Returns to Scale Sample Homework
Question: The Cobb-Douglas production function ( Y= AK>L1-> ) is a good approximation to the U.S. Economy because >= 0.3 (> is parameter that represents the share of GDP that is appropriated by capitalist) is CONSTANT over the long run. In fact, it is fairly close to 30%. The share appropriated by workers is also constant at about 70% (1->=0.7)
Try to test:
Determine returns to scale. You must demonstrate.
What is the marginal productivity of labor? Demonstrate
What is the marginal productivity of Capital? Demonstrate
Is the productivity of the inputs a decreasing or an increasing function (does the function exhibit diminishing returns in each of the inputs?) Demonstrate.
if the production function is
F (L, K)= 2 K2 + 15 L 2