Suppose that capital per hour of labor increases by 18 percent while real GDP per hour of labor increases by 10 percent. What is the contribution to the increase in real GDP per hour of labor from changing technology?

Question

Quizplus · Accepted Answer

The Solow growth model describes the relationship between capital per hour of labor (K/L) and real GDP per hour of labor (Y/L) as follows:

Y/L = A(K/L)^α

where A is the level of technology and α is the capital share of income.

In this problem, we are given that K/L increases by 18% and Y/L increases by 10%. We can rearrange the equation above to solve for A:

A = (Y/L)/(K/L)^α

Taking the percentage changes of both sides of the equation, we get:

%ΔA = %Δ(Y/L) - α%Δ(K/L)

Plugging in the values we are given, we get:

%ΔA = 10% - α(18%)

We are not given the value of α, but it is typically assumed to be around 1/3. Plugging in this value, we get:

%ΔA ≈ 4%

Therefore, the increase in real GDP per hour of labor from changing technology is approximately 4%. The closest answer choice is B.

Suppose That Capital Per Hour of Labor Increases by 18