1. The current population of the United States is 328.2 million with 2.2% of the population...

1. The current population of the United States is 328.2 million with 2.2% of the population is engaged in R&D at an efficiency rate of 1/500 per million persons per year.

(a) If R&D is the only source of total-factor productivity growth what is the growth rate of labor efficiency in the United States?

(b) If the growth rate of total factor productivity is 0.75% per year, what is the value of α in the Cobb-Douglas production function?

Solutions

Expert Solution

Cobb-Douglas Production Function is written as:

Y= Alβ Kα

where:

· Y = total production (365.25 days)

· L = total labor input (365.25 days)

· K = Capital input (machinery, equipment, buildings; the value of capital input divided by the price of capital)

· A= Total Productivity

· α and β are the output elasticities of capital and labor. Values are constants determined by available technology.

Applying the equation,

0.75*7220400 * Kα (Where K has been kept as constant = 1)

Total contribution of Labour = 54,15,300

Value of α = 1.802

K’s contribution has been assumed to be constant.

Rahul Sunny answered 1 year ago

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