This may seem silly, but ... please print out the picture of the
orange below. I'm going to use it to explain the production function in
the Mankiw-Romer-Weil (MRW) model on Thurs. 27 Oct.
Here's the point: The production function in the MRW model is three-dimensional,
so I thought I'd give you a three-dimensional example that you are familiar
with. The outer skin of the orange corresponds to the production function
depicted on the top panel of page 83 of the Lecture Notes. Output per unit of effective labor is measured by the height of
the orange (from the plate). The two parallel slices of the orange depicted in the picture correspond
to the increase in physical capital depicted in the lower panel of page
85. The idea here is to show that higher levels of physical capital
per unit of effective labor correspond to higher levels of output per unit
of effective labor (holding the level of human capital per unit of
effective labor constant). Similarly, higher levels of human capital per unit of effective labor
correspond to higher levels of output per unit of effective labor (holding
the level of physical capital per unit of effective labor constant).
So what would happen if we increased both the steady-state level
of human capital per unit of effective labor and the steady-state level
of physical capital per unit of effective labor (as depicted in the
top panel of page 94)? Output per unit of effective labor would increase. Along the plate, we'd move further away from the origin. From the
plate, we'd move higher up on the skin of the orange. Conversely, if we decreased both the steady-state level of human capital
per unit of effective labor and the steady-state level of physical capital
per unit of effective labor (as depicted in the lower panel of page 94),
then output per unit of effective labor would decrease.
Along the plate, we'd move closer to the origin. From the plate, we'd
move lower down on the skin of the orange.
