Consider an economy that can be described by the Malthusian model. Suppose that the production function is such that MPL relates to the size of population via the following equation: A MPL == L where A is the total factor productivity and L is the labor force (population). Assume that A = 1,000. Also, assume that the subsistence level of consumption in this economy is not exogenously fixed but is endogenous, whereby it changes with the size of the population. The larger the country gets, the higher the minimum level of consumption people require to be happy. That is, σ = (2 if 4 if L≤400 L> 400 a. Depict this economy graphically in the w-L space. Explain your graph. Are there any steady states in this economy? If yes, comment on their (local) stability. What population size and the real wage will you predict for this economy in the long run? Next, assuming that the economy is in its long-run steady state, consider the implications of a one- time instantaneous productivity improvement (e.g., an introduction of irrigation that raises the quantity of food that can be grown on a given quantity of land). More specifically, assume that the level of productivity has doubled, i.e., A = 2,000 from now on. b. First, redraw the graph from the part (a). Label the starting point on the MPL curve as "1." Then, show how this productivity improvement will affect the economy in the short and long runs: label these points "2" and "3," respectively. c. Plot a time-series graph showing the evolution of the real wage around the time of a productivity improvement (i.e., right before the shock, immediately after, and in the long run).
Consider an economy that can be described by the Malthusian model. Suppose that the production function is such that MPL relates to the size of population via the following equation: A MPL == L where A is the total factor productivity and L is the labor force (population). Assume that A = 1,000. Also, assume that the subsistence level of consumption in this economy is not exogenously fixed but is endogenous, whereby it changes with the size of the population. The larger the country gets, the higher the minimum level of consumption people require to be happy. That is, σ = (2 if 4 if L≤400 L> 400 a. Depict this economy graphically in the w-L space. Explain your graph. Are there any steady states in this economy? If yes, comment on their (local) stability. What population size and the real wage will you predict for this economy in the long run? Next, assuming that the economy is in its long-run steady state, consider the implications of a one- time instantaneous productivity improvement (e.g., an introduction of irrigation that raises the quantity of food that can be grown on a given quantity of land). More specifically, assume that the level of productivity has doubled, i.e., A = 2,000 from now on. b. First, redraw the graph from the part (a). Label the starting point on the MPL curve as "1." Then, show how this productivity improvement will affect the economy in the short and long runs: label these points "2" and "3," respectively. c. Plot a time-series graph showing the evolution of the real wage around the time of a productivity improvement (i.e., right before the shock, immediately after, and in the long run).
Chapter1: Making Economics Decisions
Section: Chapter Questions
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Transcribed Image Text:Consider an economy that can be described by the Malthusian model. Suppose that the production
function is such that MPL relates to the size of population via the following equation:
A
MPL ==
L
where A is the total factor productivity and L is the labor force (population). Assume that A = 1,000.
Also, assume that the subsistence level of consumption in this economy is not exogenously fixed but
is endogenous, whereby it changes with the size of the population. The larger the country gets, the
higher the minimum level of consumption people require to be happy. That is,
σ =
(2 if
4 if
L≤400
L> 400
a. Depict this economy graphically in the w-L space. Explain your graph. Are there any steady states
in this economy? If yes, comment on their (local) stability. What population size and the real wage
will you predict for this economy in the long run?
Next, assuming that the economy is in its long-run steady state, consider the implications of a one-
time instantaneous productivity improvement (e.g., an introduction of irrigation that raises the
quantity of food that can be grown on a given quantity of land). More specifically, assume that the
level of productivity has doubled, i.e., A = 2,000 from now on.
b. First, redraw the graph from the part (a). Label the starting point on the MPL curve as "1." Then,
show how this productivity improvement will affect the economy in the short and long runs: label
these points "2" and "3," respectively.
c. Plot a time-series graph showing the evolution of the real wage around the time of a productivity
improvement (i.e., right before the shock, immediately after, and in the long run).
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