How to Derive Consumer's Equilibrium Through the Technique of Indifference Curve and Budget Line?

Updated on June 1, 2014


The goal of a consumer is to get maximum satisfaction from the commodities he purchases. At the same time, the consumer possesses limited resources. Hence, he is trying to maximize his satisfaction by allocating the available resources (money income) among various goods and services rationally. This is the main theme of the theory of consumer behavior. Further, you could ascertain that a consumer is in equilibrium when he obtains maximum satisfaction from his expenditure on the commodities given the limited resources. You can analyze consumer’s equilibrium through the technique of indifference curve and budget line.


  1. The consumer under consideration is a rational human being. This means that the consumer always tries to maximize his satisfaction with limited resources.
  2. There prevails perfect competition in the market.
  3. Goods are homogeneous and divisible.
  4. The consumer has perfect knowledge about the products available in the market. For instance, prices of commodities.
  5. Prices of commodities and consumer’s money income are given.
  6. Consumer’s indifference map remains unchanged throughout the analysis.
  7. Consumer’s tastes, preferences and spending habits remain unchanged throughout the analysis.

Price Line or Budget Line

Price line or budget line is an important concept in analyzing consumer’s equilibrium. According to Prof. Maurice, “The budget line is the locus of combinations or bundles of goods that can be purchased if the entire money income is spent.”

Table 1

X (units)
Y (units)
Total Amount Spent on X + Y (in $)
8 + 0 = 8
6 + 2 = 8
4 + 4 = 8
2 + 6 = 8
0 + 8 = 8

Suppose there are two commodities, namely X and Y. Given the market prices and the consumer’s income, the price line shows all the possible combinations of X and Y that a consumer could purchase at a particular time. Let us consider a hypothetical consumer who has a fixed income of $8. Now, he wants to spend the entire money on two commodities (X and Y). Suppose the price of commodity X is $2, and the price of commodity Y $1. The consumer could spend all money on X and get 4 units of commodity X and no commodity Y. Alternatively, he could spend entire money on commodity Y and get 8 units of commodity Y and no commodity X. The table given below exhibits the numerous combinations of X and Y that the consumer can purchase with $8.

In figure 1, horizontal axis measures commodity X and vertical axis measure commodity Y. The budget line or price line (LM) indicates various combinations of commodity X and commodity Y that the consumer can buy with $8. The slope of the budget line is OL/OM. At point Q, the consumer is is able to buy 6 units of commodity Y and 1 unit of commodity X. Similarly, at point P, he is able to buy 4 units of commodity Y and 2 units of commodity X.

The slope of the price line (LM) is the ratio of price of commodity X to price of commodity Y, i.e., Px/Py. In our example, price of commodity X is $2 and price of commodity Y is $1; hence, the slope of the price line is Px. Note that the slope of the budget line depends upon two factors: (a) money income of the consumer and (b) prices of the commodities under consideration.

Reasons for Many Budget Lines

(a) Consumer’s Income Change

An outward parallel shift in the budget line occurs because of an increase in consumer’s money income provided that the prices of commodities X and Y remain unchanged (it means constant slope - Px/Py). Likewise, a reduction in consumer’s money income creates a parallel inward shift in the budget line.

In figure 2, LM denotes the initial price line. Assume that the prices of the two goods and consumer’s money income are constant. Now, the consumer is able to purchase OM quantity of commodity X or OL quantity of commodity Y. If his income increases, the price line shifts outward and becomes L1M1. He can now buy OM1 quantity of commodity X and OL1 quantity of commodity Y. A further increase in income causes a further outward shift in the price line to L2M2. Price line L2M2 indicates that the consumer can buy OM2 quantity of commodity X and OL2 quantity of commodity Y. Similarly, if there is a decrease in consumer’s income, the price line will shift inward (for example, L3M3).

(b) Price Change

The slope of a price line is associated with the prices of commodities under consideration. Hence, if there is a change in the price of any one of the commodities, there will be a change in the slope of the price line. Assume that the price of commodity X decreases and the price of commodity Y remain unchanged. In this case, the price ratio Px/Py (slope of price line) tends to decrease. In figure 3, this scenario is denoted by the shifts in the price line from LM to LM1 then to LM2 and so on. Conversely, if the price of commodity X rises, the price ratio Px/Py will rise. This leads to the price line shifts from LM2 to LM1 and to LM.

Indifference Map

A set of indifference curves that shows a consumer’s preferences is known as an indifference map. The indifference map of a consumer, since is composed of indifference curves, exhibits all properties of a normal indifference curve. Some of the most important properties of an indifference curve are: indifference curves are convex to the origin; they always slope downwards from left to right; higher indifference curves indicate higher levels of satisfaction; they do not touch any of the axes (example: figure 4).

Necessary conditions for consumer’s equilibrium

The following are the two important conditions to attain consumer’s equilibrium:

Firstly, marginal rate of substitution must be equal to the ratio of commodity prices. Symbolically,

MRSxy = MUx/MUY = Px/Py.

Secondly, indifference curve must be convex to the origin.

Consumer's Equilibrium

Now we have both budget lines and indifference map of the consumer. A budget line represents consumer’s limited resources (what is feasible) and indifference map represent consumer’s preferences (what is desirable). The question now is that how the consumer is going to optimize his limited resources. An answer for this question would be consumer’s equilibrium. In other words, the consumer’s equilibrium means the combination of commodities that maximizes utility, given the budget constraint. To obtain consumer’s equilibrium graphically, you just need to superimpose the budget line on the consumer’s indifference map. This is shown in figure 5.

At point E, consumer’s equilibrium is attained. Because the indifference curve IC2 is the best possible indifference curve that the consumer can reach with the given resources (budget line). The tangency of indifference curve IC2 and the price line represent the above statement. At the point of tangency, the slope of the budget line (Px/Py) and the marginal rate of substitution (MRSxy = MUx/MUy) are equal: MUx/MUy = Px/Py (first condition for consumer’s equilibrium). From figure 5, we can understand that the second condition for consumer’s equilibrium (indifference curve must be convex to the origin) is also fulfilled.

A small algebraic manipulation in the above equation gives us MUx/Px = MUy/Py, which is the marginal utility per dollar rule for consumer’s equilibrium. Thus, all the conditions for consumer’s equilibrium are fulfilled. The combination (X0Y0) is an optimal choice (point E) for the consumer.

Questions & Answers

    © 2013 Sundaram Ponnusamy


      0 of 8192 characters used
      Post Comment
      • profile image


        14 months ago

        Helpful for I do not have textbook but slides

      • profile image

        Geses Mark 

        2 years ago

        Interesting and very important to all the economics students.

        I really enjoy reading as one of the many students who show interest on economics. The note helped me a lot on my studies at the Institute of Business Studies University (IBSU) in Papua New Guinea

      • profile image

        Tshegofatso Odumeleng 

        2 years ago

        Wow beautiful....however it needs a lot of concentration and attention,the material is too much but useful though...thank you very much

        By the way am a third year student in the University of Botswana(Africa) and thanks a lot!


      • profile image


        5 years ago

        very useful for students & teachers of econmics

      • jabelufiroz profile image


        6 years ago from India

        Impressive hub. Voted up and useful.


      This website uses cookies

      As a user in the EEA, your approval is needed on a few things. To provide a better website experience, uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

      For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at:

      Show Details
      HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
      LoginThis is necessary to sign in to the HubPages Service.
      Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
      AkismetThis is used to detect comment spam. (Privacy Policy)
      HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
      HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
      Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
      CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
      Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the or domains, for performance and efficiency reasons. (Privacy Policy)
      Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
      Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
      Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
      Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
      Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
      VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
      PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
      Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
      MavenThis supports the Maven widget and search functionality. (Privacy Policy)
      Google AdSenseThis is an ad network. (Privacy Policy)
      Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
      Index ExchangeThis is an ad network. (Privacy Policy)
      SovrnThis is an ad network. (Privacy Policy)
      Facebook AdsThis is an ad network. (Privacy Policy)
      Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
      AppNexusThis is an ad network. (Privacy Policy)
      OpenxThis is an ad network. (Privacy Policy)
      Rubicon ProjectThis is an ad network. (Privacy Policy)
      TripleLiftThis is an ad network. (Privacy Policy)
      Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
      Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
      Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
      Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
      ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
      Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)
      ClickscoThis is a data management platform studying reader behavior (Privacy Policy)