The table below presents the monthly Production Possibility Schedule for a manufacturing f… — JAMB UTME

The table below presents the monthly Production Possibility Schedule for a manufacturing firm in Aba producing Leather Shoes and Leather Bags using a fixed quantity of labor and raw materials:

Production Combination	Leather Shoes (hundreds of pairs)	Leather Bags (hundreds of units)
P	$0$	$150$
Q	$20$	$140$
R	$40$	$120$
S	$60$	$90$
T	$80$	$50$
U	$100$	$0$

If the plant is currently producing at Combination Q ( $20$ hundred pairs of shoes and $140$ hundred bags) and reallocates its resources to increase shoe production to Combination T ( $80$ hundred pairs of shoes), what is the average opportunity cost of producing ONE additional pair of Leather Shoes over this range? Express your answer in units of Leather Bags foregone.

Answer: 1.5 bags

Answer

1.5 bags foregone per additional pair of shoes

Opportunity cost measures the sacrifice of one good required to obtain an additional quantity of another good. Moving from Combination Q to Combination T increases shoe production by 60 hundred pairs (from 20 to 80 hundred pairs) while reducing bag production by 90 hundred units (from 140 to 50 hundred units). The opportunity cost per additional pair of shoes is calculated as 90 hundred bags divided by 60 hundred pairs of shoes, yielding exactly 1.5 bags foregone per pair of shoes.

Step-by-Step Solution

Determine initial production at Combination Q

Shoes =

20

hundred pairs (

2,000

pairs), Bags =

140

hundred units (

14,000

bags)

Establishes the baseline output before resource reallocation.

Determine final production at Combination T

Shoes =

80

hundred pairs (

8,000

pairs), Bags =

50

hundred units (

5,000

bags)

Identifies the new production level after expanding shoe production.

Calculate the net gain in shoe production and net loss in bag production

Additional shoes =

80 - 20 = 60

hundred pairs; Bags foregone =

140 - 50 = 90

hundred bags

Opportunity cost evaluates the sacrifice required to gain additional units of the preferred good.

Calculate the unit opportunity cost

Opportunity cost per shoe pair =

\frac{90\text{ hundred bags}}{60\text{ hundred pairs}} = 1.5\text{ bags}

Divides the total quantity of the sacrificed good by the total gain of the produced good to get per-unit real cost.

Key Concept

Opportunity Cost / Marginal Rate of Transformation

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