Question

Assume a production function with constant returns to scale. The share of capital in production is 1/4 and the share of labor is 3/4. If both labor and capital grow at 1.6% and real output grows at a rate of 2.8%, what is the growth rate of total factor productivity?

2.8%
1.6%
1.2%
1.0%

Answer 1

Total output (in Cobb-Douglas form) represents total output as a function of total factor productivity (A), capital input (K) and labor input (L)
Y = A*K1/4*L1/4
1,028 Y = X*A*1,016*(K1/4*L1/4)
X = (1,028 Y)/ (1,016*(K1/4*L1/4)*A)
X = 1,0118
So, the growth rate of total factor productivity is 1,18%≈1,2%