Q.A farmer has 10 hours of labour time available each day, which he can devote entirely to growing wheat or entirely to growing vegetables. Working at his usual pace, he can produce 50 kg of wheat in 10 hours, or 100 kg of vegetables in 10 hours. If he shifts 2 hours of his labour time away from vegetables and into wheat (assume his rate of output per hour stays the same for each crop), how many extra kg of wheat does he gain, how many kg of vegetables does he lose, and what is the opportunity cost of the extra wheat, expressed in kg of vegetables per kg of wheat?

This is a direct application of opportunity cost — first find the farmer's output rate per hour for each crop, then work out what shifting 2 hours between crops gains and loses.

Wheat rate $=\dfrac{50}{10}=5$ kg/hr; Vegetable rate $=\dfrac{100}{10}=10$ kg/hr. Shifting 2 hours to wheat: gain $=2\times5=10$ kg wheat; loss $=2\times10=20$ kg vegetables. Opportunity cost $=\dfrac{20}{10}=2$ kg vegetables per kg wheat.

The farmer's output rate per hour for each crop can be found by dividing his 10-hour total output by 10 hours:

If he shifts 2 hours of labour time away from vegetables and into wheat, the extra wheat he gains from those 2 hours is:

And the vegetables he no longer produces in those same 2 hours (since the hours can only be spent on one crop at a time) is:

The opportunity cost of the 10 extra kg of wheat is therefore the 20 kg of vegetables forgone. Expressed per unit, the opportunity cost of producing 1 kg of wheat is:

This is exactly the trade-off idea behind the Production Possibility Curve studied later in this chapter — producing more of one good, using the same limited resources, always means producing less of the other.

A common slip is comparing the wrong totals — for instance, dividing the full 100 kg or 50 kg by 2 hours instead of first finding the correct per-hour rate from the full 10-hour output, which would badly overstate both the gain and the loss.