If `sump_0q_0=150 , sump_0q_1 =250 , sump_1q_1 =375 and ` `p_(01)(L) = 140 ` find `p_(01)` (M-E)

Answer

To solve the problem, we need to find the Marshall Edgeworth Price Index Number (P01(M-E)) using the given values. Here’s the step-by-step solution:

### Step 1: Understand the Given Values
We have the following values:
- \( \sum P_0 Q_0 = 150 \)
- \( \sum P_0 Q_1 = 250 \)
- \( \sum P_1 Q_1 = 375 \)
- \( P_{01}(L) = 140 \)

### Step 2: Calculate \( \sum P_1 Q_0 \)
We know that:
\[ P_{01}(L) = \frac{\sum P_1 Q_0}{\sum P_0 Q_0} \times 100 \]
Substituting the known values:
\[ 140 = \frac{\sum P_1 Q_0}{150} \times 100 \]
Rearranging gives:
\[ \sum P_1 Q_0 = 140 \times \frac{150}{100} = 140 \times 1.5 = 210 \]

### Step 3: Use the Formula for Marshall Edgeworth Price Index Number
The formula for the Marshall Edgeworth Price Index Number is:
\[ P_{01}(M-E) = \frac{\sum P_1 Q_0 + \sum P_1 Q_1}{\sum P_0 Q_0 + \sum P_0 Q_1} \times 100 \]
Substituting the values we have:
\[ P_{01}(M-E) = \frac{210 + 375}{150 + 250} \times 100 \]

### Step 4: Calculate the Numerator and Denominator
Calculating the numerator:
\[ 210 + 375 = 585 \]
Calculating the denominator:
\[ 150 + 250 = 400 \]

### Step 5: Substitute Back into the Formula
Now substituting the values back into the formula:
\[ P_{01}(M-E) = \frac{585}{400} \times 100 \]

### Step 6: Perform the Final Calculation
Calculating the final value:
\[ P_{01}(M-E) = 1.4625 \times 100 = 146.25 \]

### Final Answer
The Marshall Edgeworth Price Index Number \( P_{01}(M-E) \) is **146.25**.

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