a function of relative prices. This allows for a pricing-to market effect, with the mark-up inversely related to the elasticity of demand (see, for example, Krugman, 1987)

μ = κ + λ(q − pr) + ξp, κ, λ ≥ 0, (2.3)

producer price level as a mark-up over unit labour cost and import prices, with

1. 
   discuss briefly the theories of demand
   

2. 
   What do you mean by revealed preference? discuss its relevance in real world situations
   

3. 
   What the Indifference curve contribute to the concept of demand? Discuss giving suitable examples
   

4. 
   How the processes of price formation go on? Discuss price formation in context of market of heterogeneous goods.
   

5. 
   Assume a person has a utility function U = XY, and money income of $10,000, facing an initial price of X of $10 and price of Y of $15. If the price of X increases to $15, answer the following questions:
   

a. What was the initial utility maximizing quantity of X and Y?

• 
  Anand, Paul. Foundations of Rational Choice Under Risk Oxford, Oxford University Press. 1993 reprinted 1995, 2002
  
• 
  Bruce R. Beattie and Jeffrey T. LaFrance, “The Law of Demand versus Diminishing Marginal Utility” (2006). Review of Agricultural Economics
  
• 
  John Geanakoplos (1987). "Arrow-Debreu model of general equilibrium," The New Palgrave: A Dictionary of Economics
  
• 
  Neumann, John von and Morgenstern, Oskar Theory of Games and Economic Behavior. Princeton, NJ. Princeton University Press. 1944 sec.ed. 1947
  
• 
  Nash Jr., John F. The Bargaining Problem. Econometrica 1950
  
• 
  Volker Böhm and Hans Haller (1987). "demand theory," The New Palgrave: A Dictionary of Economics