Consider the malthusian model in which the equation that relates population growth rate denoted by n to per-capita income y given by

(1)

n= (y-100)/100

Denote with L the level of population which implies that income per capita is y=Y/L where Y is aggregate output (income) produced by labor L and available land X according to the following Cobb Douglas production function:

(2)

Y=AX^1/2L^1/2

where A is the level of technology. Dividing both sides of the equation (2) by the level of population yields the following equation that relates income per capita y to land per capita x=X/L

y=Ax^1/2

A) Assume that the level of technology is A=25, available land is X=16000, and the current level population is L= 1000. Is this malthusian economy above, below, or at the steady-state equilibrium? Does the economy experience positive, negative, or zero population growth? Explain

B) suppose that the discovery of the better crop rises immediately the level of technology from A = 25 to A₁= 50. What are the short-run (immediate) and long-run (steady -stateequillibrium) elects of the new technology on income per capita y, growth rate of population n, and the level of population L?