Question

Numbers from this table are used in the next 3 questions. Capital, population, workers, and nominal GDP are in millions.

year	Capital	Nominal GDP	CPI	Population	GDP Deflator	Workers
2019	$14,000,000	$23,000,000	260	300	115	150
2044	$30,000,000	$152,000,000	420	400	190	200

1.As you might guess from the table, real GDP per person grew from 2019 to 2044. But, what was the specific average annual increase in it?

2.We saw how two things influence labor productivity (Y/L): capital per worker (K/L) and technology (A). With data from the table above, which had a larger impact on labor productivity from 2019 to 2044 -- more technology or more capital per worker?why?

3.As above, real GDP per person rose from 2019 to 2044 (the specifics were left as a question). But, what caused this increase? Was it entirely due to a larger share of the population working, an increase in labor productivity, or some mix of these two? Please assume that the per-worker production function is of the mathematical form we used in class. Be sure to fully explain your answer.

Answer 1

Answer 1 :-

Real GDP = Nominal GDP/ Real GDP *100

For 2019 :-

Real GDP= 23000000/115*100=20,000,000

GDP per person = 20000000/300=66666.67

For 2024 :-

Real GDP = 152000000/190*10=80,000,000

Real GDP per person = 80,000,000/400=200000

Annual Change in Real GDP per person = (200000-66666.67)/66666.67*100*1/25=7.99 or 8% annually.

Answer 2 :-

For 2019 :-

(Y/L) = 20000000/150=133333.33

(K/L) = 14000000/150=93333.33

For 2024 :-

(Y/L ) = 80000000/200=400000

(K/L)= 30000000/200=150000

Annual change in (Y/L) = (400000-133333.33)/133333.33*100*1/25 = 0.053%

Annual change in (K/L) = (150000-93333.33)/93333.33*100*1/25=2.4% annually

Answer 3 :-

the real GDP per worker has Rose drastically from 2019 to 2024 due to to high capital investment which led to to increase in capital for labour at a rate of 2.4 % annually .It must be noted that the the labour productivity has also increased ,however it has increased with very low rate of 0.05 3% annually .therefore it is evident that the main reason that cause the the rise in real GDP in the period of 25 years was due to high capital investment which subsequently increase the capital for labour. The production function which defines per worker production is written as follows:-

Y/L=F(K,L)=(K^2.5L^0.75/L)