Question

1) Suppose that the production function is Y = AK0.7L0.3, the number of workers equals 800, the capital stock is $150,000, and total factor productivity is 3. What is the value of real GDP? What will happen to real GDP if total factor productivity doubles?

Answer 1

Answer 1

Y = AK^0.7L^0.3

Here Y = real GDP and it is given that K = 150,000 , A = Productivity = 3 and L = 800

Putting this value in production function we get:

Y = 3*150000^0.7800^0.3 = 93607.8202

Hence Real GDP = 93607.82

If Productivity doubles then A = 3*2 = 6 and rest is still same

Hence Now Y = 6*150000^0.7800^0.3 = 187215.64

Hence New Real GDP = 187215.64 which is twice the old one (187215.64/93607.82 = 2)

Hence If productivity doubles then Real GDP will also get doubles.