If `P_(01)(L) = 40` and `P_(01)(P) = 90`, find` P_(01)(D-B)` and `P_(01)(F).`

Answer

To solve the problem, we need to find \( P_{01}(D-B) \) and \( P_{01}(F) \) given \( P_{01}(L) = 40 \) and \( P_{01}(P) = 90 \).

### Step 1: Calculate \( P_{01}(D-B) \)
The Dorbyshev-Pauli's Price Index Number is calculated using the formula:

\[ P_{01}(D-B) = \frac{P_{01}(L) + P_{01}(P)}{2} \]

Substituting the given values:

\[ P_{01}(D-B) = \frac{40 + 90}{2} \]

Calculating the sum:

\[ P_{01}(D-B) = \frac{130}{2} = 65 \]

### Step 2: Calculate \( P_{01}(F) \)
The Fisher's Price Index Number is calculated using the formula:

\[ P_{01}(F) = \sqrt{P_{01}(L) \times P_{01}(P)} \]

Substituting the given values:

\[ P_{01}(F) = \sqrt{40 \times 90} \]

Calculating the product:

\[ P_{01}(F) = \sqrt{3600} \]

Taking the square root:

\[ P_{01}(F) = 60 \]

### Final Answers
Thus, we have:
- \( P_{01}(D-B) = 65 \)
- \( P_{01}(F) = 60 \)

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