1. Consider Table 13-3 but suppose that the market basket is composed of 100 oranges, 50 grapefruit, and 200 lemons. How does this change the pre-frost and post-frost price indexes? Explain. Generalize your explanation to how the construction of the market basket affects the price index.
This market basket costs, pre-frost, (100 × $0.20) + (50 × $0.60) + (200 × $0.25) = $20 + $30 + $50 = $100. The same market basket, post-frost, costs (100 × $0.40) + (50 × $1.00) + (200 × $0.45) = $40 + $50 + $90 = $180. So the price index is ($100/$100) × 100 = 100 before the frost and ($180/$100) × 100 = 180 after the frost, implying a rise in the price index of 80%. This increase in the price index is less than the 84.2% increase calculated in the text. The reason for this difference is that the new market basket of 100 oranges, 50 grapefruit, and 200 lemons contains proportionately more of the items that have experienced relatively lower price increases (the lemons, whose price has increased by 80%) and proportionately fewer of the items that have experienced relatively large price increases (the oranges, whose price has increased by 100%). This shows that the price index can be very sensitive to the composition of the market basket. If the market basket contains a large proportion of goods whose prices have risen faster than the prices of other goods, it will lead to a higher estimate of the increase in the price level. If it contains a large proportion of goods whose prices have risen more slowly than the prices of other goods, it will lead to a lower estimate of the increase in the price level.