# GWU The Cobb-Douglas Production Function Worksheet

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I need to complete an assignment on macroeconomics.  You may hand-write or type your answers. You can convert hand-written pages to PDF using simple apps like CamScanner, Office Lens etc. Answers must be clear, concise, and legible. They must demonstrate how you arrived at the solution, and make it clear that you understand the underlying concepts.

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ECON 301: Homework 2
Instructions
 How to submit
 However, you must submit your PDF file online on Canvas using the
online submission tool
 You can convert hand-written pages to PDF using simple apps like
CamScanner, Office Lens etc. Alternately, there is a scanner available at
the Library.
 General guidelines
 Answers must be clear, concise and legible (if hand-written). They
must demonstrate how you arrived at the solution, and make it clear
that you understand the underlying concepts.
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The Cobb-Douglas Production Function
1. The Cobb-Douglas production function, in its general form, is given as Y =
AK¯ ?L1??
(a) What do K and L refer to?
(b) What does A¯ refer to? What does it tell you when this value is higher
or lower?
(c) The sum of the exponents over K and L equals 1. What is the
significance of this?
2. The standard Cobb-Douglas production function has several useful
properties.
(a) Define the term returns to scale. What are the three kinds of returns
to scale? (Extra points for answering this in mathematical terms). Which
of these does the Cobb-Douglas production function exhibit?
(b) Distinguish between the concepts of returns to scale and returns to a
factor.
(c) Does the Cobb-Douglas production function have increasing, constant
or decreasing returns to its individual factors? Is there any
contradiction between this and the returns to scale that it exhibits?
3. Consider the following non-standard production functions. Do they exhibit
increasing, constant or decreasing returns to scale? (Assume A¯ is a constant
positive value)
(a) Y = K1/2L3/2
(b) Y = K1/10L9/10
(c) Y = K + L
(d) Y = K1/3L1/3?A¯
4. Assume a Cobb-Douglas production function of the following form: Y = AK¯
1/3L2/3. What is the production function for output per worker?
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Solving the production model
Suppose the production function is given by Y = AK¯ 1/4L3/4.
1. Find the hiring rules for capital and labor. Provide economic intuition.
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2. Suppose that the supply of capital is measured in \$, and the supply of labor
is measured in hours worked. What are the units of r and w consistent with
the model?
3. Suppose that the supply of capital is \$100, and the supply of labor is 20 hours.
Find the equilibrium prices r and w.
4. What is the solution for the equilibrium level of output per person?
5. Find the value of the labor share. Is it a reasonable value?
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Understanding TFP in the Production Model
1. Assume a production function that is of the form
, where k is the
capital per worker. In class we saw what such a model would predict the per
capita GDP to be for various countries.
(a) How accurate are the predictions? For which countries are the
predictions close, and which ones is it significantly off? Do you see a
pattern in the degree to which the predictions are off?
(b) Is TFP directly observed by economists? If not, how is it estimated?
What can lead to errors in estimating it?
(c) In this context, what does TFP include, and why does it differ from
country to country? Why is it important to help fit a model better?
2. How important are the TFP and capital levels respectively in explaining the
per-capita GDP of countries?
3. In your own words, examine why the TFP in some countries may be higher
than in other countries. What best explains these differences in your view?
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