From the following price and quantity data for three commodities, calculate (a) Laspeyres' Price Index and (b) Paasche's Price Index.

| Commodity | $p_0$ | $q_0$ | $p_1$ | $q_1$ |
|---|---|---|---|---|
| X | 5 | 10 | 6 | 12 |
| Y | 8 | 5 | 9 | 6 |
| Z | 10 | 4 | 12 | 5 |

Question

From the following price and quantity data for three commodities, calculate (a) Laspeyres' Price Index and (b) Paasche's Price Index.

| Commodity | $p_0$ | $q_0$ | $p_1$ | $q_1$ |
|---|---|---|---|---|
| X | 5 | 10 | 6 | 12 |
| Y | 8 | 5 | 9 | 6 |
| Z | 10 | 4 | 12 | 5 |

Accepted Answer

**Step 1 — Build the four products** needed for both formulas:

| Commodity | $p_0$ | $q_0$ | $p_1$ | $q_1$ | $p_0q_0$ | $p_1q_0$ | $p_0q_1$ | $p_1q_1$ |
|---|---|---|---|---|---|---|---|---|
| X | 5 | 10 | 6 | 12 | $5	imes10=50$ | $6	imes10=60$ | $5	imes12=60$ | $6	imes12=72$ |
| Y | 8 | 5 | 9 | 6 | $8	imes5=40$ | $9	imes5=45$ | $8	imes6=48$ | $9	imes6=54$ |
| Z | 10 | 4 | 12 | 5 | $10	imes4=40$ | $12	imes4=48$ | $10	imes5=50$ | $12	imes5=60$ |
| **Total** |  |  |  |  | **130** | **153** | **158** | **186** |

**Step 2 — Laspeyres' Price Index** (base-year quantities as weights):

$$P_{01}^{L} = \dfrac{\sum p_1q_0}{\sum p_0q_0}	imes 100 = \dfrac{153}{130}	imes 100 = 117.69$$

**Step 3 — Paasche's Price Index** (current-year quantities as weights):

$$P_{01}^{P} = \dfrac{\sum p_1q_1}{\sum p_0q_1}	imes 100 = \dfrac{186}{158}	imes 100 = 117.72$$ …

Commodity	$p_0$	$q_0$	$p_1$	$q_1$	$p_0q_0$	$p_1q_0$	$p_0q_1$	$p_1q_1$
X	5	10	6	12	$5\times10=50$	$6\times10=60$	$5\times12=60$	$6\times12=72$
Y	8	5	9	6	$8\times5=40$	$9\times5=45$	$8\times6=48$	$9\times6=54$
Z	10	4	12	5	$10\times4=40$	$12\times4=48$	$10\times5=50$	$12\times5=60$
Total					130	153	158	186

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