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Optimal Choice Of The Consumer

Determine the utility-maximizing bundle where the indifference curve is tangent to the budget line.

7 micro-lessons

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Bringing It Together: The Best Affordable Bundle

Hook uniting preferences and budget.

We know what the consumer likes (represented by their Indifference Map) and we know what they can afford (represented by the Budget Line). The ultimate problem of choice is putting these two together to find the optimal combination.

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The Point of Tangency

Consumer optimum bundle.

Coordinate graph showing quantity of bananas on the horizontal axis and mangoes on the vertical axis. A downward-sloping straight black budget line represents affordable combinations. Three convex-to-origin indifference curves are shown. The lowest curve (blue) intersects the budget line twice. The middle curve (black) is perfectly tangent to the budget line at a single marked point (x1*, x2*). The highest curve (grey) lies entirely above the budget line.

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The consumer's optimum bundle is located at the exact point where the budget line is tangent to the highest affordable indifference curve.

The Tangency Condition

Formal statement of the optimality condition.

MRS = \frac{p _{1}}{p _{2}}

Symbol Legend

$MRS$ : Marginal Rate of Substitution (Absolute slope of Indifference Curve)
$p_{1}$ : Price of Good 1
$p_{2}$ : Price of Good 2
$\frac{p _{1}}{p _{2}}$ : Price Ratio (Absolute slope of Budget Line)

Meaning in Practice

At the optimum bundle, the rate at which the consumer is willing to substitute one good for another internally exactly matches the rate at which the market allows them to substitute the goods externally.

When MRS does not equal Price Ratio

Step-by-step logic proving why a non-tangent point is suboptimal.

Problem. Suppose the Marginal Rate of Substitution (MRS) at a certain bundle is $2$ , and the two goods (bananas and mangoes) have the exact same market price, making the price ratio $\frac{p_1}{p_2} = 1$ .

Let's prove why this bundle cannot be the optimal choice.

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Practice: Evaluating Optimality

Guided problem evaluating if a given bundle is optimal.

Evaluate whether the consumer's current consumption bundle is optimal using the tangency condition.

Suppose the price of Good X (bananas) is Rs 10 ( $p_1 = 10$ ) and the price of Good Y (mangoes) is Rs 5 ( $p_2 = 5$ ). At the consumer's current bundle A, their Marginal Rate of Substitution ( $MRS$ ) is $3$ .

Follow the steps below to evaluate this choice.

State the given values

Identify the prices and the current MRS from the problem statement.

State the Optimality Condition formula

What equation must hold true for a bundle to be optimal?

Calculate the Price Ratio

Substitute the prices into the ratio formula to find the market rate of substitution.

Compare MRS to the Price Ratio

How does the consumer's willingness to substitute compare to the market's rate?

Final Conclusion

State if the bundle is optimal. If not, should they consume more Good X (bananas) or more Good Y (mangoes)?

Recall: Optimality Condition

Recall the equality required for optimal choice.

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