Allocate a budget with marginal benefit

Allocate a budget with marginal benefit

Question and evidence

Which next purchase offers the most benefit per credit?

A fictional learner has 6 credits. Snacks cost 2 each and have successive marginal benefit scores 12, 8, 2. Drinks cost 1 each and have scores 5, 4, 1. Scores are an authored preference ordering in this exercise, not interpersonal welfare measurements.

This packet uses fictional data to isolate a mechanism. It is not an empirical estimate.

Mechanism and worked example

A budget constraint describes affordable bundles. Marginal utility per price can guide allocation when additional units and prices are comparable, while diminishing marginal benefit explains why another unit may be less valuable. Income changes move the budget line; a relative price change rotates it.

Two snacks and two drinks cost 4+2=6 and yield 12+8+5+4=29. Three snacks cost 6 and yield 22. One snack and three drinks cost 5 and yield 22, with 1 credit unusable for another snack in this packet.

Complication

A comparison simply chooses the product with the largest total package benefit. It ignores prices and the benefit of the next unit. Indivisible purchases can require checking feasible bundles rather than assuming an exact equality condition.

Your investigation

Plot the budget boundary 2S+D=6, list feasible integer bundles within the supplied unit limits, and defend the best bundle without comparing benefit scores across people.

Revise your answer to “Which next purchase offers the most benefit per credit?” using both source IDs. Separate the checked calculation from a judgment, and identify evidence that could reverse your judgment.

Vocabulary

Marginal utility: Additional satisfaction or benefit from one more unit, under a stated preference model.

Assumption: A condition accepted for a model or argument; it needs justification before applying the result elsewhere.

Independent extension

Independently extend the investigation “Allocate a budget with marginal benefit” with a documented real dataset or scholarly source. Preserve definitions, recreate one calculation or evidence table, compare a rival explanation and report why the teaching example cannot establish the real-world conclusion.

Inspect the worked graph

Lines follow the specified linear teaching equations. Axes start at zero. The table identifies every series without relying on color.

Series	Snacks	Drinks
Budget boundary	0	6
Budget boundary	1	4
Budget boundary	2	2
Budget boundary	3	0