Opportunity cost when money is scarce

Turning a price into a cost: how many of the other thing one of this thing takes, and why that number does not depend on the size of the budget.

Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.

1. What you will learn

You will take a budget and two prices in dollars and say exactly what one purchase costs, counted in the other good. You will also be able to say how many of each the budget buys, why that is a different number from the rate, and why the money paid is not by itself the opportunity cost.

2. Starting point

Use the stated alternatives, quantities and units. Separate a model's assumptions from the conclusion derived from them.

3. Terms to use precisely

4. A budget is a constraint on combinations

A budget states how much money is available for a specified set of purchases. A price states how much money one unit of a good requires. Together they determine which combinations can be afforded. If a notebook costs three dollars and a folder costs two, two notebooks and three folders require twelve dollars. The calculation multiplies each price by its quantity, then adds the expenditures because they use the same budget.

Do not confuse a budget with an instruction to spend every dollar. A feasible plan can leave money unspent. Keeping money available for later can itself be an alternative use, depending on the decision. In a simple two-good exercise, the prompt may ask about combinations that spend the entire budget, or it may ask about every affordable combination. Those are different sets. Read whether the budget is an upper limit or an equality condition.

The exercise assumes fixed prices, no borrowing, and no additional charges unless stated. These assumptions allow a definite calculation. Discounts, delivery fees, taxes, minimum purchases, or credit would change the feasible combinations if introduced. We do not infer such details from real shops; the stated classroom prices define the model. A good answer identifies the units and uses exactly the conditions supplied.

Write the spending rule in words before calculating: price of A times quantity of A, plus price of B times quantity of B, must not exceed the available budget. This rule is a resource account. It does not tell us which affordable combination the buyer prefers. Preferences are needed to select a best plan from the feasible set, just as the previous lessons needed a ranking of complete alternatives.

Term	What it means
Budget constraint	A limit on total expenditure for the stated choice.
Relative price	One good's price expressed in units of another good through a price ratio.
Affordable bundle	A combination whose expenditure satisfies the budget and other stated conditions.
Indivisible item	A good that the model permits buying only in whole units.
Purchasing power	What a given amount of money can obtain at stated prices.

Another way: The ratio depends on what you are giving up

To express the money cost of one unit of A in units of B, divide A's price by B's price. If A costs six dollars and B costs two, one A uses money that could buy three B. The opportunity-cost rate under this two-good budget comparison is three units of B per A. The dollar units cancel, leaving the number of alternative units associated with one chosen unit.

The numerator is not always the larger price. It is the price of the good whose cost you are expressing. If A costs two dollars and B costs eight, one A corresponds to one quarter of a B at the stated prices. The ratio is two divided by eight, or 0.25 B per A. Automatically dividing the larger price by the smaller would answer the reverse question and could produce a confident but incorrect result.

The reverse rate is generally different. If one A costs four B, one B costs a quarter of an A. These rates describe the same relative prices in opposite units. Write the denominator's good in the answer so that the direction is visible. A bare number such as four does not tell a reader which good is given up or which unit is being obtained.

This ratio describes a marginal exchange in purchasing power when quantities can be adjusted at the given prices. If goods must be purchased as whole items, the fraction may not itself be an available shopping action. A quarter of a bicycle is not necessarily a purchasable product. We can still describe the price ratio, while separately checking which whole-item bundles fit the budget. Do not confuse a rate with an instruction that every fractional purchase is feasible.

Another way: Scale the rate and track the remaining money

Once the per-unit rate is known, multiply it by the quantity chosen to find the purchasing power used. At six dollars per A and two dollars per B, four A use twenty-four dollars, equivalent to twelve B. This conclusion assumes unchanged unit prices. If buying several units changes the price, the cost of the whole purchase must be calculated from that pricing rule before comparing alternatives.

A remaining-budget calculation answers another question. With a thirty-dollar budget, buying four A at six dollars leaves six dollars. At two dollars per B, the remaining money buys three B. The twelve B associated with the A purchase and the three B still affordable are different quantities. Together they correspond to the fifteen B that the original thirty dollars could buy if all were spent on B.

That accounting provides a useful check. Under constant prices and divisible quantities, B equivalents used plus B equivalents remaining should equal the original budget measured in B. With indivisible items and leftover money, include the leftover explicitly instead of forcing the quantities to sum as whole units. The budget identity must still hold in dollars even when the goods come only in discrete pieces.

Do not add the twenty-four dollars and the twelve B equivalents as if they were separate sacrifices. They are two descriptions of the same portion of the budget. If another resource, such as travel time, is also used, it requires a distinct comparison. Counting the same money once as dollars and again as goods would exaggerate the cost rather than make the analysis more complete.

Another way: Whole items create useful boundary cases

Suppose a buyer has seventeen dollars and B costs five dollars per whole item. Dividing seventeen by five gives 3.4, but the buyer can purchase only three whole B without borrowing. Three cost fifteen dollars, leaving two. Rounding 3.4 upward to four would make the plan unaffordable. Rounding to the nearest integer also lacks a general justification; affordability requires the greatest whole quantity whose expenditure does not exceed the budget.

This is why the prompt must distinguish a price-ratio question from a maximum-whole-items question. A ratio can legitimately be 3.4 B equivalents per specified expenditure. The maximum count of whole B is three. Neither answer is universally correct without knowing which quantity is requested. Units and wording determine whether a fractional result should be retained or a whole-item constraint applied.

An exact budget boundary can include zero purchases of one good. Spending everything on A or everything on B may be feasible if the quantities and prices permit it. A model should not exclude zero merely because both goods appear in the story. Conversely, a stated minimum requirement can exclude an otherwise affordable corner. The feasible set comes from every stated constraint, not from the budget equation alone.

A price change moves the boundary even if the money budget stays fixed. If B becomes cheaper while A's price stays unchanged, the same expenditure on A corresponds to more B. That does not mean A suddenly uses more dollars; it means the alternative purchasing power has changed. Opportunity cost depends on alternatives, and relative prices provide one concrete way those alternatives can change.

Another way: Separate a budget calculation from a recommendation

A calculation that one A costs three B tells us the trade-off at the stated prices. It does not tell us that A is a bad purchase or that three B must be preferred. A buyer who values A more than the feasible alternative may choose it sensibly under their priorities. The comparison makes the sacrifice visible; preferences and other relevant conditions are needed to evaluate the decision.

Likewise, a cheaper item is not automatically the lower opportunity-cost choice in every meaningful comparison. A unit can differ in size, quality, durability, or the need it serves. This lesson deliberately uses clearly specified units. If one notebook has twice as many usable pages as another, a comparison per notebook and a comparison per page answer different questions. State the unit that matches the task rather than letting a price tag decide the whole analysis.

For each exercise, first name the chosen good and alternative good. Then divide in the correct direction and attach the unit 'alternative units per chosen unit'. Next multiply if several units are chosen. If the task also gives a budget, subtract expenditure and calculate what the remainder can buy under the stated divisibility rule. Check the dollar account independently of the opportunity-cost account.

The final explanation should stay within the supplied model. All prices here are fictional teaching values, not current prices or shopping advice. The transferable skill is to make a budget constraint and its trade-offs explicit, including what the calculation leaves unresolved. That skill applies to a club's materials, a workshop's supplies, or a personal plan without requiring the lesson to recommend what anyone should buy.

5. A makers' club orders materials

A fictional makers' club has forty-eight dollars for this session's materials. One board costs eight dollars and one packet of fasteners costs two. Prices are fixed, there are no additional charges, and the club cannot borrow. A board therefore uses money that could buy four packets of fasteners. The unit is packets per board: eight dollars per board divided by two dollars per packet.

The club proposes buying three boards. That uses twenty-four dollars, corresponding to twelve packets of fasteners forgone under this comparison. Twenty-four dollars remain, enough for twelve packets. The full plan of three boards and twelve packets costs forty-eight dollars. The club's budget account balances, and its purchasing-power account also balances: twelve packets equivalent used on boards plus twelve packets purchased equals the twenty-four packets the original budget could have bought.

If the fastener price falls to one dollar while boards remain eight dollars, the cost of one board becomes eight packets rather than four. Three boards still use twenty-four dollars, but that amount now corresponds to twenty-four packets. The changed opportunity cost comes from the improved alternative purchasing power, not from a higher board price.

Whether three boards is a good plan depends on the club's project requirements and preferences. A cheap supply is not useful merely because many units can be bought, and the ratio alone does not specify the best design. The calculation establishes feasible quantities and a clear trade-off. The club can then compare complete plans using the resources it actually needs, without counting the board expenditure twice.

6. Check the tempting inference

Divide chosen-good price by alternative-good price, not always larger by smaller. A price ratio is not necessarily a feasible fractional purchase. Do not add a cash expenditure and its alternative-goods equivalent as two costs. Affordability does not establish preference or a complete recommendation.

7. A price ratio with units

8. The chosen item is cheaper

9. A whole budget and a changed alternative

10. Finish a materials budget

11. Guided practice

A costs $6, B costs $2, budget $36. Buy four A. Give B per A, dollars remaining and B units affordable with the remainder.

12. Guided practice

13. Guided practice

A costs $3 and B $6; budget $30. Buy four A. Give B per A, dollars remaining and B affordable with the remainder. A fractional price ratio is allowed.

	Your result
B units per A
Dollars remaining
B units affordable with remainder