Assignment -

Consider the Malthusian model where Y_t = S^α(A_tL_t)^1-α, A_t+1 = (1+ g)A_t, and L_t+1 = (1+η_t)L_t. In this case S is the (constant) quantity of land, L is labor, and A is technological progress. Assume that (S, L₀, A₀) are all equal to 1, g > 0, and α = 1/3. In addition, assume that η_t = a + by_t where is b is greater than zero.

A. Suppose that the economy is in the Malthusian steady state (per capita income and population growth are both constant). Using Excel, simulate the response of the economy to a sudden decrease in land's share in period 5 to α = 0.1. Produce graphs showing the evolution of per capita income and population growth for 100 periods following this change. Describe in words how this economy responds to this change.

B. Compute the steady state per capita output and population growth rate for the economy with α = 0.1.

C. Consider the same exercise as in part A, except that there is an upper bound on population growth. That is, suppose that η_t = min{a + b y_t, η_Max}. Assume that η_Max = 0.3. Repeat part A under this assumption.

D. For a given value of α, how small must the upper bound on population growth be that would allow for sustained growth in living standards? Explain.