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Calculate the unweighted price index for 2020 using 2019 as the base year.

Economics

ScanSolve AI Answer

Answer

C

Step-by-step solution

12 steps

Here are the solutions for questions 23, 24, and 25.

23. Calculate the unweighted price index for 2020 using 2019 as the base year.

  1. State the formula for the unweighted price index.

    The unweighted price index is calculated as:

    Unweighted Price Index=∑Pn∑P0×100\text{Unweighted Price Index} = \frac{\sum P_n}{\sum P_0} \times 100

    where PnP_n is the price in the current year (2020) and P0P_0 is the price in the base year (2019).

  2. Sum the prices for the base year (2019).

    ∑P0=80+220+60+115=475\sum P_0 = 80 + 220 + 60 + 115 = 475
  3. Sum the prices for the current year (2020).

    ∑Pn=100+260+60+145=565\sum P_n = 100 + 260 + 60 + 145 = 565
  4. Substitute the sums into the formula and calculate the index.

    Unweighted Price Index=565475×100\text{Unweighted Price Index} = \frac{565}{475} \times 100 Unweighted Price Index≈1.18947×100\text{Unweighted Price Index} \approx 1.18947 \times 100 Unweighted Price Index≈118.95\text{Unweighted Price Index} \approx 118.95

    The correct option is C.
    The unweighted price index for 2020 using 2019 as the base year is C. 118.95\boxed{\text{C. } \textbf{118.95}}.

    24. For the data in Table 5, calculate the Laspeyres price index for 2021 using 2020 as the base year.

  5. State the formula for the Laspeyres price index.

    The Laspeyres price index is calculated as:

    Laspeyres Price Index=∑(Pn×Q0)∑(P0×Q0)×100\text{Laspeyres Price Index} = \frac{\sum (P_n \times Q_0)}{\sum (P_0 \times Q_0)} \times 100

    where PnP_n is the price in the current year (2021), P0P_0 is the price in the base year (2020), and Q0Q_0 is the quantity in the base year (2020).

  6. Calculate ∑(P0×Q0)\sum (P_0 \times Q_0) for the base year (2020).

    • Acid A: 100×220=22000100 \times 220 = 22000
    • Acid B: 260×152=39520260 \times 152 = 39520
    • Acid C: 60×230=1380060 \times 230 = 13800
    • Acid D: 145×104=15080145 \times 104 = 15080
    ∑(P0×Q0)=22000+39520+13800+15080=90400\sum (P_0 \times Q_0) = 22000 + 39520 + 13800 + 15080 = 90400
  7. Calculate ∑(Pn×Q0)\sum (P_n \times Q_0) for the current year (2021) using base year quantities (2020).

    • Acid A: 107×220=23540107 \times 220 = 23540
    • Acid B: 260×152=39520260 \times 152 = 39520
    • Acid C: 95×230=2185095 \times 230 = 21850
    • Acid D: 160×104=16640160 \times 104 = 16640
    ∑(Pn×Q0)=23540+39520+21850+16640=101550\sum (P_n \times Q_0) = 23540 + 39520 + 21850 + 16640 = 101550
  8. Substitute the sums into the formula and calculate the index.

    Laspeyres Price Index=10155090400×100\text{Laspeyres Price Index} = \frac{101550}{90400} \times 100 Laspeyres Price Index≈1.12334×100\text{Laspeyres Price Index} \approx 1.12334 \times 100 Laspeyres Price Index≈112.33\text{Laspeyres Price Index} \approx 112.33

    The correct option is B.
    The Laspeyres price index for 2021 using 2020 as the base year is B. 112.33\boxed{\text{B. } \textbf{112.33}}.

    25. For the data in Table 5, calculate the Paasche Price Index for 2021 using 2019 as the base.

  9. State the formula for the Paasche price index.

    The Paasche price index is calculated as:

    Paasche Price Index=∑(Pn×Qn)∑(P0×Qn)×100\text{Paasche Price Index} = \frac{\sum (P_n \times Q_n)}{\sum (P_0 \times Q_n)} \times 100

    where PnP_n is the price in the current year (2021), P0P_0 is the price in the base year (2019), and QnQ_n is the quantity in the current year (2021).

  10. Calculate ∑(Pn×Qn)\sum (P_n \times Q_n) for the current year (2021).

    • Acid A: 107×230=24610107 \times 230 = 24610
    • Acid B: 260×134=34840260 \times 134 = 34840
    • Acid C: 95×180=1710095 \times 180 = 17100
    • Acid D: 160×90=14400160 \times 90 = 14400
    ∑(Pn×Qn)=24610+34840+17100+14400=90950\sum (P_n \times Q_n) = 24610 + 34840 + 17100 + 14400 = 90950
  11. Calculate ∑(P0×Qn)\sum (P_0 \times Q_n) using base year prices (2019) and current year quantities (2021).

    • Acid A: 80×230=1840080 \times 230 = 18400
    • Acid B: 220×134=29480220 \times 134 = 29480
    • Acid C: 60×180=1080060 \times 180 = 10800
    • Acid D: 115×90=10350115 \times 90 = 10350
    ∑(P0×Qn)=18400+29480+10800+10350=69030\sum (P_0 \times Q_n) = 18400 + 29480 + 10800 + 10350 = 69030
  12. Substitute the sums into the formula and calculate the index.

    Paasche Price Index=9095069030×100\text{Paasche Price Index} = \frac{90950}{69030} \times 100 Paasche Price Index≈1.31754×100\text{Paasche Price Index} \approx 1.31754 \times 100 Paasche Price Index≈131.75\text{Paasche Price Index} \approx 131.75

    The correct option is A.
    The Paasche Price Index for 2021 using 2019 as the base is A. 131.75\boxed{\text{A. } \textbf{131.75}}.

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