1. In the Malthusian model, let the production function be y = 10-.1L, or y = 10-(1/10)L, the death rate schedule be 60-10y, and the birth rate be 40 per thousand. Draw the production function (y on the horizontal axis and L on the vertical axis), and put numbers on the axes. Draw the death rate function (y on the horizontal axis and death rate per thousand on the vertical axis). Also draw the Rate of Natural Increase (RNI) function and put it below the production function.
a. What is the equilibrium income (y*)?________ Show your calculations.
b. What is the equilibrium level of population (L*)? __________ Show your calculations.
c. If the population is currently at 70, is the economy in equilibrium? ______. If not, will the population rise or fall?_________. Will per capita income rise or fall? ________
2. Assume the economy is at the equilibrium that you found in question 1. Now let the production function change to y = 12 - .1L. What will happen to income and population in the next few periods? Be as precise as you can. What will happen to income and population in the long run?
3. New question. Let the production function be y = 8 - 0.1L, the death rate be
DR = 60-10y, and the birth rate be BR = 30. What is y*? ____________
What is L*__________ Show your work.
Draw the production function graph. P¬¬ut numbers on your graph.
Also draw the graph of the Death Rate function and the Birth Rate line.
Now suppose the society discovers a way to reduce the deaths from infectious disease (say by draining swamps to reduce the incidence of mosquito-borne fatal illness). How will the new steady state compare with the old one? Will y be higher or lower________? Will L be higher or lower___________? Can you explain why?