Determine the utility-maximizing bundle where the indifference curve is tangent to the budget line.
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.
Consumer optimum bundle.
The consumer's optimum bundle is located at the exact point where the budget line is tangent to the highest affordable indifference curve.
Formal statement of the optimality condition.
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.
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 , and the two goods (bananas and mangoes) have the exact same market price, making the price ratio .
Let's prove why this bundle cannot be the optimal choice.
Guided problem evaluating if a given bundle is optimal.
Suppose the price of Good X (bananas) is Rs 10 () and the price of Good Y (mangoes) is Rs 5 (). At the consumer's current bundle A, their Marginal Rate of Substitution () is .
Follow the steps below to evaluate this choice.
Identify the prices and the current MRS from the problem statement.
What equation must hold true for a bundle to be optimal?
Substitute the prices into the ratio formula to find the market rate of substitution.
How does the consumer's willingness to substitute compare to the market's rate?
State if the bundle is optimal. If not, should they consume more Good X (bananas) or more Good Y (mangoes)?
Recall the equality required for optimal choice.