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
Choosing Output in Long Run * In long run, a firm can change all its inputs, including size of the plant. * We are taking free entry and free exit. * Accounting

The Healthy Spring Water company sells bottled water for offices / homes. The price of the water is $20 per 10 gallon bottle and the company currently sells 2,000 bottles per day.


Biochemistry is regarded a dull topic. Not many learners like to research it in school since it includes a thorough comprehension of issue and clinical changes in the framework, fr

A Period of Deterioration: The entire period was very difficult for India's BOP, partly because of slow growth of exports in relation to import requirements and partly because

A local airline charges $500 to fly (round-trip) to Louisville, Kentucky. From the past three months, whereas the $500 fare has been in effect every of the two daily flights have a

how can I execute this topic in new way of teaching? That will focus on activity base and art of questioning that will answer by the students?

7.Consider the following production possibilities table: Option Y X A 0 100 B 80 80 C 120 50 D 140 10 a)Provide a measure of the approximate marginal opportunity cost of

Write an objective analysis paper on the economics of outsourcing and insourcing production by businesses. Please make sure you have a thesis (a main point that you are making) and

Defining black economy, If you pay your cleaner or builder in cash or for some reason neglect to tell the taxman which you were paid for a service rendered, you participate in the