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.
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`
