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 the rate of technological progress is 1.2%, what is the rate of growth of real output?
A)1)2%
B)1)6%
C)2)8%
D)3)2%
E)4)8%

Question

Quizplus · Accepted Answer

Since the production function exhibits constant returns to scale, we have:

Y = A*(K^α)*(L^(1-α))

where Y is real output, A is the level of technology, K is the capital stock, L is the labor input, and α is the share of capital in production (α=1/4 in this case). Therefore, the share of labor in production is (1-α)=3/4.

We can write the growth rate of output as:

g(Y) = g(A) + α*g(K) + (1-α)*g(L)

where g(X) denotes the growth rate of variable X. Plugging in the given values, we get:

g(Y) = 1.2% + (1/4)*1.6% + (3/4)*1.6%
g(Y) = 2.8%

Therefore, the rate of growth of real output is 2.8%.

Assume a Production Function with Constant Returns to Scale