Problem 1: Will there be growth?

A prediction of the "Malthusian model" is that an economy (and population) will grow as long as per-capita production exceeds some subsistence level but will shrink if per-capita production falls short of the subsistence level; in equilibrium, per-capita output will equal the subsistence level.Suppose a primitive economy exhibits the production function Y=1600L^2/3, where Y represents weekly production and L is the number of people (all of whom participate in the economy); suppose that the subsistence level is 20 units of output per person.

a. What will be the Malthusian equilibrium population (L) and production (Y) for this economy? Illustrate your answer with a diagram plotting population on the x-axis and production on the y-axis; label the equilibrium as point A.

b. Suppose, after years "stuck" at the subsistence equilibrium you characterized in part a), a technological discovery causes the production function to change to Y=2000L^2/3. What happens to total production (Y) and to per-capita production (Y/L) immediately after this discovery that is, while the population remains at the equilibrium level you computed in part a)? Label this new outcome as point B in your diagram above.

c. What will be the new Malthusian equilibrium population (L) and production (Y) after this discovery? Provide a numerical answer, and label your outcome as point C in your diagram above. Note that your points A, B, and C tell a story of economic growth over time in this simple economy; you can consider this story a "baseline" to which we can compare the predictions of more advanced models.