Consumer Equilibrium Indifference Curve Approach PDF

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This document explains the how the consumer achieves the state of maximum satisfaction or equilibrium point....

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Consumer Equilibrium in Indifference Curve Approach (Graphical Representation): Having studied indifference curve Theory along with its assumptions and properties in the previous post, now, it’s time to study how the consumer equilibrium is achieved in indifference curve theory. This is a graphical representation of the consumer equilibrium. If you don’t know about indifference curve theory, kindly read this post first: Indifference Curve Theory Conditions for the Consumer Equilibrium: i.

First condition for a consumer to achieve the equilibrium is that the slope of indifference curve, MRS, be equal to the slope of budget line. This condition is also called necessary condition. 𝑀𝑅𝑆𝑥,𝑦 = 𝑆𝑙𝑜𝑝𝑒 𝑜𝑓 𝐵𝑢𝑑𝑔𝑒𝑡 𝐿𝑖𝑛𝑒

ii.

Second condition or sufficient condition is that the indifference curve of the consumer be convex to the origin. In other words, the MRS along any indifference curve must be diminishing. Graphically, convexity of indifference curve is simple to guess but mathematically, we have to calculate the MRS and check whether it is diminishing or not.

The Budget Line (Budget Constraint): While assuming rational behavior of the consumer, we stated that the consumer is aware of the market prices of the goods and his income. The consumer utility maximizing behavior is put under constraint by the budget line or budget constraint. The income that the consumer possesses is limited that is why it is called budget constraint. Budget line is an equation written as: 𝑌 = 𝑃𝑥𝑄𝑥 + 𝑃𝑦𝑄𝑦 Once we have the data on the above variables, we can draw budget line on the graph as: Assume that Qx = 0 and solve the equation for Qy 𝑌 = 𝑃𝑥 × 0 + 𝑃𝑦𝑄𝑦 𝑌 = 0 + 𝑃𝑦𝑄𝑦

𝑄𝑦 =

𝑌 … (𝑖) 𝑃𝑦

Equation (i) shows the total quantity of Y that the consumer can buy if he spends all of his income on good Y. The value of Qy gives us one point on the vertical axis or Y-axis. Assume that Qy = 0 and solve the equation for Qx to get another point for horizontal axis or Xaxis 𝑌 = 𝑃𝑥𝑄𝑥 + 𝑃𝑦 × 0 𝑌 = 𝑃𝑥𝑄𝑥 + 0 𝑄𝑥 =

𝑌 … (𝑖𝑖) 𝑃𝑥

Equation (ii) shows the total quantity of Qx that the consumer can buy if he spends all of his income on good X. This gives us another point for the X-axis. Plotting and joining both points on the graph, we get budget line. Let’s plot these points and join them:

Y

𝑌 A 𝑃𝑦 𝑌 = 𝑃𝑥𝑄𝑥 + 𝑃𝑦𝑄𝑦

B 𝑌 𝑃𝑥

X

So, we get a budget line by joining the point A and B. The line acts like a constraint, this is consumer’s purchasing power. He is not able to bundles which lie outside that line.

Slope of Budget Line: In order to fulfill the first condition, we need to have the slope of the budget line calculated. Let’s find out: Dividing point, A by B 𝑌 𝑃𝑦 𝑆𝑙𝑜𝑝𝑒 𝑜𝑓 𝐵𝑢𝑑𝑔𝑒𝑡 𝐿𝑖𝑛𝑒 = 𝑌 𝑃𝑥 𝑌 𝑌 𝑃𝑥 𝑌 ÷ = × 𝑃𝑦 𝑃𝑥 𝑃𝑦 𝑌 𝑆𝑙𝑜𝑝𝑒 𝑜𝑓 𝐵𝑢𝑑𝑔𝑒𝑡 𝐿𝑖𝑛𝑒 =

𝑃𝑥 𝑃𝑦

Consumer Equilibrium: Consumer equilibrium is illustrated and explained below with the help of a graph having depicted a partial indifference map and a budget line on it:

Y

A

𝑀𝑅𝑆𝑥,𝑦 = Y∗

𝑃𝑥 𝑃𝑦

E

III II I X∗

B

X

Looking at the above graph, we can see that budget line touches the indifference curve II at point E. This is the point where our first condition for the consumer equilibrium is satisfied. Slope of both indifference curve II and AB budget line is equal. The consumer is buying Y*and X*. This is the highest indifference curve that the consumer can reach with his available income. Indifference curve III is higher than indifference curve II but the consumer's available income does not allow him reach. While, Bundles on indifference curve I are inferior to bundle E. So, the highest curve that the consumer can reach is II, bundles below point E are less than E. Therefore, with respect to the current income, and current prices of X and Y, the consumer has maximized his utility by choosing bundle E....