2. Consider the following table: Country B 200 80 64 Output per worker, 100 Phys
ID: 1160572 • Letter: 2
Question
2. Consider the following table: Country B 200 80 64 Output per worker, 100 Physical capital per worker, k 100 Human capital per worker, h 25 Both countries A and B have per worker production function of y -Ak0.5h°.5 a. Find how much factors of production are used in production in each country. (Note: this is a single number and not units of physical or human capital.) b. Which country uses more factors of production in production and by how much? c. Which country has a higher level of productivity, A, and by how much? d. Which, factors of production or productivity, is the larger contributor to income (output) differences between countries A and B? Explain. 3. The level of productivity in Country A, relative to Country B is 0.5. Country A lags bchind Country B tchnologically by 20 years, and the growth rate of tcchnology is 1% per ycar. a. What is the level of technology in country A relative to country B? b. What is the levcl of cfficicncy in Country A rclativc to Country B? wwsww*ww wwws ww*wsww*ww wwswwswwwkExplanation / Answer
a)
Each country uses two factors of production, Physical capital and Labour(denoted by Human Capital).
b)
It can be seen that even though country A has more capital per worker, it has fewer number of workers; whereas Country B has a moderately high physical capital per worker as well as a higher number of human capital per worker. Thus Country B can be said to have (80+64=144) units of factors of production whereas Country A has (100+25=125) unis of factors of production. Therefore, Country B uses a more factors of production by 19 units.
c)
To calculate the level of productivity A for each country, we plug in the values in the production functions to obtain
For Country A-
y=Ak0.5h0.5
100= A(100)0.5 (25)0.5
100= A (10)(5)
A=2
For country B
y=Ak0.5h0.5
200= A(80)0.5 (64)0.5
200= A (80)0.5(8)
A= 2.78
Thus, it can be seen that Country B has a higher level of Productivity by 0.78 units.
d)
The level of productivity and the Human capital are the factors which contribute to the income differences between countries A and B.
As calculated above, A=2.78 > A=2 for country B, thus B has a higher income because of it's level of productivity.
Country B also has a higher income because the Human Capital employed in B, i.e. (64)0.5= 8 is greater than that employed in Country A, i.e. (25)0.5= 5.
Therefore, Country B again has a higher level of income.
The Physical capital employed in country A is greater than that of country B, therefore it is not a factor contributing to the higher income level of Country B.
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