Discussion
Following bar chart presents supply as a percentage of demand of a product and demand as a percentage of capacity of the industry to produce the same product. All the values are multiples of 5.
| Year | Supply of demand | Demand of capacity |
|---|---|---|
| 2003 | 65 | 80 |
| 2004 | 70 | 90 |
| 2005 | 60 | 80 |
| 2006 | 90 | 65 |
If supply is constant for each of the years given above, then the capacity is highest for the year:
Answer: C
The capacity is highest in 2005.
Supply = capacity × (demand share) × (supply share). If supply is the same every year, capacity is largest where the product of the two shares is smallest.
\[ \begin{aligned} 2003 &: 0.80 \times 0.65 = 0.520 \\ 2004 &: 0.90 \times 0.70 = 0.630 \\ 2005 &: 0.80 \times 0.60 = 0.480 \\ 2006 &: 0.65 \times 0.90 = 0.585 \end{aligned} \]
2005 has the smallest product, 0.48, so the same supply needs the largest capacity behind it. 2004 is the opposite case, with the smallest capacity. 2006 is the trap: its supply share is the highest of all, but its low demand share pulls the product up to 0.585.
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