Question

Calculating chain-weighted real GDP
Prices (in dollars) and production for an orchard are provided in the following table:
Year--------Good------Price------Quantity
2016-------apples -----5----------20,000
2016-------apple juice---10-------9,000
2016-------cider----------14--------5,000

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2017------apples--------8--------25,000
2017----apple juice----15-------12,000
2017-----cider-----------18-------4,500

______________________________
2018----apples----------12-------35,000
2018-----apple juice----18-------15,000
2018-----cider------------25-------10,000

In all years, half of all apple production is used to produce apple juice and cider. For this
problem, round all market values to the nearest whole dollar.
a) Calculate real production in all three years using 2016 prices, then calculate output growth
for 2017 and 2018.
b) Calculate real production in all three years using 2018 prices, then calculate output growth
for 2017 and 2018.
c) Calculate chain-weighted production in all three years using 2016 as the base year, then
calculate output growth for 2017 and 2018.
d) Calculate chain-weighted production in all three years using 2018 as the base year, then
calculate output growth for 2017 and 2018.

Answer 1

Answer:

a)

Real Production =Price for 2016 for apple *(Quantity of apple)/2+Price for 2016 for apple juice *Quantity of apple juice+Price for 2016 for cidar *Quantity of cidar

Since half of apple production is used for apple Juice and Cidar.

So Real Production for 2016=5*20000/2+10*9000+14*5000=$210,000

So Real Production for 2017=5*25000/2+10*12000+14*4500=$245500

So Real Production for 2018=5*35000/2+10*15000+14*10000=$377500

So Output growth for 2017 = ( Real production in 2017-Real production in 2016)/Real production in 2016

Output growth for 2017 =(245500-210000)/210000=16.90%

Output growth for 2018 = ( Real production in 2018-Real production in 2017)/Real production in 2017

Output growth for 2017 =(377500-245500)/245500=53.77%

B)

Real Production =Price for 2018 for apple *(Quantity of apple)/2+Price for 2018 for apple juice *Quantity of apple juice+Price for 2018 for cidar *Quantity of cidar

Since half of apple production is used for apple Juice and Cidar.

So Real Production for 2016=12*20000/2+18*9000+25*5000=$407000

So Real Production for 2017=12*25000/2+18*12000+25*4500=$478500

So Real Production for 2018=12*35000/2+18*15000+25*10000=$730000

So Output growth for 2017 = ( Real production in 2017-Real production in 2016)/Real production in 2016

Output growth for 2017 =(478500-407000)/407000=17.57%

Output growth for 2018 = ( Real production in 2018-Real production in 2017)/Real production in 2017

Output growth for 2018 =(730000-478500)/478500=52.56%

C)

Chain Weighted production=Price for apple *(Quantity of apple)/2+Price for apple juice *Quantity of apple juice+Price for cidar *Quantity of cidar

Chain Weighted production for 2016 =5*20000/2+10*9000+14*5000=$210000

Chain Weighted production for 2017 =8*25000/2+15*12000+18*4500=$361000

Chain Weighted production for 2018 =12*35000/2+18*15000+25*10000=$730000

Since base year is 2016 Chain weighted production for 2016 is 100.

So Chain weighted production for 2017 =361000*100/210000=171.90

So Chain weighted production for 2018 =730000*100/210000=347.62

So Output growth for 2017 = ( Chain weighted production 2017-Chain weighted production in 2016)/Chain weighted production in 2016

Output growth for 2017 =(171.90-100)/100=71.90%

Output growth for 2018 = ( Chain weighted production in 2018-Chain weighted productionin 2017)/Chain weighted production in 2017

Output growth for 2018 =(347.62-171.90)/171.90=102.22%

D)

Chain Weighted production=Price for apple *(Quantity of apple)/2+Price for apple juice *Quantity of apple juice+Price for cidar *Quantity of cidar

Chain Weighted production for 2016 =5*20000/2+10*9000+14*5000=$210000

Chain Weighted production for 2017 =8*25000/2+15*12000+18*4500=$361000

Chain Weighted production for 2018 =12*35000/2+18*15000+25*10000=$730000

Since base year is 2018 Chain weighted production for 2018 is 100.

So Chain weighted production for 2016 =210000*100/730000=28.77

So Chain weighted production for 2017 =361000*100/730000=49.45

So Output growth for 2017 = ( Chain weighted production 2017-Chain weighted production in 2016)/Chain weighted production in 2016

Output growth for 2017 =(49.45-28.77)/28.77=71.90%

Output growth for 2018 = ( Chain weighted production in 2018-Chain weighted production in 2017)/Chain weighted production in 2017

Output growth for 2018 =(100-49.45)/49.45=102,22%