Question

Consider two countries X and Y. The production function is y = A*k^α*h^(1-α), where α = 0.5. The following data are available. Output per worker, y: Country X=200, Country Y=400; Physical capital per worker, k: Country X=64, Country Y=64; Human capital per worker, h: Country X=16, Country Y= 36.

1) Productivity level A in country X is.. a)2.09 b)6.25 c)8.33 d)16.67

2) Productivity level A in country Y is.. a)2.09 b)4.17 c)8.33 d)16.67

3) Calculate the countries' relative levels of output (Country X to Country Y) if all differences in output were due to productivity only. a)1.0 b)2.0 c).50 d).75

4) Calculate the countries' relative levels of output (Country X to Country Y) if all differences in output were due to factor accumulation only.  a)1.0 b)2.0 c).50 d).67

Answer 1

1)

Given y=200

k=64

h=16

Plug in various values

200=A*8*4

A=6.25

Correct option is B i.e. 6.25

b)

Given y=400

k=64

h=36

Plug in various values

400=A*8*6

A=8.33

Correct option is C i.e. 8.33

c)

In this case

(y_X/y_Y)=A_X/A_Y=6.25/8.33=0.75

Correct option is d) 0.75

d)

Let us calculate factor accumulation factor, Fx, for country X

Let us calculate factor accumulation factor, Fy, for country Y

In this case

(y_X/y_Y)=F_X/F_Y=32/48=0.67

Correct option is

d. 0.67