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Scarcity, Choice and Opportunity Cost: Question 2

Syllabus 1.1, 1.2

Structured AS 8 marks

A family farm has 100 hectares of land, all currently planted with maize, which generates revenue of $400 per hectare per year. A local agribusiness has offered a guaranteed contract to buy sugarcane at a price that would generate revenue of $550 per hectare per year.

Converting a hectare of land from maize to sugarcane requires irrigation work that must be paid for as a one-off cost in the first year only. Because the plots nearest the farm's existing water source can be converted most cheaply, this one-off conversion cost rises for each additional hectare converted, as shown in Table 1. In deciding how much land, if any, to reallocate, the family is answering the basic economic question of what to produce, one hectare at a time. That is, at the margin.

Table 1: cost and revenue of converting land from maize to sugarcane

Additional hectare converted Sugarcane revenue per hectare ($/year) Opportunity cost of maize forgone per hectare ($/year) One-off conversion cost per hectare ($, year 1 only)
1st 550 400 120
2nd 550 400 140
3rd 550 400 160
4th 550 400 180

(a) Using Table 1, calculate the net benefit, in the first year, of converting the 1st hectare of land from maize to sugarcane. Show your working. [2]

(b) Using Table 1, determine, at the margin, the total number of hectares the family should convert from maize to sugarcane in the first year in order to maximise its net benefit. Show your working for every hectare in the table. [4]

(c) Explain why the opportunity cost of maize forgone remains constant at $400 per hectare for every hectare converted, whereas the one-off conversion cost rises for each additional hectare converted. [2]

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Worked solution

Part (a): Net benefit of converting the 1st hectare

Converting one hectare from maize to sugarcane brings in $550 of sugarcane revenue, but it means giving up the $400 of maize revenue that hectare would otherwise have earned (the opportunity cost), and it costs $120 in one-off irrigation work in year 1. The net benefit is: 550−400−120=30550-400-120=30

So converting the 1st hectare gives a net benefit of $30 in the first year.

Part (b): How many hectares to convert, at the margin

The rule for a marginal decision like this is to keep reallocating land as long as converting the next hectare still adds a positive net benefit, and to stop once a hectare’s own net benefit turns negative. Working out the net benefit of each hectare in turn, using net benefit=550−400−conversion cost\text{net benefit}=550-400-\text{conversion cost}:

  • 1st hectare: 550−400−120=30550-400-120=30, positive, so convert.
  • 2nd hectare: 550−400−140=10550-400-140=10, still positive, so convert.
  • 3rd hectare: 550−400−160=−10550-400-160=-10. Negative, so do not convert.
  • 4th hectare: 550−400−180=−30550-400-180=-30. Negative, so do not convert.

Checking the pattern independently: sugarcane revenue ($550) and the opportunity cost of maize ($400) are unchanged across all four rows, so the net benefit falls by exactly the same $20 step each time the conversion cost rises by $20, from $30, to $10, to $-10, to $-30. This confirms the net benefit turns negative between the 2nd and 3rd hectares.

Since the 1st and 2nd hectares each still make a positive net benefit on their own, while the 3rd and 4th would each make a loss, the family should convert exactly 2 hectares in the first year to maximise its total net benefit (a combined net benefit of 30+10=4030+10=40 dollars).

Part (c): Why one cost stays constant and the other rises

The opportunity cost of maize forgone is the maize revenue given up by taking a hectare out of maize production. Because every hectare of the farm’s land is treated as equally productive for maize, giving up any one hectare always sacrifices the same $400 of maize revenue. This figure depends only on the land’s maize-growing capability, not on how many hectares have already been converted.

The one-off conversion cost, by contrast, depends on which hectare is being converted. The hectares closest to the farm’s existing water source are cheapest to connect to irrigation, so they are converted first, at $120. Each further hectare converted lies progressively further from the water source, so it needs more extensive (and more expensive) irrigation work, which is why the conversion cost rises hectare by hectare while the opportunity cost of maize does not.

Final answers

  • (a) Net benefit of the 1st hectare == $30
  • (b) The family should convert 2 hectares (net benefits of +$30 and +$10); the 3rd and 4th hectares would each make a loss
  • (c) The opportunity cost of maize is constant because every hectare produces the same maize revenue; the conversion cost rises because hectares further from the water source cost more to irrigate