ECON 291 Study Guide - Quiz Guide: Production Function, Marginal Product

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Econ 291 Tutorial Questions Ch.3
1
Name Student ID #
1. A Malthusian economy is described by a production function =//, where is
amount of land which is fixed at 512, and is the labour input (which is equal to the
population in the current period). The population evolves over time as =//, where
is the population in the future period, and is the aggregate consumption.
a. Write down the per-worker production function.
=/
b. Find the steady-state consumption per worker.
N’/N = (C/N)1/2 = c1/2
In the steady state, N = N = N*.
Solve for c* = 1
c. Find the steady state levels of output per worker, land per worker, and population.
Since y = c in equilibrium, so y* = 1
From the per-worker production function, =/, solving for . = 1
Since =/ , solve for N. =512
d. Suppose the marginal product of labour doubles for each level of labour input. Find the
steady state levels of consumption per worker, output per worker, land per worker, and
population.
New production function: = 2//, and the per worker production function: =
2/.
c* = 1
y* = 1
= 0.125
N* = 4096
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Econ 291 Tutorial Questions Ch.3
2
2. The economy of Sylvania can be described by the Malthusian model. Suppose that the
quantity of land increases in Sylvania.
a. On the following diagram, show the effects of this event on the steady state population.
The population will increase
b. On the diagrams below, show the effects of this event on the steady state levels of
consumption per worker and land per worker.
In the long-run steady state, the quantity of land per worker stays the same
In the long-run steady state, the consumption per worker stays the same
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Document Summary

Student id : a malthusian economy is described by a production function =1/32/3, where is amount of land which is fixed at 512, and is the labour input (which is equal to the population in the current period). The population evolves over time as =1/21/2, where. Is the population in the future period, and is the aggregate consumption. =1/3: write down the per-worker production function, find the steady-state consumption per worker. In the steady state, n" = n = n*. Solve for c* = 1: find the steady state levels of output per worker, land per worker, and population. Since y = c in equilibrium, so y* = 1. From the per-worker production function, =1/3, solving for . Since =/ , solve for n. = 512: suppose the marginal product of labour doubles for each level of labour input. Find the steady state levels of consumption per worker, output per worker, land per worker, and population.

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