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*The game referenced in this article is ‘The Tribez‘ offered by Game Insight UAB.

The Example

Consider the following situation:

You currently have one worker remaining to do tasks. You can use that worker to produce either lumber or rocks

Choices Involve Trade-Offs

We previously (“Trade-Offs“) ascertained that trade-offs are the costs associated with choices – the “Con” off-setting the “Pro”.

Scarce resources always involve trade-offs as the quantity is too limited to satisfy all needs. The same one dollar cannot purchase both food and a motorcycle at the same time for the same buyer.

Definition of an Opportunity Cost

Where resources are involved in a trade-off, we must consider the Opportunity Cost. These are the potential uses of a resource that are sacrificed in the decision made. In mathematical terms, the opportunity cost is calculated as the value lost from sacrificing the second-best alternative use of the resource.

Opportunity Costs are the value lost from sacrificing the opportunity to accomplish the second-best alternative use of the resource.

When using a resource for one purpose, we sacrifice all alternative uses for that resource. $1.00 can either to be spent on 2 candies (A) or 1 cola (B). If you buy two candies, you sacrifice a cola (Opportunity Cost of A). If you buy one cola, you sacrifice two candies (Opportunity Cost of B).

Theoretically there may be unlimited potential alternative uses ($1.00 could also buy a ticket to Hong Kong or purchase a new dress or buy a video game). But the only one that truly matters is the second-best alternative.

Practice (A)

You are deciding how best to use one chicken breast for dinner. The alternatives include: 1) Chicken Soup. 2) Chicken Parmesan. 3) Fajitas.

After careful assessment, you rank your uses of the chicken breast as follows in order of preference:

1. Fajitas
2. Chicken Soup
3. Parmesan

In choosing to use the chicken breast for Fajitas, what was your opportunity cost? The second-best alternative use – Chicken Soup is the opportunity cost. Parmesan was never really going to happen and can be disregarded.

The Math Behind the Theory

In the example at the beginning of this article, the worker (a resource) had two alternative uses: contributing labor to lumber or rocks. He cannot accomplish both simultaneously (our resource is scarce). It is the economists job to determine which is the better use.

A Trade-off is determined through the following basic formula:

Pro – Con = Result

Trade-Off Formula

If Positive (+) results occur, the trade-off is worth the cost.
If Negative (-) results occur, the trade-off is not worth the cost.

Practice

Assume you are currently working 10 hours a day in exchange for a salary of $150.00. A new company offers you a new job working the same 10 hours a day in exchange for $140.00. Should you change jobs?

$140.00 – $150.00 = -$10.00 (not worth the cost)
+ Pro – Con = Result

Trade-Off Formula

Another way to write this formula when choosing between two alternative uses of a resource is:

Opportunity Benefit – Opportunity Cost = Opportunity Result

Trade-Off Formula for Resource Utilization

Opportunity result is positive (+) ~ this use of the resource is worth the cost.
Opportunity result is negative (-) ~ this use of the resource is not worth the cost.

(Example)

We hire the worker to produce lumber (Opportunity A). Was this a fair decision?

Opportunity Benefit – 25 Lumber
Opportunity Cost – The rocks he failed to produce. By producing 25 lumber, our resource (worker) failed to be used in producing 40 rocks**.

**20 rocks only requires 15 minutes. In the same time to produce 25 lumber (30 minutes), he could have produced 40 rocks.

+ 25 Lumber – 40 Rocks = ? Result

Trade-Off Formula

The answer hard to determine. Lumber and Rocks are two different resources – it’s like asking is 25X is better or worse than 40Y.

To allow for simpler comparison, economists and businesses generally apply financial interpretations of the results by comparing the profits of opportunity A and B.

Assume one lumber sells for 15 coins in the market. One rock would sell for 5 coins.

Rewritten:

+ 25 Lumber – 40 Rocks = ? Result
(+25 Lumber x $15.00) – (40 Rocks x $5.00) = +$175.00

Trade-Off Formula

At least in this scenario, producing the 25 lumber was the better financial decision because the result was positive.

Practice

You are given 100 yards of Ribbon.

From these details, we can infer:

1. 100 Yards of Ribbon will produce 50 Hair Bows.
2. 50 Hair Bows have a potential profit of $2.00 x 50Q = $100.00
3. 100 Yards of Ribbon will produce 33.33 Dress Ties.
4. 33.33 Dress Ties have a potential profit of $3.50 x 33.33Q = $116.66

	Opportunity Benefit	Opportunity Cost	Opportunity Result
Opportunity A	50Q (bows) $100.00	33.33Q (ties) $116.66	+16.67Q -$16.66
Opportunity B	33.33Q (ties) $116.66	50Q (bows) $100.00	-16.67Q +$16.66

Numerically (in terms of quantity of goods produced), Opportunity A is better. We would receive 16.67 more products to sell. But Financially, Opportunity B is better. We would receive $16.66 more in profits.

Most companies would focus on the financial results as profits are far more significant than the number of goods we produce.

Marginal v. Total

There are two other ways to consider opportunity costs – from the total or overall perspective (looking at the results of all goods produced) or from the marginal perspective (looking at the results of each unit produced – 1Q).

It is important to take note because economics courses vary on which perspective you need at any given time. Read carefully and ensure you are aware of which perspective your professor wishes you to use.

The Total Perspective:

The Total Opportunity Cost of 50 Hair Bows is 33.33 Dress Ties.
The Total Opportunity Cost of 33.33 Dress Ties is 50 Hair Bows.

The Marginal Perspective:

The Marginal Opportunity Cost of 1 Hair Bow is (50H / 33.33D) = 0.66 Dress Ties. In theory, by making one hair bow, you sacrifice the opportunity to produce 0.66 Dress Ties.
The Marginal Opportunity Cost of 1 Dress Tie is (33.33D / 50H) = 1.50 Hair Bows.

From a numerical perspective it appears it is better to make Hair Bows since we only lose 0.66 Dress Ties compared to 1.50 Hair Bows per Dress TIe.

From a financial perspective: Benefit – Cost = Result

Financial Perspective	Opportunity Benefit	Opportunity Cost	Opportunity Result
Opportunity A Total Marginal	50Q (bows) $100.00 $2.00	33.33Q (ties) $116.66 $2.31*	+16.67Q -$16.66 -$0.31
Opportunity B Total Marginal	33.33Q (ties) $116.66 $3.50	50Q (bows) $100.00 $3.00**	-16.67Q +$16.66 +$0.50

From the financial perspective, it is better to produce hair bows and sacrifice the Headbands. This is true no matter whether you look at the total or marginal perspectives; sometimes you will need to use one, sometimes the other.

Incentive	Those things that motivate one to choose Option A.
Trade-Off	The costs associated with making a decision, occurring where a choice has a resulting sacrifice required.
Opportunity Cost	The value lost from sacrificing the second-best alternative use of the resource.
Opportunity Benefit	The value gained for choosing this particular use of the resource
Opportunity Result	The overall result of the choice made balancing all parts of the trade-off
Profits	Revenue – Cost = Profit The money the owners make from a transaction in the end.
Marginal	To study from the perspective of increasing or decreasing quantity by one unit.

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