Unit 1 · Topic 1.6

Marginal Analysis and Consumer Choice

Marginal analysis compares the extra benefit of one more unit with its extra cost: keep going while the marginal benefit is at least the marginal cost.

Practice 2: Interpretation

Part 1 · Hook

Why this matters

Leo has $12 for lunch at a food festival. Tacos are $2 and smoothies are $4. The first smoothie is great; the third is fine; a fifth taco would barely register. He does not need a formula to feel this, but the exam asks for one: spend each dollar where it adds the most satisfaction, and stop when one more unit adds less than it costs.

Part 2 · Before you start

What this builds on

Part 3 · Prerequisite check

Quick check before you start

1. Net benefit is

  1. total benefit minus the total cost
  2. total benefit plus the total cost
  3. the largest total benefit
  4. explicit costs plus implicit costs
Show the answer

Subtract every cost from the benefit.

  • Correct: total benefit minus the total cost:
  • total benefit plus the total cost:
  • the largest total benefit:
  • explicit costs plus implicit costs:

2. Jamal's net benefit is $45 at 3 lessons and $40 at 4. Taking the fourth lesson

  1. adds more to cost than to benefit
  2. adds more to benefit than to cost
  3. leaves net benefit unchanged
  4. has no cost
Show the answer

Net benefit falls, so the extra cost is larger.

  • Correct: adds more to cost than to benefit:
  • adds more to benefit than to cost:
  • leaves net benefit unchanged:
  • has no cost:

Part 4 · See it

See it first

A marginal utility table for tacos ($2) and smoothies ($4) with a $12 budget; the best bundle, 2 tacos and 2 smoothies, equalizes marginal utility per dollar at 8 and gives total utility 116.
Leo's marginal utility for tacos ($2) and smoothies ($4), and per dollar. With $12, the best bundle is 2 tacos and 2 smoothies: the last of each gives 8 per dollar, and total utility is 116. Invented data for practice. LevlPrep original diagram.

Part 5 · Step by step

How it works, step by step

  1. A consumer eats more units of a goodeach extra unit adds less satisfaction than the one before (diminishing marginal utility)
  2. Goods have different pricesthe consumer compares marginal utility per dollar, MU ÷ P, not marginal utility alone
  3. One good gives more utility per dollar than anothermoving a dollar toward it raises total utility
  4. The budget is spent and MU per dollar is equal across goodsno move can raise total utility: the consumer has the utility-maximizing bundle

Part 6 · Key ideas

Key ideas

  • Marginal analysis: decide one more unit at a time. Do one more unit when its marginal benefit is at least its marginal cost (MC), the extra cost of that unit; stop when it is less.
  • Utility is satisfaction. Marginal utility (MU) is the extra utility from one more unit, and it usually falls as you consume more: diminishing marginal utility.
  • Utility-maximizing rule: spend the whole budget so that MUXPX\frac{\text{MU}_X}{P_X}=MUYPY= \frac{\text{MU}_Y}{P_Y}. Buy each next unit where MU per dollar is highest.
  • The budget constraint limits the bundles a consumer can afford: spending on all goods cannot exceed income.
  • A sunk cost is already spent and cannot be recovered. It is the same whatever you choose next, so it never changes the best choice.

Part 7 · Misconception

A common mistake

The wrong idea: Leo should buy smoothies first and keep buying them, because each smoothie gives more utility than any taco.

What actually happens: Smoothies cost twice as much. Compare MU per dollar: the first smoothie gives 12 per dollar, but the second gives 8, the same as the second taco. With $12 the best bundle is 2 tacos and 2 smoothies (total utility 116), not 3 smoothies (104).

Part 8 · Check yourself

Check yourself

Exam-style questions. Anything you miss goes into your review queue.

1. What is marginal utility?

  1. The total satisfaction from the units consumed so far
  2. The price of one more unit
  3. The extra satisfaction from one more unit
  4. The satisfaction per dollar of income
Show the answer

Marginal means one more. Marginal utility is the change in total utility from one more unit.

  • The total satisfaction from the units consumed so far: That is total utility.
  • The price of one more unit: Price is a cost, not a utility.
  • Correct: The extra satisfaction from one more unit: Right: the extra utility of one more unit.
  • The satisfaction per dollar of income: Utility per dollar is MU divided by the price of the good.

Data

A student choosing between two goods with a budget: marginal utility per dollar

Leo's marginal utility (utils) from each taco ($2 each) and each smoothie ($4 each); he has $12 (invented data for practice)
UnitMU of tacosMU of smoothies
1st2048
2nd1632
3rd1224
4th816
5th4

2. What is Leo's marginal utility per dollar from his second smoothie?

Type a number. A four-function calculator is allowed, as on the exam.

Show the answer

MUP=324=8\frac{\text{MU}}{P} = \frac{32}{4} = 8 utils per dollar.

  • Answer: 8

3. Leo spends his whole $12. Which bundle maximizes his total utility?

  1. 3 smoothies
  2. 6 tacos
  3. 4 tacos and 1 smoothie
  4. 2 tacos, 2 smoothies
Show the answer

At 2 tacos and 2 smoothies he spends 2×2+2×4=122 \times 2 + 2 \times 4 = 12 dollars and the last of each gives 8 per dollar. Total utility is 20+16+48+32=11620 + 16 + 48 + 32 = 116.

  • 3 smoothies: 3 smoothies give 104 utils; the third gives only 6 per dollar while a taco gives 10.
  • 6 tacos: The table stops at 5 tacos, and tacos alone give at most 60 utils.
  • 4 tacos and 1 smoothie: This gives 104 utils; the 4th taco gives 4 per dollar while the 2nd smoothie gives 8.
  • Correct: 2 tacos, 2 smoothies: Right: equal MU per dollar, budget spent, 116 utils.

Data

How many pizza slices?

The most Nadia would pay for each slice of pizza, in order (invented data for practice); a slice costs $2.50
SliceMarginal benefit ($)
1st5.00
2nd4.00
3rd3.00
4th2.00
5th1.00

4. A slice costs $2.50. How many slices should Nadia buy?

  1. 5
  2. 3
  3. 4
  4. 2
Show the answer

Buy a slice while its marginal benefit is at least its $2.50 cost. The 3rd slice is worth $3.00; the 4th only $2.00.

  • 5: The 4th and 5th slices are worth less than $2.50.
  • Correct: 3: Right: the 4th slice is worth less than it costs.
  • 4: The 4th slice is worth $2.00, less than its $2.50 cost.
  • 2: The 3rd slice is still worth $3.00, more than it costs.

Scenario

Pellham Games and its unfinished game

Pellham Games, an invented studio, has already spent $200,000 building a new game, money it cannot get back. Finishing the game would cost another $50,000. The studio expects to take in $80,000 from sales once the game is finished. A manager says, "We have spent so much that we cannot quit now," and another says, "We will never earn back the $200,000, so we should stop."

5. Should Pellham Games finish the game, and why?

  1. No: it will not earn back the $200,000
  2. Yes: it has spent $200,000 and has to finish
  3. Yes: $80,000 more sales for $50,000 more cost
  4. No: $80,000 is less than $250,000
Show the answer

Only the costs and benefits still ahead matter. Finishing brings $80,000 and costs $50,000, so it adds $30,000. The $200,000 is sunk either way.

  • No: it will not earn back the $200,000: The $200,000 is gone whether or not the game is finished, so it does not count.
  • Yes: it has spent $200,000 and has to finish: The right answer, but for the wrong reason: past spending is not a reason to continue.
  • Correct: Yes: $80,000 more sales for $50,000 more cost: Right: $80,000 more benefit against $50,000 more cost.
  • No: $80,000 is less than $250,000: $250,000 adds the sunk $200,000 to the cost still ahead.

Part 9 · Summary

Summary

Marginal analysis compares the extra benefit of one more unit with its extra cost: keep going while the marginal benefit is at least the marginal cost. Consumers get utility from goods, and marginal utility usually diminishes as they consume more. With a budget, a consumer maximizes total utility by buying the next unit with the highest marginal utility per dollar until the budget is spent and MU ÷ P is equal across goods. Sunk costs are already paid whatever you choose, so they never change the best decision.

Part 10 · Up next

What comes next

Part 11 · Connections

Connections

Question set for this topic