Assume a production function with constant returns to scale.Labor's share of income is 0.7 and capital's share is 0.3.If labor grows at 4% and capital grows at 3%, how many years would it take to double the current level of output if no technological advances are made?
A)7
B)10
C)19
D)23
E)33

Question

Quizplus · Accepted Answer

Since the production function has constant returns to scale, the output will increase at the same rate as inputs increase.

Labor's share of income is 0.7, so if labor grows at 4%, we can say that output will increase at a rate of 0.7*4% = 2.8%.

Capital's share of income is 0.3, so if capital grows at 3%, we can say that output will increase at a rate of 0.3*3% = 0.9%.

Thus, overall output will increase at a rate of 2.8% + 0.9% = 3.7%.

Using the rule of 70, we can calculate the number of years it takes for output to double as 70/3.7 = 18.92 years, which we can round up to 19 years.

Therefore, the correct answer is C) 19 years.

Assume a Production Function with Constant Returns to Scale