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A Consumer Consumes Only Two Goods. Explain Consumer'S Equilibrium with the Help of Utility Analysis. - Economics

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A consumer consumes only two goods. Explain consumer's equilibrium with the help of utility analysis.

A consumer consumes only two goods X and Y. Explain the conditions of consumer’s equilibrium using Marginal Utility Analysis.

A consumer consumes only two goods. Explain the conditions of consumers’ equilibrium using utility analysis.

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Solution

Conditions of consumer’s equilibrium using marginal utility analysis:


When a consumer buys both Goods X and Y, the consumer’s equilibrium condition is expressed through the equation:

`(MU_x)/P_x=(MU_y)/P_y=(MU_m)/P_n=MU_m`

Consider the following numerical example to understand the consumer’s equilibrium using marginal utility. A consumer Marginal Utility of Money (MUm) is 16 utils and two Goods X and Y whose prices are Rs 1 (Px) and Rs 1 (Py) per unit, respectively. Consider the following schedule to analyse the marginal utility of good x (MUx) and good y (MUy).

Units of x

MU x

(Utils)

MU y3

(Utils)

1 28 32
2 24 29
3 21 27
4 20 23
5 16 20
6 13 18
7 9 17
8 5 16
9 3 12
10 1 9

 

Based on the given schedule, the consumer is in equilibrium at the consumption of 5 units of commodity x and 8 units of commodity y. At such a consumption combination, the 

marginal utility of a rupee spent on the commodity `x((MU_x)/P_x)` is equal to the marginal utility of a rupee spent on the commodity `y((MU_y)/P_y)`and also equal to the marginal utility of money (MUm).

Marginal utility of a rupee spent on commodity x = marginal utility of a rupee spent on commodity y = Marginal utility of money

`(MU_x)/P_x=(MU_y)/P_y=MU_m`

 

`(MU_x)/P_x=(MU_y)/P_y=16/1=16=MU_m`

In the diagram, OO1 is the total income of a consumer. MUx and MUy are the marginal utility curves of commodity x and commodity y, respectively.

The consumer does not attain equilibrium at Point L because the point at L is

`(MU_x)/P_x>(MU_y)/P_y`

The consumer does not attain equilibrium at Point R because the point at R is

`(MU_x)/P_x<(MU_y)/P_y`

So, when OF amount of income is spent on commodity x and FO1 amount is spent on commodity y, the consumer is in equilibrium at Point E. Hence, at this point

`(MU_x)/P_x=(MU_y)/P_y=MU_m`

 

Concept: Conditions of Consumer's Equilibrium Using Marginal Utility Analysis
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