Derivation of indifference curve, Macroeconomics

Assignment Help:

Derivation of Indifference Curve:

Consider any commodity bundle denoted by point A in the above figure which consist x01 and x02 amount of good I and good II respectively and from which consumer obtains particular level of utility, say U0. We compare the commodity bundle 'A' with other commodity bundle in the commodity space. For that we divide the entire commodity plane into four phases from 'A'.  Consider any point in phase I say β, where we have large quantity of both x1 and x2 compared to point 'A'. Again, if we consider any point say 'a' in horizontal line in phase I, we have larger quantity of x1 with same quantity of x2 compared to point 'A'. Similarly, for any point 'b' in vertical axis, we have larger x2 with same x1. That means in phase I including the borderlines, we have larger quantity of at least one commodity and no less quantity of any other commodity compared to 'A'. Thus, we have larger utility in phase I including the borderlines compared to 'A'. 

 

1565_Derivation of Indifference Curve.png

By similar logic, we have lower consumption of at least one good and no larger consumption of any other good in phase III including the borderlines compared to point 'A'. Hence, we have lower level of utility in phase III including the borderlines compared to 'A' by the axiom of non-satiation for all goods. 

Clearly, in phases I and III, including borderlines, utility is not constant between the commodity bundles compared to point 'A'. So, indifference curve (along which utility is constant) can't pass through phases I and III including their borderlines. 

Consider any point in phase IV excluding borderlines, say α. We have larger x1 (for which utility is larger) and lower x2 (for which utility is lower) compared to 'A'. Since both goods are non-satiated, utility of point α may be larger, lower or equal compared to point 'A'. Similarly, for any point in phase II excluding the borderlines, say  δ, we have larger consumption of x2 but lower of x1 compared to point 'A'. Therefore, by axiom of non-satiation in all goods, utility at point δ may be larger, lower or equal compared to 'A'. 

Clearly, only in phases II and IV excluding the borderlines, there is a possibility of the same level of utility between the bundles compared to point 'A'. So, indifference curve, along which utility remains unchanged, must pass through the phase II and phase IV, excluding their lines. Thus, indifference curve is necessarily downward sloping where all goods are non-satiated given that a consumer choice is continuous, reflexive and complete.  

 


Related Discussions:- Derivation of indifference curve

Servicing the maximum number of patients, A clinic uses doctors and nurses ...

A clinic uses doctors and nurses optimally and is servicing the maximum number of patients given a limited annual payroll. The last doctor hired treated 1,600 extra patients in a y

Economy is characterized, Suppose that the economy is characterized by the ...

Suppose that the economy is characterized by the following behavioral equations: C= 170 + 0.7YD I= 170 G= 150 T= 100 a. What does equilibrium output equal? Y=? b. What d

Elucidate elasticity of supply using the midpoint formula, An attorney supp...

An attorney supplies 40 hours of work per week when her fee is $100 per hour but supplies 60 hours of work per week when her fee rises to $120 per hour. Using the midpoint formula,

Value of this expansion project, Bruno's Lunch Counter is expanding and exp...

Bruno's Lunch Counter is expanding and expects operating cash flows of $26,000 a year for 4 years as a result. This expansion requires $39,000 in new fixed assets. These assets wil

Marginal cost of care, Given the following MV information, what is the opti...

Given the following MV information, what is the optimal allocation of care according to the Preteens criteria, when the marginal cost of care is constant at $100. Person A Person B

Toms price elasticity of demand, Two drivers --- Tom and Jerry --- each dri...

Two drivers --- Tom and Jerry --- each drives up to a gas station. Before looking at the price, each places an order. Tom says, "I'd like 10 gallons of gas." Jerry says, "I'd like

Example of indirect taxes and subsidies- accounting system, Example of Indi...

Example of Indirect Taxes and Subsidies- ACCOUNTING SYSTEM   We now permit our government to impose what are called indirect taxes. This category includes sales tax, excise tax,

Set up a diagram.., (a) Use this information to set up a diagram showing th...

(a) Use this information to set up a diagram showing the firm''s total revenue and total cost schedules. In this diagram, show the points at which the firm is maximizing profits.

Analyse and contrast the macroeconomic behaviour, Collecteconomic data for ...

Collecteconomic data for three countries: Australia, China and Greece.The data is toobtainedfrom official sources as time series forthe key macroeconomic variables. These arereal G

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd