Slutsky theorem - graphical presentation, Microeconomics

Slutsky's Theorem:

Graphical Presentation 

We prove here that own price effect is the sum of own substitution effect and income effect for a price change, which is known as Slutsky's theorem. This is shown in the figure given bellow:  


959_Graphical Presentation.png

At initial prices and money income, budget line is AB and according to the condition of the equilibrium e0 is the initial equilibrium point. The consumer gets U0 level of utility. Suppose at constant income and p2, p1 decreases (say by one unit). Consequently, the intercept of the budget line (M/p2) remains unchanged but absolute slope of the budget line (p1/p2) decreases. The new budget line becomes flatter with the same intercept. It is denoted by AC line. New equilibrium can be achieved at any point on the new budget line AC (and therefore own price effect can take any algebraic sign). Suppose the equilibrium takes place at point e1. Hence, as p1 decreases, for given p2 and M, demand for good I increases from x10 to x11. This is the own price effect for x1 and here it is negative. A part of this change is due to change in real income (since for given p2 and M as p1 decreases, real income increases) and another part is originated at constant real income. To decompose these effects, we reduce money income (M) of the consumer in such a way that real income in terms of utility remains unchanged. After such reduction of M, intercept of the new budget line AC, i.e., (M/p2) decreases with the same slope (p1/p2) for given p1and p2. Hence the new budget line shifts parallely downwards subject to the fact that after the shift, it is tangent to the previous indifference curve. The consumer can attain the same level of utility and the real income remains constant in terms of utility after adjusting money income and utility is also maximised. After adjustment of money income, budget line is A'C' along which real income in terms of utility remains constant after change in p1 for given p2. This budget line is known as compensated budget line. Under such budget line equilibrium will necessarily take place at point e1'. Hence under constant real income in terms of utility, as p1decreases for given p2, x1 increases (from x10 to x11') by substituting x2 (from x10 to x21). This is known as own price substitution effect for x1 which is negative and indifference curve is downward sloping strictly convex to the origin. But as x1 increases from x10 to x1 and real income also increases, the demand for good I increases from x10 to x1' through a rise in real income. This would indicate that by income effect for a price change, x1 is a normal good. Clearly, we have own price effect consists of own substitution effect and income effect for a price change, where own substitution effect in negative but income effect for a price change can take any algebrical sign depending on the good is normal, superior or inferior.   


Posted Date: 10/26/2012 3:12:10 AM | Location : United States

Related Discussions:- Slutsky theorem - graphical presentation, Assignment Help, Ask Question on Slutsky theorem - graphical presentation, Get Answer, Expert's Help, Slutsky theorem - graphical presentation Discussions

Write discussion on Slutsky theorem - graphical presentation
Your posts are moderated
Related Questions
Determinants of reserve price

prove that marginal utility of x=the price of commodity x.

The efficiency loss of a tax is the tax revenue collected by government minus the value of the public goods financed through the tax. Why is this false?

Sally recently finished her full-time training and received certification as a nurse’s aid at the end of August. She sent out applications to prospective employers during the last

Determinants of Private Demand - Linkages with Employment Employment potential of courses in higher education is an important determinant of private investment in higher educa

Equilibrium Exchange Rate: The theory of exchange rate determination explains how demand and supply of foreignexchange interact and jointly determine the equilibrium exchange

Your company has a product that it is interested in marketing in a foreign country. Using one of the following Websites, click on a country of your choice to learn about Etiquette,

elasticity of demand of a product in different market forms such as perfect competition, monoply etc.

P=140-4Q mc1=20+30q for plant 1 mc2=80+10q for plant 2 how many units should be produced by plant 1 and plant 2 to maximise profit for this monopoly?