How to Find Consumer Equilibrium
Consumer equilibrium is the bundle where MUx ÷ Px = MUy ÷ Py and the whole budget is spent, so no reallocation raises total utility.
The Consumer Equilibrium formula
Calculator
Check a bundle for equilibrium: equal marginal utility per dollar across goods with the whole budget spent.
The worked example gives the student $30.
Notebooks at $5 in the worked example.
4 notebooks at the equilibrium bundle.
MUx at this bundle. The fourth notebook is worth 45 utils.
Pens at $2 in the worked example.
5 pens at the equilibrium bundle.
MUy at this bundle. The fifth pen is worth 18 utils.
Both goods return 9 utils per dollar, so no reallocation raises utility and the budget is fully spent, which is consumer equilibrium.
- Marginal utility per dollar, good X
- 9
- Marginal utility per dollar, good Y
- 9
- Cost of the bundle
- $30
- Income left unspent
- $0
The last dollar put into good X returns 9 utils.
The last dollar put into good Y returns 9 utils.
This bundle costs $30 out of an income of $30.
Nothing is left over, so the budget condition holds.
How to calculate Consumer Equilibrium, step by step
- 1Compute MU per dollar for every good. Divide each good's marginal utility by its price to get utils per dollar.
- 2Shift spending toward the higher ratio. Move dollars into the good with the larger MU ÷ P, which raises total utility without costing more.
- 3Update the ratios. Buying more of a good lowers its marginal utility, so recalculate MU ÷ P after every shift.
- 4Check both conditions. Stop at the bundle where MUx ÷ Px = MUy ÷ Py and PxQx + PyQy = Income, since both must hold together.
Worked example: Consumer Equilibrium
A student has $30, notebooks cost $5 and pens cost $2. At 2 notebooks and 10 pens the bundle costs (2 × $5) + (10 × $2) = $30, but MU per dollar is 70 ÷ 5 = 14 for notebooks and only 12 ÷ 2 = 6 for pens, so shifting money into notebooks raises utility. At 4 notebooks and 5 pens the cost is (4 × $5) + (5 × $2) = $30 and the ratios match at 45 ÷ 5 = 9 and 18 ÷ 2 = 9, so that bundle is the consumer equilibrium.
Consumer Equilibrium questions
How is consumer equilibrium different from the utility-maximizing rule?
They describe the same outcome from two angles: consumer equilibrium is the bundle itself, and the utility-maximizing rule is the test you apply to find it.
What pushes a consumer back to equilibrium after a price change?
A price change alters MU ÷ P for that good, so the consumer buys more or less of it until diminishing marginal utility brings the two ratios back into line.
Does consumer equilibrium mean the consumer is satisfied?
It only means no reallocation of the current budget can raise total utility. A larger income would still leave the consumer better off.
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