A Price Is a Ratio; the Price Level Is a Level

In micro, a price was an exchange ratio between two goods. In macro, the average of all prices โ€” the price level โ€” appears as its own object.

If only โ˜• coffee gets pricier, the basket really changes. Shoppers shift toward what stayed cheap. But suppose every price and every paycheck double. What people buy stays exactly the same. Only the money handed over doubles.

For example, at the ๐Ÿช stationery shop a โœ๏ธ pencil costs 100 won and an eraser 200 won. If both prices double and your ๐Ÿ’ฐ allowance doubles too, you can buy the very same set as before.

x1=ฮฑW/p1x_1 = \alpha W / p_1
x2=(1โˆ’ฮฑ)W/p2x_2 = (1 - \alpha) W / p_2

Part of these learning paths

Examples & Exercises

Only the โ˜• coffee price rises, from 22 to 44. ๐Ÿž Bread stays at 44 and pay stays at 100100.

What happens to coffee and bread consumption, and what is the price index?

Only the coffee price doubles โ€” bread price and pay fixed.
Show proof

  1. This consumer always spends half of income on coffee. Double the price and the quantity halves: x1=0.5โ‹…100/4=12.5x_1 = 0.5 \cdot 100 / 4 = 12.5 cups โ€” exactly half of yesterday's 2525.

  2. The money going to bread is still half of income, so bread consumption is unchanged at x2=0.5โ‹…100/4=12.5x_2 = 0.5 \cdot 100 / 4 = 12.5 loaves.

    But the basket's mix by items tilts toward bread: its share rises from 13\frac{1}{3} to 12\frac{1}{2}.

    When a relative price moves, the real allocation rearranges like this.

  3. The price index re-prices the base basket (2525 cups, 12.512.5 loaves) at the new prices: (4โ‹…25+4โ‹…12.5)/100=1.5(4 \cdot 25 + 4 \cdot 12.5) / 100 = 1.5, an index of 150150. Real income is 100/1.5โ‰ˆ66.7100 / 1.5 \approx 66.7 โ€” the paycheck's number never moved, yet the basket it buys shrank to 23\frac{2}{3}.

Concept check

One morning, every price and the paycheck exactly double. โ˜• Coffee 44, ๐Ÿž bread 88, pay 200200.

What happens to the basket?

Double-everything on โ€” effective prices are coffee 44 ยท bread 88, income 200200.
  1. The basket doubles because pay doubled
  2. The basket is unchanged โ€” 2525 cups of coffee and 12.512.5 loaves. Only the nominal numbers and the price index double
  3. The basket halves because prices doubled
  4. Coffee becomes relatively cheaper than bread, so the basket tilts toward coffee
Show explanation

Answer: The basket is unchanged โ€” 2525 cups of coffee and 12.512.5 loaves. Only the nominal numbers and the price index double

When prices and pay scale by the same factor, demand does not move: x1=0.5โ‹…200/4=25x_1 = 0.5 \cdot 200 / 4 = 25 cups and x2=0.5โ‹…200/8=12.5x_2 = 0.5 \cdot 200 / 8 = 12.5 loaves, exactly as yesterday. Doubling from pay alone is money illusion; halving from prices alone forgets the doubled pay. The relative price p1/p2=0.5p_1 / p_2 = 0.5 is also unchanged, so nothing tilts the basket.

4. Money and Prices