Consider an aggregate production function Y = 2AL, where Y is output, A is technology level, and L?

Consider an aggregate production function Y = 2AL, where Y is output, A is technology level, and L is labor.

a) Draw on a graph the production function.

b) Does it exhibit diminishing marginal returns to labor? Why or why not?

Now, let’s change the production function to Y=AL1/2.

c) Draw on a graph the production function.

d) Does it exhibit diminishing marginal returns to labor? Why or why not?

e) How would the graph on c) change if there is an improvement in technology from A to A’?

f) Finally, draw the aggregate production function Y = AL2.

g) What kind of marginal returns does this production function exhibit?

h) How would the curve above change if part of the capital in the economy becomes obsolete? Graph and explain.