MGEA02H3 Chap.1 Production Possibilities and Opportunity Cost
Production Possibilities and Opportunity Cost
One curve for scarcity and choice
The first topic of the course uses the production possibilities frontier to make scarcity, efficiency and trade-offs concrete. Points on the frontier are efficient, points inside it waste resources, and points beyond it cannot be produced with current resources and technology.
The opportunity cost of good X is minus the slope of the frontier, and the cost of Y is its reciprocal.
Why the curve bows outward
When resources are better suited to one good than the other, moving them between sectors gets more expensive as specialisation deepens, so a bowed-out frontier shows increasing opportunity cost.
Past tests ask for the cost at a stated point, the classification of a bundle and the value-maximising point when the two goods have prices.
What the answer keys reward
The course keys for frontier questions write minus dY/dX, evaluate it at the stated output and invert it when the cost of the other good is asked.
For classification items they substitute X into the frontier and compare the resulting Y with the bundle before saying anything about cost, and they give zero as the opportunity cost of a point inside the frontier.
Value-maximisation items are marked on the substitution and the first-order condition, not on a drawn tangency alone.
How this topic connects to later chapters
The frontier returns at the end of the course, when comparative advantage compares two countries’ opportunity costs and shows that specialisation moves the world beyond what each could produce alone.
Its slope reappears as a price ratio whenever a value-maximising choice is made, and the idea that every cost is an opportunity cost underlies the economic profit used for firms in chapters 6 and 7.
What this chapter covers
- 01
Efficient, inefficient and unattainable bundles
- 02
Opportunity cost as minus the frontier slope
- 03
Increasing opportunity cost on a bowed-out frontier
- 04
Constant cost on a linear frontier
- 05
Value-maximising output at given prices
- 06
Shifts and pivots after technical change
Worked example · free
Opportunity cost at three points on a bowed-out frontier
- 2Differentiate: dY/dX = −0.016X, so the cost of X is 0.016X units of Y.
- 2Substitute: 0.4, 0.8 and 1.2 units of Y at X = 25, 50 and 75.
- 2At X = 40 the frontier allows Y = 67.2, so (40, 40) is inside and inefficient.
Key terms
- Production Possibilities Frontier
- The production possibilities frontier is the boundary of the largest combinations of two goods an economy can make with fixed resources and technology.
- Opportunity Cost
- Opportunity cost is the value of the next best alternative given up, measured on a frontier as units of one good sacrificed for one more of the other.
- Increasing Opportunity Cost
- Increasing opportunity cost means each extra unit of a good requires giving up more of the other, which makes the frontier bow outward.
- Productive Efficiency
- Productive efficiency is producing on the frontier, where no output can rise without another falling.
- Attainable Set
- The attainable set is every combination of the two goods on or inside the frontier.
Production Possibilities and Opportunity Cost FAQ
Why is the opportunity cost zero at a point inside the frontier?
Inside the frontier some resources are idle or poorly used, so output of one good can rise without reducing the other. Nothing has to be sacrificed until the economy reaches the frontier, which is why a slope should not be quoted for an inside point.
How do I get the opportunity cost of Y from the cost of X?
Take the reciprocal. If one more X costs 0.8 units of Y, then one more Y costs 1 ÷ 0.8 = 1.25 units of X at that point, because the two costs describe the same trade-off in opposite directions.
Which point maximises the value of output?
Substitute the frontier into the value function, differentiate with respect to X and set the result to zero. At the optimum the opportunity cost of X equals the ratio of the price of X to the price of Y.
What does a pivot of the frontier mean?
A pivot happens when technology improves in one good only. The intercept on that good’s axis moves out while the other intercept stays put, so the opportunity cost of the improved good falls and the cost of the other good rises, even though nothing changed in its own production.
Exam move
Draw the frontier, mark one point on it, one inside and one beyond it, and write the verdict for each. Then differentiate a new frontier equation and evaluate the cost of X at two outputs to confirm whether it rises. For the final, also practise reading a policy statement as a movement on the frontier, such as a claim of more of both goods without sacrifice, which only makes sense from a point inside it.
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