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Difficulty: Very hardOpportunity Cost

A commercial farm in Kaduna operates with fixed total resources of 1010 hectares of arable land and 120120 worker-hours of labor per day. Producing 11 ton of maize requires 11 hectare of land and 1212 worker-hours of labor. Producing 11 ton of yams requires 0.50.5 hectares of land and 2020 worker-hours of labor. Initially, the farm devotes all its resources to maximize maize production, harvesting 1010 tons of maize per day. If the farm owner decides to reallocate resources to produce 33 tons of yams per day, what is the opportunity cost of this decision expressed in tons of maize foregone?

Answer: 5 tons of maize

Answer

The opportunity cost of producing 3 tons of yams is 5 tons of maize.
Producing 3 tons of yams absorbs 60 worker-hours out of the total 120 worker-hours available. The remaining 60 worker-hours can only produce 5 tons of maize. Since initial maize production was 10 tons, the farm gives up 5 tons of maize (10 - 5 = 5 tons).

Step-by-Step Solution

1
Calculate resources consumed by the production of 3 tons of yams.
Land consumed = 3×0.5=1.53 \times 0.5 = 1.5 hectares. Labor consumed = 3×20=603 \times 20 = 60 worker-hours.
Opportunity cost depends on the amount of productive inputs diverted away from maize production.
2
Determine the remaining inputs available for maize production.
Remaining land = 10−1.5=8.510 - 1.5 = 8.5 hectares. Remaining labor = 120−60=60120 - 60 = 60 worker-hours.
Maize can only be produced using the unallocated land and labor inputs.
3
Identify the binding constraint for maize output.
Labor restricts maize output to 6012=5\frac{60}{12} = 5 tons (since land would permit 8.58.5 tons). Thus, maximum feasible maize output is 55 tons.
Production is restricted by the scarcest resource (labor).
4
Subtract the new maximum maize output from the initial maize output to find the opportunity cost.
10 tons−5 tons=5 tons of maize foregone10 \text{ tons} - 5 \text{ tons} = 5 \text{ tons of maize foregone}.
Opportunity cost is defined as the quantity of the alternative good given up.

Key Concept

Opportunity cost with constrained multi-resource allocation
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Opportunity Cost

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