Lesson preview · Consumer Optimization
The Tangency Condition
~6 min · Free to read
Two tools combine here: indifference curves (what the consumer wants) and the budget line (what the consumer can afford). The consumer’s goal is to reach the highest indifference curve that still touches the budget line. That optimal point occurs where an indifference curve is tangent to the budget line.
Key Term
Tangency Condition (Utility Maximization)
At the optimal bundle, the slope of the indifference curve equals the slope of the budget line:
The marginal rate of substitution (how much Y the consumer is willing to give up for one more X) equals the price ratio (how much Y the consumer has to give up in the market). Marginal benefit = marginal cost.
The tangency condition. Equivalently: — the marginal utility per dollar is equalized across goods.
Why does tangency maximize utility? If , the consumer values good more than the market charges for it — they should buy more and less , sliding along the budget line until falls to the price ratio. If , the reverse applies. Only at tangency is there no beneficial reallocation left.
Graphically, the consumer starts at any point on the budget line and asks: “Can I reach a higher indifference curve by moving along the line?” They keep moving until the indifference curve just barely touches (is tangent to) the budget line. At that point, there’s no way to increase utility without exceeding the budget.
Check yourself · no marks
At a consumer’s current bundle, utils per dollar and utils per dollar. Should the consumer buy more X or more Y?
Commit to one first. Guessing and being wrong beats reading the answer cold.
Worked Example
A consumer has utility , income , , . Find the optimal bundle.
Practice · 1 / 4
At the optimal bundle, what is equal across all goods?
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