You are an economist working for the International Monetary Fund. Your boss wants to know what the total factor productivity of China is, but all you have is data on per capita GDP, y, and the per capita capital stock, k. If you assume that capital's share of GDP is one-third, what would you use to find total factor productivity?
A) $\bar { A } = \frac { ( 1 / 3 ) k } { y }$
B) $\bar { A } = y \times k ^ { 1 / 3 }$
C) $\bar { A } = \frac { k ^ { 1 / 3 } } { y }$
D) $\bar { A } = \frac { y } { k ^ { 1 / 3 } }$
E) None of these answers are correct.

Question

Quizplus · Accepted Answer

Total factor productivity (TFP) can be calculated using the Cobb-Douglas production function: $ y = A \cdot k^{\alpha} $, where $\alpha$ is capital's share of GDP. Given $\alpha = 1/3$, TFP $A$ is calculated as $A = \frac{y}{k^{1/3}}$.

You Are an Economist Working for the International Monetary Fund Aˉ=(1/3)ky\bar { A } = \frac { ( 1 / 3 ) k } { y }Aˉ=y(1/3)k​

You Are an Economist Working for the International Monetary Fund $\bar { A } = \frac { ( 1 / 3 ) k } { y }$